Competitive Strategy
Competitive Strategy Options and Games
Benoît Chevalier-Roignant Lenos Trigeorgis
The MIT Press Cambridge, Massachusetts London, England
© 2011 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. For information about special quantity discounts, please email
[email protected] .edu This book was set in Times Roman by Toppan Best-set Premedia Limited. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Chevalier-Roignant, Benoit, 1983– Competitive strategy: options and games/Benoit Chevalier-Roignant and Lenos Trigeorgis; foreword by Avinash K. Dixit. p. cm. Includes bibliographical references and index. ISBN 978-0-262-01599-8 (hardcover: alk. paper) 1. Options (Finance) 2. Investment analysis. 3. Game theory. I. Trigeorgis, Lenos. II. Title. HG6024.A3C48535 2011 332.6—dc22 2010053619 10
9
8
7
6
5
4
3
2
1
Contents
Glossary xi Symbols xix Foreword by Avinash Dixit Preface xxv 1
The Strategy Challenge
xxiii
1
1.1 1.2 1.3
The Changing Corporate Environment 3 What Is Strategy? 10 Two Complementary Perspectives on Strategy 1.3.1 Corporate Finance and Strategy 15 1.3.2 Game Theory and Strategy 20 1.4 An Integrative Approach to Strategy 35 1.5 Overview and Organization of the Book 41 Conclusion 43 Selected References 43 I
STRATEGY, GAMES, AND OPTIONS
2
Strategic Management and Competitive Advantage 2.1
2.2
15
45 47
Strategic Management Paradigms 48 2.1.1 External View of the Firm 48 2.1.2 Internal View of the Firm 50 Industry and Competitive Analysis 50 2.2.1 Macroeconomic Analysis 57 2.2.2 Industry Analysis: Structure–Conduct–Performance Paradigm 58 2.2.3 Porter’s Industry and Competitive (Five-Forces) Analysis 59
vi
Contents
2.3
Creating and Sustaining Competitive Advantage 2.3.1 Value Creation 66 2.3.2 Generic Competitive Strategies 70 2.3.3 Sustaining Competitive Advantage 72 Conclusion 73 Selected References 74 3
Market Structure Games: Static Approaches
66
75
3.1 3.2
Monopoly 76 Duopoly 81 3.2.1 Bertrand Price Competition 86 3.2.2 Cournot Quantity Competition 92 3.2.3 Strategic Substitutes versus Complements 97 3.3 Oligopoly and Perfect Quantity Competition 99 3.4 Market Structure under Incomplete Information 102 Conclusion 107 Selected References 107 4
Market Structure Games: Dynamic Approaches
109
4.1
Commitment Strategy 110 4.1.1 Concept of Commitment 111 4.1.2 Taxonomy of Commitment Strategies 118 4.1.3 Sequential Stackelberg Game 131 4.2 Bargaining and Cooperation 135 4.2.1 Bargaining 135 4.2.2 Cooperation between Cournot Duopolists in Repeated Games 138 4.2.3 Co-opetition: Sometimes Compete and Sometimes Cooperate? 147 Conclusion 151 Selected References 151 5
Uncertainty, Flexibility, and Real Options 5.1
5.2
153
Strategic Investment under Uncertainty—The Electricity Sector 154 5.1.1 Need for New Investment in Europe 154 5.1.2 Sources of Uncertainty 156 5.1.3 Generation Technologies and Business Risk Exposure 159 Common Real Options 162
Contents
vii
5.3
Basic Option Valuation 169 5.3.1 Discrete-Time Option Valuation 176 5.3.2 Continuous-Time Options Analysis 184 Conclusion 189 Selected References 189 Appendix 5A Multistep Cox–Ross–Rubinstein (CRR) Option Pricing 190 II
OPTION GAMES: DISCRETE-TIME ANALYSIS
6
An Integrative Approach to Strategy: Option Games
193
6.1
195
Key Managerial Issues: Optimal Timing and Flexibility versus Commitment 196 6.1.1 Optimal Investment Timing under Uncertainty 196 6.1.2 The Trade-off between Flexibility and Commitment 197 6.2 An Illustration of Option Games 197 6.3 Patent-Fight Strategies 206 6.4 An Application in the Mining/Chemicals Industry 209 Conclusion 217 Selected References 217 7
Option to Invest
219
7.1 7.2
Deferral Option of a Monopolist 219 Quantity Competition under Uncertainty 224 7.2.1 Cournot Duopoly 224 7.2.2 Asymmetric Cournot Oligopoly 235 7.3 Differentiated Bertrand Price Competition 238 Conclusion 240 Selected References 242 8
Innovation Investment in Two-Stage Games 8.1 8.2
243
Innovation and Spillover Effects 243 Innovation and Patent Licensing 253 8.2.1 Patent Licensing: Deterministic Case 253 8.2.2 Patent Licensing under Uncertainty 261 8.3 Goodwill/Advertising Strategies 264 Conclusion 271 Selected References 272
viii
Contents
III
OPTION GAMES: CONTINUOUS-TIME MODELS
9
Monopoly: Investment and Expansion Options
275
277
9.1
Option to Invest (Defer) by a Monopolist 278 9.1.1 Deterministic Case 281 9.1.2 Stochastic Case 284 9.2 Option to Expand Capacity 298 9.2.1 Additional (Lumpy) Capacity Investment 299 9.2.2 Incremental Capacity Investment 303 Conclusion 306 Selected References 307 Appendix 9A Contingent-Claims Analysis of the Option to Invest in Monopoly 308 10
Oligopoly: Simultaneous Investment
311
10.1 Oligopoly: Additional Capacity Investment 312 10.1.1 Existing Market Model: Expansion Option 312 10.1.2 New Market Model: Investment (Defer) Option 314 10.2 Oligopoly: Incremental Capacity Investment 317 10.3 Perfect Competition and Social Optimality 322 Conclusion 325 Selected References 325 Appendix 10A Derivation Based on Dynamic Programming 326 11
Leadership and Early-Mover Advantage
331
11.1 A Basic Framework for Sequential Investment in a Duopoly 331 11.2 Duopoly with Sequential Investment under Uncertainty 339 11.3 Oligopoly with Sequential Investment under Uncertainty 348 11.4 Option to Expand Capacity 352 Conclusion 357 Selected References 357 12
Preemption versus Collaboration in a Duopoly
359
12.1 Preemption versus Cooperation 360 12.1.1 Preemption 363 12.1.2 Cooperation in an Existing Market 370 12.2 Option to Invest in a New Market under Uncertainty
372
Contents
ix
12.2.1 Symmetric Case 373 12.2.2 Asymmetric Case 379 12.2.3 Size of Competitive (Cost) Advantage 382 12.3 Option to Expand an Existing Market 389 12.3.1 Symmetric Case 389 12.3.2 Asymmetric Case 393 Conclusion 395 Selected References 396 Appendix 12A Strategy Space and Solution Concept 397 Appendix 12B Perfect Equilibrium in Deterministic Setting 398 Appendix 12C Perfect Equilibrium in Stochastic Setting 400 13
Extensions and Other Applications
403
13.1 Exogenous Competition and Random Entry 404 13.2 Real-Estate Development 405 13.3 R&D and Patenting Applications 407 13.4 Investment with Information Asymmetry 411 13.5 Exit Strategies 415 13.6 Optimal Capacity Utilization 417 13.7 Lumpy Capacity Expansion (Repeated) 419 13.8 Other Extensions and Applications 421 Conclusion 423 Selected References 423 Appendix: Basics of Stochastic Processes
425
A.1 Continuous-Time Stochastic Processes 426 A.1.1 Brownian Motion 427 A.1.2 Mean-Reversion Process 438 A.1.3 General Itô Processes 440 A.2 Forward Net Present Value 441 A.3 First-Hitting Time and Expected Discount Factor 447 A.3.1 Exercise Timing and First-Hitting Time 447 A.3.2 Expected Discount Factor 448 A.3.3 Profit-Flow Stream with Stochastic Termination 452 A.4 Optimal Stopping 453 Conclusion 458 Selected References 458 References 461 Index 473
Glossary
Accommodated entry Entry is accommodated if structural entry barriers are low and entry-deterring strategies are ineffective or too costly. An incumbent attempts to adopt strategies and build competitive advantage early on to cushion the future negative effects of accommodated competitive entry. Action An action or move by one of the players in a simultaneous game is a choice or decision she can make that affects the other player(s). Barriers to entry Barriers or factors that allow an incumbent firm to earn positive economic profits or excess rents by making it unprofitable for newcomers to enter the industry. Competitive markets are characterized by low entry barriers. Blockaded entry A condition where the incumbent need not undertake any entry-deterring strategies to enjoy monopoly rents in the marketplace. Structural or administrative barriers are sufficient conditions for blockaded market entry. Call option A contract or situation that gives its holder the right, but not the obligation, to buy or acquire an underlying asset at a predetermined price over a specified period (maturity). Chicken game
See “war of attrition.”
Closed-form solution A solution that gives an analytical answer to a mathematical formulation. Closed-loop strategies In dynamic games, closed-loop strategies allow players to condition their play on both the previous moves by the players and on calendar time. All past actions of all players is common knowledge at the beginning of each stage. Closed-loop equilibrium The equilibrium forms a perfect equilibrium in closed-loop strategies; that is, the closed-loop strategies form a Nash
xii
Glossary
equilibrium in each and every subgame (on and off the equilibrium path). Commitment
See “strategic commitment.”
Commitment value The incremental value (positive or negative) accruing to a firm from making a strategic commitment. Cost advantage One of the main strategies to achieve a competitive advantage is to seek to attain lower costs, while maintaining a perceived benefit comparable to that of competitors. A relative cost advantage influences the optimal investment timing of competing firms. Cost of capital The rate of return expected or required by an equally risky asset or investment to induce investors to provide capital to the firm. The cost of capital reflects the systematic (or market) risk of a traded asset perfectly correlated with the investment or asset to be valued. Deterred entry A situation occurring when an incumbent can keep an entrant out by employing an entry-deterring strategy. Dominant strategy A strategy that is the best decision for a player regardless of the action or strategy chosen by its opponent. Early-mover advantage An advantage from moving early that enables a firm to make a higher economic profit than its rivals. An early-mover advantage can stem from the uncontested market presence of a leader that enjoys monopoly rents for some time. Sources of sustainable earlymover advantages include the learning-curve effect (economies of cumulative production and learning), brand-name reputation—especially in situations where buyers are uncertain about product quality (“experience goods”)—, or high customer switching costs. Economic profit A profit concept that represents the difference between the profits earned by investing resources in a particular activity and the profits that would have been earned by investing the same resources in the best alternative activity in the market. Opportunity costs are subsumed in economic profits. Economies of scale Cost savings achieved when the unit production cost of a product decreases with the number of units produced. Economies of scope These involve cost savings externalities among product lines or production activities. Elasticity The elasticity of a variable with respect to a given parameter is the percentage change in the value of the variable resulting from a one
Glossary
xiii
percent change in the value of the parameter, all other factors remaining constant. European option An option that can only be exercised at maturity, not earlier. Extended (or expanded) net present value (E-NPV) The total value of a project including the option or flexibility value and the impact of any strategic commitment or interaction effects. Fixed costs Costs that are independent of the scale of production and are locked in for a given period of time. Some distinguish among fixed and sunk costs though the difference is subtle: “fixed” often refers to short-term commitments, while “sunk” or nonrecoverable costs generally involve a longer planning horizon. Focal-point argument In the event of multiple equilibria, the focalpoint argument suggests that an equilibrium that appears “natural” or logically compelling is the one more likely to arise. Games of incomplete information Games where players do not know some relevant characteristics of their opponents (e.g., their payoffs, available action sets or their beliefs). Games of perfect information Games where all players possess all relevant information. Extensive-form games of perfect information have the property that there is exactly one node or decision point in each information set. Game theory A branch of mathematics and economic sciences concerned with the analysis of optimal decision-making in multiplayer settings. Chess is a well-known example. Solution concepts meant to provide predictions on the likely outcomes impose certain behavioral restrictions on players. Information set The information a decision maker has at the moment she makes a decision. Isolating mechanisms Economic forces put in place by a firm to limit the extent to which its competitive advantage can be duplicated, eroded, or neutralized through the resource-creation activities of competitors. Learning-curve effect Learning-based cost advantage that results from accumulating experience and know-how in productive activities over time. Market structure Characteristic of a market in terms of number and size (power) distribution of firms. Monopoly, duopoly, and perfect competition are classic examples of market structure.
xiv
Glossary
Markov property This property asserts that for certain stochastic processes or dynamic problems, all the past relevant information is summarized into the latest value of a variable or price. One cannot therefore use past information to predict the future state of the variable. Efficient markets and Itô processes have this Markov property. Maturity The period or last moment at which an option can be exercised. If the option can be exercised before this date, it is called an American option; if only at maturity, a European option. Myopic strategy A strategy that does not take into account or is independent of the investment decisions of rivals. Nash equilibrium A classic equilibrium solution concept used in the analysis of multiplayer games: each player pursues its individual optimizing actions given the best actions of the other players. In equilibrium, no player has an incentive to unilaterally deviate. Nature Acts of nature are treated as the actions of a quasi-player that makes random choices at specified points in a game. Net present value (NPV) The NPV paradigm is well established in corporate finance. The net present value of a project is the present value of the expected cash flows minus the (present value of) required investment costs. In the absence of managerial flexibility, a stand-alone investment is deemed acceptable if its net present value is positive. Node A decision point in a game at which a player (or nature) can take an action. Open-loop strategies Strategies where players cannot observe the previous play of the opponents and therefore condition their play on calendar time only. Such strategies are also called “precommitment strategies.” Open-loop equilibrium A Nash equilibrium solution that is obtained when firms adopt open-loop strategies ignoring their rivals’ actions over the history of the game. Option A contract or situation that gives its holder the right but not the obligation to buy or acquire (if a call) or sell (if a put) a specified asset (e.g., common stock or project) by paying a specified cost (the exercise or strike price) on or before a specified date (the expiration or maturity date). If the option can be exercised before maturity, it is an American option; if only at maturity, a European option. Option to invest or option to defer An American-type call option embedded in projects where management has the right (but no obliga-
Glossary
xv
tion) to delay the project start for a certain time period. The exercise price is the cost needed to initiate the project. Option valuation Valuation process by which the total value or “expanded net present value” (E-NPV) of an investment opportunity is determined. The valuation approach is meant to capture management’s flexibility to adapt its decisions to the evolving uncertain circumstances. Path dependence A situation occurring when past circumstances or history condition the current outcome and can preclude or favor certain path evolutions in the future. Payoff The utility, reward, or value a player receives when the game is played out. In the option games context, the payoff can be the real option value (e.g., the value of a plant with the option to expand production). Perfect Nash equilibrium
See “subgame perfect Nash equilibrium.”
Players The individuals, firms, or actors that make decisions in a game situation. Each player’s goal is to maximize her payoff or value by choosing the best action or sequence of actions (strategy). Precommitment strategies
See “open-loop strategies.”
Preemption A situation whereby a firm invests ahead of its rivals to hinder their entry or profitable operation. Such a situation is often related to the presence of some first-mover advantage. Proprietary option An option held by a firm that entitles it to the full exclusive benefits resulting from exploiting the option. A monopolist firm has a proprietary investment option. Real option The flexibility arising when a decision maker has the opportunity to adapt or tailor a future decision to information and developments that will be revealed in the future. A real option conveys the right, but not the obligation, to take an action (e.g., defer, expand, contract, or abandon a project) at a specified cost (the exercise price) for a certain period of time, contingent on the resolution of some exogenous (e.g., demand) uncertainty. Real options analysis The field of application of option-pricing theory to valuing real investment decisions. Risk-neutral valuation A valuation method underlying option pricing analysis that adjusts for risk in the expectation of cash flows (certaintyequivalent), enabling discounting of future values at the risk-free interest rate. This contrasts to the standard valuation approach (NPV) consisting
xvi
Glossary
in discounting the (actual) expected cash flows at a (higher) risk-adjusted discount rate. Risk neutral Situations where investors are indifferent between a sure payoff (certainty-equivalent) and a risky outcome of equal expected value. By extension, the same description is used for the corresponding valuation method. Shared option An option simultaneously held or shared by several firms in the industry. Shared options characterize competitive industries where incumbent firms share the same investment opportunities. Shared options are more involved to analyze as they must account for rival reactions or interactions. Option holders’ investment behavior and project values are affected by the proprietary or shared nature of real options. Soft commitment (or accommodating stance) A strategic investment commitment that makes the rival firm better off in the (later) competition stage. In Cournot quantity competition, a soft commitment leads the committing firm to produce relatively less, while in Bertrand price competition a soft commitment induces the firm to maintain a higher price. Stochastic processes A set or collection of random variables such that the value of the process at any future time t is random though specified by a given probability distribution. Strategic commitment A strategic decision or move intended to alter the competitors’ behavior or beliefs about future market competition. Such commitments are generally difficult or costly to reverse. Strategic complements (or reciprocating actions) These characterize actions in situations where firms react (in equilibrium) in a reciprocating or complementary manner (i.e., reaction functions are upward sloping). For example, I will be nice to you if you are nice to me. In case of price competition, price-setting actions are strategic complements. Strategic substitutes (or contrarian actions) These characterize actions in situations where firms react (in equilibrium) in a contrarian or opposite manner (i.e., reaction functions are downward sloping). For example, you take advantage of me if I am nice to you. In case of quantity competition, capacity-setting actions are strategic substitutes. Strategy A behavioral rule adopted by a player that prescribes which contingent action(s) to choose at each stage in a game. A strategy specifies for each decision node or information set which action to pursue. Open-loop and closed-loop strategies refer to different strategy types:
Glossary
xvii
open-loop strategies make more restrictive assumptions on the information the players possess over the game play. Subgame perfect Nash equilibrium Solution concept used in dynamic games under complete information: (continuation) strategies form a Nash equilibrium at each and every stage of the game—even those stages that will not be actually played in equilibrium (“off the equilibrium path”). Sunk costs Investment costs that cannot be recouped. Once incurred, sunk costs are irrelevant for future decision-making. Tough commitment (or aggressive stance) A strategic commitment intended to hurt the rival. In Cournot quantity competition, tough commitment induces the committing firm to produce more, while in Bertrand price competition the firm will cut its price and enter a price war. Variable costs Costs, such as direct labor or commissions to sales people, that vary as the output level rises. War of attrition (or chicken game) In a duopoly involving a secondmover (follower) advantage, both firms have an incentive to be a follower or wait to be the last to move, leading to a “war of attrition.”
Symbols
i, j
Competing firms (in a duopoly)
−i
All other firms except firm i (in oligopoly)
n
Number of firms (in a competitive industry or market)
π i (⋅) π i (⋅)
Firm i ’s certain (deterministic) profit function
p (⋅)
Deterministic (inverse) demand function
p (⋅)
Uncertain (inverse) demand function
a, b
Known constant parameters in the (inverse) demand function
qi
Quantity produced by firm i
Q
Total quantity produced by all firms in the industry
ci
Firm i ’s variable (unit) cost
Ki
Up-front strategic investment outlay by firm i (in commitment games)
s
Degree of substitution (in differentiated Bertrand price competition)
x γ
R&D effort (in R&D investment games) Degree of R&D spillover (sharing) effects
k
Risk-adjusted discount rate (cost of capital)
r
(Instantaneous) risk-free interest rate
δ
Asset cash flow or dividend yield, convenience yield (for commodities), competitive erosion, or opportunity cost of waiting
g
Actual growth rate (drift parameter) for geometric Brownian motion
gˆ
Risk-neutral growth rate (for geometric Brownian motion)
Firm i ’s uncertain (stochastic) profit function
xx
Symbols
α αˆ
Actual growth rate for arithmetic Brownian motion
σ
Volatility (for the arithmetic or geometric Brownian motion)
h
Small time interval
dt
Infinitesimal time interval (h → dt )
q
Actual (empirically observed) probability (of up move)
p
Risk-neutral probability (of up move)
u
Up-move multiplicative factor in a binomial tree (process)
d
Down-move multiplicative factor in a binomial tree (process)
Ii
Investment outlay (cost) for firm i
e
Expansion factor (base value V expanded by e percent upon paying investment cost I , giving eV − I)
λ
Poisson jump arrival rate (frequency)
ρ
Correlation coefficient
E0 [⋅]
Expectation based on actual probabilities (conditional on time- 0 information)
Eˆ 0 [⋅]
Risk-adjusted expectation based on risk-neutral probabilities (conditional on time-0 information)
var ( )
Variance (or σ 2 )
t0
Starting time
t
Current time
T T
Time (years) to maturity of the option (in discrete-time models)
T * Bt (T )
Risk-neutral growth rate for arithmetic Brownian motion
random first-hitting time (i.e., the random time at which the pre-set investment trigger XT is first reached) Optimal random first-hitting time (i.e., the random time the optimal investment trigger X * is first reached) Value (at time t ) of a bond paying 1 euro at random future time T . It also represents the expected discount factor.
zt
A standard Brownian motion or Wiener process
εp
Price elasticity of demand (ε p (Q) ≡ −[∂Q ∂p] × ( p Q))
β (βˆ )
Dummy variable of the fundamental quadratic function (^ for the risk-neutral version)
β1 (βˆ 1) Positive root of the fundamental quadratic function (elasticity of the option to invest)
Symbols
xxi
β 2 (βˆ 2 ) Negative root of the fundamental quadratic function (elasticity of the option to exit) x0
Time-0 value of the stochastic process in the case of arithmetic Brownian motion
x t
Stochastic process value at time t in the case of arithmetic Brownian motion ( x t ≡ ln ( X t ))
X0
Time-0 value of the stochastic process in the case of geometric Brownian motion
X t
Time-t value of the process in the case of geometric Brownian motion
XT
Value of the stochastic process at maturity T in discrete-time option games, or the preset investment trigger—not necessarily the optimal one—in continuous-time option games
X*
Optimal investment trigger (*)
M
Monopolist firm’s total value (with investment timing or expansion option)
S
Total firm value (with investment timing or expansion option) in an oligopoly characterized by simultaneous investment
L
Leader’s value (with investment timing or expansion option) in sequential investment option games
F
Follower’s value (with investment or expansion option) in sequential investment option games
*
(Superscript) denotes optimal or equilibrium value
^
(Superscript) denotes risk-neutral or risk-adjusted expectation, variable or parameter Euro
M
Million
Bn
Billion
≡
Means “is defined to be”
Foreword
President Truman once said: “Give me a one-handed economist. All of my economic advisers say ‘On the one hand this, on the other hand that.’” Economists do indeed recognize that there are multiple forces at work in most situations, and it takes quite subtle analysis to understand their interaction and balance. This book is an admirable effort at such an economic analysis. When facing an uncertain future, remaining flexible until more information arrives has value, because one can cherry-pick to make investments only when the prospects are relatively favorable. This is the starting intuition of real option theory. But in game theory, the strategy of making irreversible commitments to seize first-mover advantage and present rival players with a fait accompli to which they must adapt can have its own value. So what does one do when facing an uncertain future in the company of rivals? This is a difficult problem, conceptually as well as mathematically. The last two decades have brought a trickle of research contributions that address some aspect of this dilemma. In this book, Benoît Chevalier-Roignant and Lenos Trigeorgis synthesize and consolidate much of this literature and skillfully extend it. Generations of students and researchers over the next decade or two will find the book an invaluable starting point for their own work. The authors also deserve congratulations for their excellent exposition. They begin with very simple and clear overviews of the issues, concepts and models from the separate areas of real options and game theory. They focus on applications to industrial organization and business. For students in any of these areas, this book can serve as a hypermarket for one-stop intellectual shopping. I will endeavor a personal remark. I was involved in some of the early research on real option theory. I also contributed to popularizing game theory. But I seem to suffer from a kind of attention-deficit disorder in
xxiv
Foreword
research; therefore I got interested in, and diverted to, other fields like political economy and governance institutions. I am happy that my contributions to real option theory are still remembered, and feel honored to be asked to write a preface to this book. But, returning to the real options literature after many years to read this book, I also feel like Rip Van Winkle, amazed at how much has changed in the intervening years. Although I have enjoyed my excursions into other fields, perhaps I should have stayed and contributed to these equally exciting developments that have combined options and games to produce better twohanded economists. Avinash Dixit Princeton, NJ June 2010
Preface
In real life most situations corporate managers face are characterized by both strategic and market uncertainties with respect to the economic environment. Following the liberalization and deregulation of Western economies, very few industries remain protected, whereas most companies face fierce competition in their respective economic sectors. Certain European governments used to favor high administrative barriers shielding certain “natural monopolies” from competitive entry. Such protected monopolies included the telecommunications, electricity, and gas sectors. European governments recently had to enforce deregulation schemes, opening up many economic activities to new, potentially foreign market participants. At the same time sectors traditionally populated by many firms have undergone significant consolidation, yielding oligopolistic situations with a reduced number of players. These two ongoing concurrent phenomena—liberalization and continuing consolidation— highlight the emphasis corporate managers increasingly put on strategic uncertainty and market structure. Besides strategic uncertainty, managers face increasing market uncertainty. With a reduced life cycle for many products, firms can no longer rely on a given offering but have to renew their product portfolio frequently to sustain or enhance their revenue stream in light of competitive pressures. The IT industry has evolved most rapidly, putting companies unable to respond to market developments and technological uncertainty at a severe disadvantage. At the core of this dilemma lies a classic trade-off between commitment and flexibility. Managers can stake a claim by making large capital investments today influencing their rivals’ behavior or take a “wait-andsee” or step-by-step approach to avoid possible adverse market consequences tomorrow. The assessment and optimal management of strategic options is critical for firms to succeed in today´s constantly changing
xxvi
Preface
business environment. Whether to invest in a new product or enter a new market is a critical decision management should address with proper analytical tools in assessing options and deciding whether to make this or that strategic move. This book aims to make accessible to a wide audience recent results on how to achieve and quantify balance between flexibility and commitment through the new approach of “option games.” We believe that this approach can play an important role in managing modern business in a changing global marketplace. Option games help model situations where a firm that has a real option to (dis)invest in specific projects faces competition. Such situations lead to two, sometimes conflicting, main sources of value for the firm. First, there is a value of waiting or flexibility related to the real option that the firm holds to make future better-informed decisions. Second, there is a value of commitment in light of the strategic interaction with competitors. The trade-off between these two forces calls for a careful balancing act. From a modeling perspective, the examination of such a trade-off calls for a combination of the real options and game theory approaches to decision-making. In the first part of the book, we discuss prerequisite concepts and tools concerning basic game theory, industrial organization, and real options analysis. We are then in a position to amalgamate these diverse fields into a unified framework for option games. This makes the task at hand very ambitious because these fields of research normally require different tool kits and needed results are scattered around in disparate parts of the literature. We aim to fill this gap here by synthesizing the existing literatures to provide a consistent and accessible account of options and games. We combine some of the best materials, tools, and ideas found in diverse books and research works on game theory (e.g., Fudenberg and Tirole 1991; Osborne 2004), industrial organization (Tirole 1988), and real options analysis (Dixit and Pindyck 1994; Trigeorgis 1996) and go beyond current knowledge to chart new territory. The current book brings important materials and ideas together in a unified framework, which makes it much easier for managers and academics to enter and understand this new field. The second part of the book presents the new approach in discrete time, while the last part on continuous-time option games is not covered in any systematic way anywhere and is an important addition. For pedagogical convenience and for the sake of simpler and clearer exposition and buildup of the basic ideas, we first present each of the building blocks step by step to form the supporting foundation and columns of the structure, with the richer theory coming later
Preface
xxvii
(culminating toward chapter 12) as the keystone that will complete the arch.1 The book should be especially appealing to the academic community, particularly in the areas of strategy, economics, and finance. It is the first book that combines the aforementioned fields in such a way that it is accessible to an audience that is not necessarily expert in all fields involved. The book should also be of interest to (academically trained) practicing managers who are interested in applying these ideas. It provides many strategic insights and a ready-to-use tool kit offering quantitative guidance for important competitive trade-offs faced by the modern firm. We attempted to strike a balance between making the book accessible to a wider audience while simultaneously making it challenging and rigorous, subjecting the art of strategy to a scientific inquiry. The book provides a very pragmatic and intuitive, yet rigorous approach to strategy formulation. We owe an intellectual debt to the many scholars who made significant contributions to the related literatures and to the many individuals who provided us with generous comments, criticism, ideas, and suggestions. We thank Avinash Dixit for his feedback, prologue, and encouragement. Marcel Boyer, Marco Días, Kuno Huisman, Grzegorz Pawlina, Sigbjørn Sødal, and Jacco Thijssen made invaluable detailed comments and provided suggestions for improvement on the entire manuscript. Several other colleagues offered valuable comments on select parts of the book or on specific chapters: Christoph Flath, John Khawam, Bart Lambrecht, Richard Ruble, and Bruno Versaevel. We also thank Stefan Hirth, Helena Pinto, Artur Rodrigues, and Han Smit for useful comments. We thank Robert J. Aumann, Rainer Brosch, Peter Damisch, Marco Días, Avinash Dixit, Eric Lamarre, Scott Mathews, Robert C. Merton, Reinhard Selten, and Jean Tirole for enhancing the relevance of this book with their valuable interviews and comments. The authors would like to thank Arnd Huchzermeier for his support. Jane MacDonald from the MIT Press has been most enthusiastic, efficient, and supportive. Last but not least, we would like to thank our families, alive or departed, for their love and support. 1. Chapter 12 can be thought of as the climax of the book, but we need to introduce various key notions (e.g., investment trigger, open-loop vs. closed-loop equilibrium) in a step-bystep fashion to facilitate and smooth out the exposition. Several of the issues left unresolved in the earlier parts of the book are addressed in chapter 12.
1
The Strategy Challenge
At a time when national monopolies have been losing their secular wellprotected positions owing to market liberalization in the European Union and elsewhere across the globe, strategic interdependencies and interactions have become a key challenge for managers in many corporations. Strategic questions abound: How should a firm sustain or gain market share? How to differentiate oneself from others in the grueling global marketplace? When precisely should a firm enter or exit an industry when it faces uncertainty and significant entry and exit costs? Recent developments in economics, finance, and strategy equip management facing such challenges with a concrete framework and tool kit on how to behave strategically in such a complex and changing business environment. Corporate finance and game theory provide complementary perspectives and insights regarding strategic decision-making in business and daily life. Box 1.1 motivates the relevance of game theory to the understanding of daily life situations. The option games approach followed in this book paves the way for a more rigorous approach to strategy formulation in many contexts. It helps integrate in a common, consistent framework the recent advances made in these diverse disciplines, providing powerful insights into how firms should behave in a dynamic, competitive and uncertain marketplace. We first highlight in section 1.1 several environmental factors that justify why firms should be careful when formulating their corporate strategies in an uncertain, competitive business environment. In section 1.2 we discuss how an understanding of competitive strategy in terms of sound economic principles is useful to managers. Two complementary but separate perspectives on strategy (corporate finance and game theory) are discussed in section 1.3. We address the need for an integrative approach to corporate strategy in section 1.4. We provide an overview of the book organization in section 1.5.
2
Chapter 1
Box 1.1 Game theory in daily life
All Is Fair in Love, War, and Poker Tim Harford, BBC News Online What Do Love, War, and Poker Have in Common? High stakes, perhaps. Certainly, in all three you spend a lot of effort trying to work out what the other side is really thinking. There is another similarity: economists think they understand all three of them, using a method called “game theory.” Threats and Counterthreats Game theory has been used by world champion poker players and by military strategists during the cold war. Real enthusiasts think it can be used to understand dating, too. The theory was developed during the Second World War by John von Neumann, a mathematician, and Oskar Morgenstern, an economist. Mr. von Neumann was renowned as the smartest man on the planet—no small feat, given that he shared a campus with Albert Einstein—and he believed that the theory could be used to understand cold war problems such as deterrence. His followers tried to understand how a nuclear war would work without having to fight one, and what sort of threats and counterthreats would prevent the US and the Soviets bombing us all into oblivion. Since the cold war ended without a nuclear exchange, they can claim some success. Understand the World Another success for game theory came in 2000, when a keen game theorist called Chris “Jesus” Ferguson combined modern computing power with Mr. von Neumann’s ideas on how to play poker. Mr. Ferguson worked out strategies for every occasion on the table. He beat the best players in the world and walked away with the title of world champion, and has since become one of the most successful players in the game’s history. Game theory is a versatile tool. It can be used to analyze any situation where more than one person is involved, and where each side’s actions influence and are influenced by the other side’s actions. Politics, finding a job, negotiating rent, or deciding to go on strike are all situations that economists try to understand using game theory. So, too, are corporate takeovers, auctions, and pricing strategies on the high street. Financial Commitment But of all human interactions, what could be more important than love? The economist using game theory cannot pretend to hand out advice on
The Strategy Challenge
3
Box 1.1 (continued)
snappy dressing or how to satisfy your lover in the bedroom, but he can fill some important gaps in many people’s love lives: how to signal confidence on a date, or how to persuade someone that you are serious about them, and just as importantly, how to work out whether someone is serious about you. The custom of giving engagement rings, for instance, arose in the United States in the 1930s when men were having trouble proving they could be trusted. It was not uncommon even then for couples to sleep together after they became engaged but before marriage, but that was a big risk for the woman. If her fiancé broke off the engagement she could be left without prospects of another marriage. For a long time the courts used to allow women to sue for “breach of promise” and that gave them some security, but when the courts stopped doing so, both men and women had a problem. They did not want to wait until they got married, but unless the man could reassure his future wife, then sleeping together was a no-no. The solution was the engagement ring, which the girl kept if the engagement was broken off. An expensive engagement ring was a strong incentive for the man to stick around—and financial compensation if he did not. Not Committed Modern lovers might think the idea of engagement ring as guarantee is a thing of the past, but they can still use game theory to size up their partners. When a couple with separate homes move in together, selling the second home is an important signal of commitment. That second home is an escape route—valuable only if the relationship is shaky. If your partner wants to hang on to his bachelor pad, do not let him tell you it is merely a financial investment. Game theory tells you that he is up to something. Reprinted with permission of BBC News, bbc.co.uk/news. Publication date: August 17, 2006.
1.1 The Changing Corporate Environment The competitive environment around the globe is becoming increasingly challenging for managers as modern economies have witnessed tremendous changes over the last three decades. In this constantly evolving environment, where firms must often make quick decisions that have long-term impact, it is anybody’s guess what might happen in the future— market developments often prove expectations wrong. Firms must carefully commit to specific strategies while developing adaptive capabilities
4
Chapter 1
in an ever-changing marketplace. Globalization, deregulation, and the emergence of new economies (e.g., Brazil, Russia, India, and China) have created both threats and opportunities for incumbent firms who now have to adapt more effectively to the rapidly changing global environment or suffer damage by new entrants and risk extinction. Following the liberalization and deregulation of European economies, only a limited number of industries have remained secure, while most companies across the board face serious competitive pressures. At the same time other economic sectors traditionally characterized by a large number of companies have undergone significant consolidation, resulting in oligopoly structures with a reduced number of players. The recent economic crisis has amplified these consolidation pressures. The mining giant Rio Tinto has recently merged with BHP Billiton, forming a virtual duopoly together with Brazilian mining giant Vale. M&A deals have similarly reshaped the automotive sector, with the recent acquisitions of Chrysler by Fiat, of Porsche and Suzuki by Volkswagen, and of Mitsubishi by PSA (Peugeot, Citroën). British Airways together with Iberia claim the top two position in the fiercely competitive European airline business. In the United States, the merger between United Airlines and Continental Airlines created one of the world’s biggest airlines. A dramatic concentration has also taken place in the banking sector: out of the top five investment banks worldwide, only two (Goldman Sachs and Morgan Stanley) have remained independent. Notable banking deals include the acquisition of Washington Mutual by JP Morgan Chase, of Countrywide by Bank of America, and of the Belgian bank Fortis by BNP Paribas. These two concurrent phenomena—liberalization and consolidation— have put higher on the corporate agenda the assessment of strategic uncertainty. Italy’s dominant state electricity authority, Enel, is a good case in point. Just a decade ago Enel was in a very comfortable position, enjoying an established natural monopoly in the Italian electricity market with the benediction of the national government. The main concern for Enel during this period was to minimize or keep under control its mix of input or production costs, as the output electricity price was regulated. Several years later Enel lost its preferential monopoly position due to the liberalization of the European markets, and the competitive environment facing Enel changed dramatically. Enel was forced to sell half of its generating assets to half a dozen smaller local rivals, creating more competition in its home base. Electricity price deregulation accompanied by oil and other fuel price fluctuations have added considerable pressure
The Strategy Challenge
5
and uncertainty for Enel. With further deregulation other European competitors (e.g., the dominant electricity producer of France, EDF) also entered the Italian electricity market. Today Enel has to consider the actions of local as well as international competitors on the national soil, as well as contemplate investing itself in new or emerging markets, such as Russia, to sustain or leverage its once dominant position in the area. Just as its European and global counterparts, Enel now faces a broader range of uncertainties and challenges: How to cope with increased energy (input) and electricity demand (output) uncertainties? How to compete with local and global rivals in an ever-changing local and global competitive landscape? How to assure and diversify its energy portfolio mix in a globalized marketplace? How to formulate and dynamically adjust its strategy, knowing when to compete, threaten, bargain, or cooperate with its rivals? These are the kind of questions we will be addressing in this book. Many situations corporate managers face today are characterized by both market and strategic uncertainty with respect to the economic environment. When one desires to address such complex issues, some simplification of reality is useful to focus on the fundamental trade-offs. Some simple models in management are being revised as they offer rather simplistic approaches that no longer describe current economic reality. The field of investment under uncertainty falls in this category. Prevailing management approaches often lead to investment decisions detrimental to the overall firm’s long-term well-being. In an increasingly uncertain and competitive environment, corporate managers need appropriate management tools that can provide long-term guidance. This book describes a novel approach aimed to enable managers make rational decisions in a competitive environment under uncertainty. It allows managers to quantify and balance the conflicting impacts of managerial flexibility and the strategic value of early investment commitment in influencing rivals’ strategic behavior. Real options analysis is widely considered to be more reflective of reality than traditional financial methods (e.g., net present value) in that it takes managerial flexibility into account.1 To avoid dealing with complex models, however, standard real options analysis often ignores 1. Investment under uncertainty is part of the mainstream literature on finance, economics, and strategic management. In the last decades financial theory has been supplemented with real options analysis. Use of the financial options analogue can be insightful in assessing flexibility embedded in real asset situations. The real options approach to investment has reached a corporate finance textbook status and is currently applied in leading corporations for guiding real-world strategic investment decisions.
6
Chapter 1
the strategic interactions among option holders, analyzing investment decisions as if the option holder has a proprietary right to exercise. This simplifying perspective is far from being realistic in many situations because firms generally compete with rivals. Several firms may share an option in the industry and hence option exercise strategies cannot be formulated in isolation. Rather, optimal investment behaviors must be determined as part of an industry equilibrium. As a consequence of this more pragmatic view of the nature of the competitive environment, a new theory called “option games” has emerged. This theory combines the concepts and tools offered by traditional real options analysis with game theory principles designed to help figure out how players behave in strategic conflict situations. The option games approach we elaborate on herein provides powerful insights into understanding strategic interactions and challenges traditional thinking that presumes that firms pursue strategies in isolation. Game theory is for the most part deterministic. Option games help management better intuit how uncertainty can be modeled in a strategic setting. This approach helps improve prediction and understanding of industry dynamics in highly uncertain industries. It enhances previous industrial organization literature on strategic investment in a deterministic setting to better explain the strategic investment behavior of firms under changing conditions. Box 1.2 provides an overview of the challenges commercial airframe manufacturers Box 1.2 Evolving strategy in commercial aviation
Boeing Bets the House on Its 787 Dreamliner Leslie Wayne In recent years Boeing has stumbled badly, ceding its decades-long dominance in commercial aviation to Airbus and becoming mired in a string of scandals over Pentagon contracts. The terrorist attacks of 2001 depressed demand at a time when the company’s product line paled against appealing new planes from Airbus. In one year alone, from 2001 to 2002, Boeing’s profits dropped 80 percent. But the view from Seattle, the headquarters of Boeing’s commercial jet operations, has more of that Chinese pep-rally spirit than such gloomy talk might indicate . . .. With revenue having grown for the second consecutive year, to $54.8 billion in 2005, and a record number of orders on its books, Boeing has had a huge gain in its stock price—to more than $80 a share, more than three times its nadir of $25 in 2003. Boeing’s 1,002 orders last
The Strategy Challenge
Box 1.2 (continued)
year fell short of Airbus’s 1,055. But Boeing’s orders included more widebody planes, which analysts valued at $10 billion to $15 billion more than Airbus’s. But what is really driving the high spirits at Boeing—and the high stock price—is a plane that has not yet taken to the skies: the 787. It is Boeing’s first new commercial airplane in a decade. Even though it will not go into service until 2008, its first three years of production are already sold out— with 60 of the 345 planes on order going to China, a $7.2 billion deal. Other big orders have come from Qantas Airways, All Nippon Airways, Japan Airlines, and Northwest Airlines. Big orders mean big money, of course—and that is good, because analysts estimate that Boeing and its partners will invest $8 billion to develop the 787. Boeing is also risking a new way of doing business and a new way of building airplanes: farming out production of most major components to other companies, many outside the United States, and using a carbonfiber composite material in place of aluminum for about half of each plane. If it works, Boeing could vault back in front of Airbus, perhaps decisively. If it fails, Boeing could be relegated to the status of a permanent also-ran, having badly miscalculated the future of commercial aviation and unable to meet the changing needs of its customers. “The entire company is riding on the wings of the 787 Dreamliner,” said Loren B. Thompson, an aviation expert at the Lexington Institute, a research and lobbying group in Arlington, Virginia, that focuses on the aerospace and military industries. “It’s the most complicated plane ever.” Boeing calls the 787 Dreamliner a “game changer,” with a radically different approach to aircraft design that it says will transform aviation. A lightweight one-piece carbon-fiber fuselage, for instance, replaces 1,200 sheets of aluminum and 40,000 rivets, and is about 15 percent lighter. The extensive use of composites, already used to a lesser extent in many other jets, helps improve fuel efficiency. To convince potential customers of the benefits of composite—similar to the material used to make golf clubs and tennis rackets—Boeing gives them hammers to bang against an aluminum panel, which dents, and against a composite one, which does not. At the same time, the 787 has new engines with bigger fans that are expected to let the plane sip 20 percent less fuel per mile than similarly sized twin-engine planes, like Boeing’s own 767 and many from Airbus. This is no small sales point, with oil fetching around $70 a barrel and many airlines struggling to make a profit even as they pack more passengers into their planes. “The 787 is the most successful new launch of a plane—ever,” said Howard A. Rubel, an aerospace analyst at Jeffries & Company, an investment bank that has advised a Boeing subsidiary . . .. The 787 is designed to carry 220 to 300 people on routes from North America to Europe and Asia. Boeing is counting on it to replace the workhorse 767, which is being
7
8
Chapter 1
Box 1.2 (continued)
phased out, and, it hopes, a few Airbus models as well. Its advantages go beyond fuel efficiency: Boeing designed the 787 to fly long distances while keeping passengers relatively comfortable. That approach grows out of another gamble by Boeing—that the future of the airline business will be in point-to-point nonstop flights with medium-size planes rather than the current hub-and-spoke model favored by Airbus, which is developing the 550-seat A380 superjumbo as its premier long-haul jetliner. Flying point to point eliminates the need for most passengers to change planes, a competitive advantage so long as the Dreamliner is as comfortable and as fast as a bigger aircraft. And after talking with passengers around the world, Boeing designed the 787 to have higher humidity and more headroom than other airplanes, and to provide the largest windows of any commercial plane flying today. “We are trying to reconnect passengers to the flying experience,” said Kenneth G. Price, a Boeing fleet revenue analyst. With airlines squeezing every last cent and cutting back service, “flying is not enjoyable,” Mr. Price said. “Every culture fantasizes about flying,” he added. “All superheroes fly. But we were taking a magical experience and beating the magic out.” Even more innovative for Boeing is the way it makes the 787. Most of the design and construction, along with up to 40 percent of the estimated $8 billion in development costs, is being outsourced to subcontractors in six other countries and hundreds of suppliers around the world. Mitsubishi of Japan, for example, is making the wings, a particularly complex task that Boeing always reserved for itself. Messier-Dowty of France is making the landing gear and Latecoere the doors. Alenia Aeronautica of Italy was given parts of the fuselage and tail. Nor are these foreign suppliers simply building to Boeing specifications. Instead, they are being given the freedom, and the responsibility, to design the components and to raise billions of dollars in development costs that are usually shouldered by Boeing. This transformation did not come overnight, of course, nor did it begin spontaneously. Boeing changed because it had to, analysts said. “Starting in 2000, Airbus was doing well,” said Richard L. Aboulafia, an aerospace analyst with the Teal Group, an aviation research firm in Fairfax, Va. “Boeing had to reconsider how it did business. That led to the framework for the 787—getting the development risk off the books of Boeing and coming up with a killer application.” Boeing plans to bring the 787 to market in four and a half years, which is 16 to 18 months faster than most other models. All of that is good, Mr. Aboulafia added, if it works. It is a tall order for a wholly new plane being built with new materials, many from new suppliers and assembled in a new way. “The 787 is operating on an aggressive timetable and with aggressive performance goals,” he said. “It leaves no margin for error.”
The Strategy Challenge
Box 1.2 (continued)
Never before has Boeing farmed out so much work to so many partners—and in so many countries. The outsourcing is so extensive that Boeing acknowledges it has no idea how many people around the world are working on the 787 project. Airbus, Boeing’s sole rival in making big commercial airliners, is also making a big bet on the future, but in a different direction. The companies agree that in 20 years, the commercial aviation market may double, with today’s big orders from China, India, and the Middle East to be followed by increased sales to American and European carriers as they reorganize and reduce costs. By 2024, Boeing estimates, 35,000 commercial planes will be flying, more than twice the number now aloft, and 26,000 new planes will be needed to satisfy additional demand and replace aging ones. But how passengers will get from place to place, and in what planes, will depend on whether Boeing or Airbus has correctly forecast the future. Boeing believes that passengers will want more frequent nonstop flights between major destinations—what the industry calls “city pairs.” That is what led to the big bet on the Dreamliner, a midsize wide-body plane that can fly nonstop between almost any two global cities—say, Boston to Athens, or Seattle to Osaka—and go such long distances at a lower cost than other aircraft. Airbus believes that airplane size is more important than frequent nonstop flights and that passengers will stick with a hub-and-spoke system in which a passenger in, say, Seattle, will fly to Los Angeles and transfer to an Airbus 380 to go to Tokyo before catching a smaller plane to Osaka. That view has led it to spend $12 billion to develop the double-deck A380, the largest passenger jet ever—a bet that is as crucial to its future as the 787 is to Boeing’s. “We have a fundamental difference with Airbus on how airlines will accommodate growth,” said Randolph S. Baseler, Boeing’s vice president for marketing. “They are predicting flat growth in city pairs. We are saying that people want more frequent nonstop flights. They believe airplane size will increase, and we believe that airplanes will not increase in size that much. Those two different market scenarios lead to two different product strategies.” The market, of course, will determine the winner, but given the industry’s long lead times, that may not be clear for 10 to 20 years. For now, airlines have ordered 159 copies of the A380—which has a list price of $295 million and is scheduled to enter service this year—and more than twice as many 787s, which list for $130 million and are scheduled to enter service in two years. Publication date: May 7, 2006.
9
10
Chapter 1
have faced over the recent years, focusing on the changes in corporate strategy of Boeing compared with Airbus. A manager from Boeing discusses in box 1.3 the use of real options to capture and assess the diverse sources of uncertainty in his business; an analysis of the strategic interplay vis-à-vis Airbus is highlighted. 1.2 What Is Strategy? Corporate strategy is high on the agenda of every major corporation.2 The strategy a firm formulates and how it implements that strategy will determine to a large extent whether it will survive and be successful in the marketplace or become extinct. Formulating the right strategy in the right place at the right time is not an easy task. It requires deep analysis and ready-to-implement, adaptable solution programs. Our approach to strategy is based on the premise that strategic management is a structured, rational discipline relying on rigorous market and competitive analysis. One can understand why firms succeed or fail by analyzing their decision processes in terms of consistent principles of market economics and rational strategic actions. This is the reason why a large literature in strategic management relies on economic theory as it provides a reliable, rigorous foundation to understanding specific developments and reactions taking place in the market place. Good firm performance is considered the result of soundly formulated and well-implemented strategies. Grant (2005) identifies the following elements as key to a successful strategy: (1) simple, agreed-upon, longterm objectives; (2) deep understanding of the competitive landscape; (3) objective appraisal of the firm’s internal resources and capabilities; and (4) effective implementation. There are no easy “recipes for success” applicable to each firm in every industry.3 The pursuit of one-size-fits-all 2. Although it is commonly agreed that strategy is critical in today’s changing corporate environment, there is no universally agreed-upon definition of business strategy. According to Chandler (1962), strategy is “the determination of the basic long-term goals and objectives of an enterprise and the adoption of courses of action and the allocation of resources necessary for carrying out these goals.” According to Mintzberg et al. (2002), strategy is “the pattern or plan that integrates an organization’s goals, policies and action sequences into a cohesive whole.” 3. There are two main approaches to strategy formulation. The first approach looks at specific firms or case studies examining why these firms are successful and tries to deduce success factors that might be applicable to other firms. This is the “best-practices” approach. Herein we take a different approach. We formulate a conceptual framework for strategic management and assess if it provides prescriptive insights into real-world managerial problems.
The Strategy Challenge
Box 1.3 Interview with Scott Matthews, Boeing
1. Do you believe real options is more suitable than other capital budgeting approaches to provide managerial guidance? Where and to what extent is real options analysis used at Boeing? Real options provides a more informed decision for our strategic projects. Of special significance are the scenarios that we build around the real options analyses that help us understand both the risks and the opportunities of any venture. To date, real options analysis has been used mostly on large-scale projects. Because of the higher investment amounts, these large projects pose particular risks that require more careful analyses including the use of real options techniques. 2. What are the sources of uncertainty you face at Boeing, and how do you manage them with options, physical or contractual? Boeing projects have many sources of uncertainty. We build models that attempt to integrate technology development, design, manufacture, supply chain, and market forces, including possible actions of our competitors. These models have dozens, even hundreds, of variables modeled using various Monte Carlo and discrete event simulation capabilities. Usually there are just a handful of principal uncertainty drivers which are determined using sensitivity analysis. We then apply a series of targeted investments to investigate and better understand the true scale of these uncertainties. Since the uncertainty landscape is in constant evolution, due to both our risk mitigation efforts as well as exogenous events, we continue to update the model and modify our investments as appropriate. These are
11
12
Chapter 1
Box 1.3 (continued)
often modeled as real option investments with a type of varying volatility, as we are attempting to both reduce uncertainty while at the same time increase the value of the subsequent project stage. 3. Do you see a usefulness for game theory and option games in Boeing’s strategic thinking, for example, vis-à-vis Airbus? We find that game-theoretical approaches provide additional insight to a solution set as long as the number of actors is limited to just a few players. At a certain point market considerations dominate and provide a better approach to modeling the scenarios. We have managed to execute a few plays against our competitors, the origin of which could be traced back to strategic gaming scenarios and market timing. When we are successful, these plays are often highly leveraged, and therefore take on the characteristics of well-placed option investments. However, like other companies in dynamic markets, we find our competitive response limited by timing or technology and product availability considerations.
success factors has failed to provide a coherent direction to guide the actions and decisions of firms. Ghemawat (1991) criticizes the success factors approach and identifies commitment as a main driver of corporate success or failure. He sees commitment as a well-thought-out plan of action affecting the firm in the long term. A successful strategy should exhibit consistent but adaptive behavior over time and involve certain strategic commitments that might sometimes hinder managerial flexibility. This feature of strategy implies that, in an uncertain environment, resolving the investment or commitment timing issue is critical to a firm’s success. A firm should not always invest or commit immediately, but should be prepared to decide at the right moment to reap the benefits of a developing opportunity. As suggested by Dixit and Pindyck (1994), investment situations where decisions are costly or impossible to reverse compel corporate managers to be cautious and careful to make decisions at the right time. Strategy should also be dynamic in that it should be adaptable to changing market circumstances or competitive dynamics. Following Rumelt (1984, p. 569), the essence of competitive strategy is being in “constant search for ways in which the firm’s unique resources can be redeployed in changing circumstances.” The increasing cone of market and strategic (competitive) uncertainty makes the dynamic formulation of strategy key to survival and success in a changing marketplace. Box 1.4
The Strategy Challenge
Box 1.4 Flexible strategy and real options
Stay Loose: By Breaking Decisions into Stages, Executives Can Build Flexibility into Their Plans Lenos Trigeorgis, Rainer Brosch, and Han Smit, Wall Street Journal In turbulent times adaptability is critical. That’s why today flexibility is more valuable than ever in business strategy. Markets, technologies, and competition are becoming more dynamic by the day. To succeed in this environment, companies need to position themselves to capitalize on opportunities as they emerge, while limiting the damage if adversity hits. This requires a whole new level of flexibility. Good managers have always been able to think on their feet. But many widely applied tools of strategy development were designed for relatively stable environments. As a result business strategy may too often lock managers into decisions that turn out to be flawed because something outside their control doesn’t go as planned. What is needed is a systematic translation of managers’ flexibility into strategy—a plan that lays out a series of options for managers to pursue or decline as developments warrant. That is the essence of what is known as “real options” analysis, an approach that borrows from the workings of the financial markets. Just as stock options, for instance, give the holder the right, but not the obligation, to buy or sell shares at a given price at some time in the future, real options give executives the right, but not the obligation, to pursue certain business initiatives. Start Small Instead of making rock-hard plans and irreversible long-term commitments, the idea is to create flexibility by breaking decisions down into stages. When building a new plant, for example, it may be tempting to realize the full economies of scale by building the biggest facility the company can manage. But it may be wiser to first build a smaller plant that can be easily expanded later on. That way, if the market for the products the plant produces should decline, a smaller investment has been put at risk. At that point managers have the option to scale down or abandon operations. On the other hand, if things turn out well, they have the option to expand the plant. As a mind-set this approach encourages managers to be flexible in their planning. In more concrete terms it allows them to value investment decisions and business initiatives in a new way. Instead of making a decision based on a rigid financial analysis of a given project as a whole, managers can analyze, from the start, the financial implications of each step along the way and every potential variation—without committing to anything
13
14
Chapter 1
Box 1.4 (continued)
before they must. Once the project is under way, they also can account for the changing value of each option as events unfold. All that information gives them a clearer framework for decisions on whether to launch a project and whether to proceed, hold back, or retreat at each stage. What does this look like in practice? A leading European automaker was considering two investment alternatives for the production of a new vehicle. Under one alternative, production would be based entirely in one country. Under the other, the company would set up plants around the world, allowing it to switch production from site to site to take advantage of fluctuations in exchange rates or labor costs. The cost of the flexible system would be higher. But the company decided that the value of that flexibility, with its promise of cost savings and increased profits, exceeded the difference in cost between the two alternatives. So it chose the multinational plan. Competitive Edge Real options analysis can also be useful in helping strategic planners address the challenges of competition. Many managers already incorporate game theory into their planning to help predict how competition will play out. But with competition emerging and evolving more rapidly than ever, supplementing game theory with real options analysis can help companies be more flexible in how they react. Consider, for example, the question of whether a company should aim to preempt competition or choose to cooperate with other players in a way that could expand the market. This is a question of growing relevance as sometimes competing technologies are at the heart of more products. In deciding whether to fight or cooperate, companies can use real options analysis to better quantify the value of each contingency, including the value of the options that would be lost or gained depending on what competitive course is chosen. What this all adds up to is a portfolio of corporate real options, each with a value that will change along with the company’s developing markets. Those who manage that portfolio most effectively will be in the best position to realize their company’s growth potential. Reprinted with permission of The Wall Street Journal, Copyright © 2007 Dow Jones & Company, Inc. Publication date: September 15, 2007.
The Strategy Challenge
15
discusses the need for strategic plans to be flexible and adaptable in a changing environment. Since strategic decisions have long-term consequences, one should look not only at today’s advantages or drawbacks but also at the long-term consequences and value of such decisions. The trade-off between the benefits of commitment (as part of a consistent strategy over time) and remaining flexible and adaptive to changing circumstances calls for an integrative approach weighing the merits of flexibility against commitment. 1.3 Two Complementary Perspectives on Strategy Two approaches to strategy are of particular interest as they provide insights that help management deal with the flexibility or commitment trade-off: corporate finance and game theory. These disciplines are generally considered separate but are in fact complementary. We discuss each one next. 1.3.1
Corporate Finance and Strategy
At first sight the link between corporate finance and strategy may not be that clear. Within corporations, finance is in charge of raising firm resources, while the strategy department is concerned with how to allocate these resources strategically. The two departments deal, however, with two sides of the same coin. Financial managers are concerned with how to finance a project at a reasonable cost. They are aware that resource providers (e.g., shareholders or banks) will carefully scrutinize what the firm plans to do with the resources they are asked to provide, carefully assessing the firm’s strategic plans and the quality of its management. The formed opinion of the resource providers will influence the cost of the resources the firm has access to. A good financial manager cannot therefore ignore the firm’s strategy. Understanding and communicating the firm’s strategy should be one of her primary tasks. Following a finance theory approach, the objective of the firm is to maximize the wealth (utility) of shareholders. According to the Fisher separation theorem, this objective is achieved when maximizing the firm’s market value. A fundamental question in corporate finance is how to attain this objective. As part of corporate finance, capital budgeting considers this problem from an investment perspective, being concerned with the optimal allocation of scarce resources among alternative
16
Chapter 1
projects.4 A key issue is how to address the intertemporal trade-off faced by a firm between paying more dividends or cash distributions now and investing in growth projects meant to generate future cash flows. The established criterion in capital budgeting is the discounted cashflow (DCF) or net present value (NPV) method. The approach involves a relatively easy-to-understand logic and methodology that consists in assessing the current value of a project based on the expected future cash flows it will generate, net of the related costs. Management estimates the stream of future expected cash flows over the project’s life and discounts them back to the present using a risk-adjusted discount rate, obtaining the project’s present value V . It then subtracts the (present value of) investment outlays, I , obtaining the current (t = 0) net present value:5 NPV = V − I .
(1.1)
Alternatively, the present value represents the discounted sum of economic profits.6 The economic profit in a given period represents the firm’s total revenue earned in that period minus all relevant opportunity costs, including the cost of capital. Following the DCF or NPV paradigm, the firm creates shareholder value by following the NPV rule, prescribing to immediately undertake projects with positive NPV, meaning NPV > 0 or V > I . In the absence of managerial flexibility, net present value is the main valuation measure consistent with the firm’s objective to maximize shareholders’ wealth.7 Other valuation measures, such as payback period, accounting rate of return, or internal rate of return are considered inferior to NPV and sometimes even inconsistent. The above finance theory often appears rather technical and not so relevant for strategic management practice. Already in Myers (1984), a 4. Corporate finance provides a useful frame to help managers make investment and financing decisions. Two subfields of corporate finance are particularly relevant for corporate managers: capital budgeting, or how to make investment decisions, and financing, or how to finance projects at the lowest cost available. It is commonly agreed that real investments are more important for creating shareholder value than financial engineering. 5. Consider a project generating over its lifetime (T years) expected cash inflows E [ Rt ] in each future year t. Launching the project is costly, involving expected cash outflows t t E [Ct ]. Let V ≡ ∑Tt =0 E [Rt ] (1 + k ) and I ≡ ∑Tt =0 E [Ct ] (1 + k ) denote the present value of the stream of cash inflows and outflows, respectively. k denotes the appropriate riskadjusted discount rate. The necessary cash outflow I might be a single investment outlay incurred at the outset or the present value of a series of outflows. 6. The economic value added (EVA) approach is based on this notion. 7. Throughout the book, we ignore agency problems inside a firm that may invalidate the NPV rule. Myers (1977) discusses the problem of “underinvestment.” Managers acting in the shareholders’ interest may reject projects with positive NPV when the firm is close to bankruptcy since investing in these projects would only benefit debt-holders.
The Strategy Challenge
17
gap between finance and strategy was identified. Myers offers three main explanations for this gap: NPV is often mistakenly applied Firms in practice often pursue financial objectives that are inconsistent with basic financial theory. They may focus on short-term results rather than long-term value creation. For instance, firms may worry about the impact of their strategic decisions on today’s P&L and on today’s balance sheet.8 Financial theory in fact stresses the importance of taking a long-term perspective to enhancing firm value over short-term creative accounting.9 The balance sheet or income statement are accounting instruments presenting snapshots of the moment or period and do not necessarily mirror real long-term value creation. Another pitfall is that some managers may pursue corporate diversification to reduce total risk for their own benefit.10 In addition managers often treat available divisional resources as being limited. This internally imposed constraint is in sharp contrast with the basic finance assumption that firms have ready access to capital markets at the prevailing cost of capital. Even if acquiring new financial resources may be more costly, the project should be adopted if the project brings more value than it costs to undertake it. •
Finance and strategy mind-sets differ They represent two cultures looking at the same problem. In perfect competition the firm presumably makes no excess economic profit. Strategists are thus looking for deviations from perfect competition to generate excess profits. Such deviations result from distinctive sustainable competitive advantages. Given the linkage between competitive advantage and excess economic profits, strategists often find it superfluous to determine the net present value (as the discounted sum of economic profits) once they have identified the source of competitive advantages. •
NPV has limited applicability The DCF approach involves the estimation of a risk-adjusted discount rate, a forecast of expected cash flows, and an assessment of potential side effects (e.g., erosion or synergies between projects) or time-series links between projects. The last aspect is most difficult to handle with traditional techniques because
•
8. Other common mistakes include the inconsistent treatment of inflation (deflated cash flows discounted back at a discount rate assuming inflation) and unrealistic hurdle rates (use of discount rates that take into account both systematic and diversifiable risk). 9. Short-term orientation is allegedly rampant in countries relying heavily on the capital markets. 10. Risk reduction through portfolio diversification had better be undertaken by investors directly in the capital markets; corporate diversification undertaken by managers is a less efficient means to diversify risk.
18
Chapter 1
today’s investment decisions may constrain or open up new future opportunities. NPV has other drawbacks. First, the NPV paradigm views investment opportunities as now-or-never decisions under passive management. This precludes the possibility to adjust future decisions to unexpected future developments in industry cycles, demand, or prices. Firms need to position themselves to capitalize on opportunities as they emerge while limiting the damage arising from adverse circumstances. If market developments deviate significantly from the expected future scenario, managers can generally revise their future decisions to protect themselves from adverse downward movements or tap on favorable developments and further growth potential. Applying the NPV rule strictly is ill-advised when managers can adjust their planned investment programs or delay and stage their investment decisions. Managers following the prescriptions offered by NPV may find themselves locked into decisions that are flawed when something outside their control does not go as planned. Second, NPV typically assumes a constant discount rate for each future time and state scenario regardless of whether the situation is favorable. Table 1.1 summarizes situations where NPV might give a good approximation of reality and when it might be misleading. Finally, NPV typically overlooks the consequences of competitive actions. Strategy is in need of a quantitative tool that allows for dynamic consideration of changing circumstances. Academics have attempted early on to use alternative approaches to overcome the problems inherent in NPV, particularly to deal with uncertainty and the dynamic nature of investment decision-making. Such methods include sensitivity analysis, Table 1.1 Use of NPV for financial and corporate real assets
Appropriate
Inappropriate
Financial assets
Corporate real assets
Valuation of bonds, preferred stocks, and fixed-income securities Valuation of relatively safe stocks paying regular dividends
Valuation of flows from financial leases
Valuation of companies with significant growth opportunities Valuation of call and put options
Source: Myers (1984, p. 135).
Valuation of “cash cows” Valuation of projects with substantial growth opportunities Valuation of R&D projects
The Strategy Challenge
19
simulation, and decision-tree analysis. Each has had, however, known drawbacks. Sensitivity analysis considers each variable in isolation, thereby ignoring correlations among them. Simulation (e.g., Monte Carlo) faces the same risk-adjustment (discount rate) problem as NPV and generally requires additional adjustment to handle certain recursive problems (e.g., American options) because it is a forward-looking process. Sensitivity analysis and standard simulation are static approaches in that they assume that management is precommitted to a previously agreedupon course of action. In real life this hardly holds. Managers have valuable flexibility and can adapt to the actual market developments once uncertainty gets resolved. They may, for example, abandon a onceundertaken project if the prospects prove gloomy. Managers may also have other options to alter project features in view of the actual market development. Decision-tree analysis (DTA) can be seen as a refined version of NPV aimed to take into consideration the dynamic nature and across-time linkages of decision-making. DTA attributes probabilities to different states of the world and determines in each case the strategy management should optimally formulate (e.g., increase the production scale, switch off the plant, exit the market). In this respect DTA considers the options management has and provides better insights on the dynamic structure of the problem. Trigeorgis and Mason (1987) point out that DTA fails, however, to be economically sound. The discount rate might not be constant over time or across states as typically assumed. Determining the real probabilities of occurrence of each state is often quite involved. Real options analysis (ROA) is an enhanced version of decision-tree analysis that provides improvement in terms of risk-adjustment and determination of probabilities.11 This enhancement is the result of using insights from option-pricing theory.12 Just as stock options give the holder the right, but not the obligation, to buy or sell shares at a given price at some time in the future, real options gives executives the right, but not the obligation, to pursue certain business initiatives. ROA is operationally similar to DTA, with the key difference that the probabilities are riskadjusted, which allows the use of the risk-free discount rate. Real options 11. Several corporate-finance textbooks subsume DTA into real options analysis. We disagree. Real options is the application of option-pricing theory (contingent claims analysis) and risk-neutral pricing to real investment situations (Myers 1977). 12. An alternative to NPV for risk-adjusting risky future cash flows is to consider the certainty equivalents of the uncertain future cash flows and discount them at the risk-free rate. This alternative approach for risk adjustment is a cornerstone of risk-neutral pricing and real options analysis.
20
Chapter 1
analysis is an innovative capital-budgeting tool suitable for the analysis of dynamic decision making under exogenous uncertainty. It enables quantifying strategic considerations that justify sometimes undertaking projects with negative (static) net present value or delaying projects with positive NPV. Box 1.5 highlights the challenges managers face under uncertainty, the inability of NPV to cope with them, and the usefulness of real options in practice. 1.3.2
Game Theory and Strategy
Corporate life would be rather comfortable if a single firm were the only one operating in the marketplace. As a monopolist the firm could Box 1.5 Uncertainty, NPV, and real options in practice
Getting Real: Want to Take More Uncertainty out of Capital Investment Decisions? Try Real Options S. L. Mintz, CFO Magazine “The Edsel is here to stay.” That’s what Ford Motor Co. chairman Henry Ford II told Ford dealers in 1957. “There is no reason why anyone would want a computer in their home.” Thus intoned Digital Equipment Corp. founder Kenneth Olsen in 1977. Even for business leaders with vision, the future is difficult to predict. So where does that leave less-than-legendary executives come budget-planning season? Stuck, largely, with the same venerable tools that guided their predecessors and their predecessors: net present value and gut instinct. Short of denigrating tools that account for many great successes (along with memorable flubs), many executives are wondering if that’s all there is. “There is definitely room for improvement,” concedes Rens Buchwaldt, CFO of Bell & Howell Publishing Services, in Cleveland. Large capitalinvestment decisions—whether it’s launching a new automobile, or building a chip-fabrication plant, or installing an ERP system, or making any number of other very pricey investments—hurl companies toward uncertain outcomes. Huge sums are at risk, in a competitive climate that demands ever-faster decisions. Is there a better way to evaluate capital investments? A growing and vocal cadre of academics, consultants, and CFOs say there is one: real options. Fans insist that real options analysis extends quantitative rigor beyond discount rates and expected cash flows. “Everybody knew there was some kind of embedded value” in strategic options, says an oil industry finance
The Strategy Challenge
Box 1.5 (continued)
executive. Real options analysis, he says, brings that embedded value to light. By quantifying the fuzzy realm of strategic judgment, where leaps of faith govern decisions, real options analysis fosters the union of finance and strategy. “It’s a way to be a little more precise about intuitive feelings,” says Tom Unterman, CFO of $3 billion Times Mirror Co., the Los Angeles based news and information company. A real options analysis recently bolstered the company’s decision to back away from an acquisition, says Unterman, and wider use of the approach is foreseeable. “We are quite actively looking for ways to apply it,” he says. Casting investment opportunities as real options increased both the top and bottom lines at Cadence Design Systems Inc., a San Jose, California, based provider of electronic design products and services. “We have closed a number of transactions that we would not have closed before,” CEO Ray Bingham declares . . .. The Value of Flexibility Unlike net present value measurements, real options analysis recognizes the flexibility inherent in most capital projects—and the value of that flexibility. To executives familiar with stock options, real options should look familiar. A stock option captures the value of an investor’s opportunity to purchase stock at a later date at a set price. Similarly a real option captures the value of a company’s opportunity to start, expand, constrain, defer, or scrap a capital investment depending on the investment’s prospects. When the outcome of an investment is least certain, real options analysis has the highest value. As time goes by and prospects for an underlying investment become clearer, the value of an option adjusts. Sweep away the rocket science, and real options analysis presents a more realistic view of an uncertain world beset by constant shifts in prices, interest rates, consumer tastes, and technology. To focus strictly on numerical value misses the depth and complexity of real options discipline, observes Nalin Kulatilaka, a professor of finance at Boston University School of Management. Kulatilaka is an evangelist for a methodology that obliges managers to weigh equally all imaginable alternatives, good and bad. Real options analysis liberates managers from notions of accountability that mete out blame when plans don’t go as expected. That’s not a healthy environment for workers or companies that need to be nimble all the time, if not right all the time. “The best decision may lead to a bad outcome,” says Soussan Faiz, manager of global valuation services at oil giant Texaco Inc. “If you are judged on a bad outcome, guess what? People will say,
21
22
Chapter 1
Box 1.5 (continued)
‘Why go through that?’” To succeed today, companies must create new options. But unless managers are rewarded for creating them, Faiz warns, “it ain’t gonna happen.” Certainty Is a Narrow Path By taking uncertainty into account, real options analysis fosters a more dynamic view of the world than net present value does. Net present value ultimately boils down to one of two decisions: go or no-go. When the net present value of expected cash flows is positive, companies usually proceed. As a practical consequence managers concentrate on prospects for favorable outcomes. Prospects for unfavorable outcomes get short shrift. In this analysis certainty enjoys a premium—and that’s a narrow path. Even without gaming the numbers to justify projects, this upside bias invites unpleasant surprises. “Unfortunately, discounted cash flow collapses to a single path,” says Texaco’s Faiz. Management and measurement are intertwined, she explains, yet companies manage with an eye to options, but measure performance as if options don’t exist. In the oil business, oil prices don’t remain low for the life of a project; they bounce back. “The likelihood of prices being low for the rest of the project is zero or nearly zero,” says Faiz. But even if prices do remain stagnant, defying the odds, managers don’t snooze the whole time. They wake up and react. Net present value, however, treats investments as if outcomes are cast in stone. This, needless to say, is not realistic. “Net present value makes a lot of heroic assumptions,” warns Tom Copeland, chief corporate finance officer of Monitor, a strategy consultancy in Cambridge, Massachusetts. Typically a multiyear project is plotted along a single trajectory worth pursuing only if the net present value exceeds zero or some hurdle rate. This type of reasoning may satisfy requirements for a midterm exam, says Copeland, but situations in the real world change constantly as new information surfaces. Most managers realize that flexibility ought to be included in valuations, Copeland says. “The bridge they have to cross is understanding the methodology to capture the value of flexibility.” Out of the Ivory Tower Experts have touted the merits of real options for at least a decade, but the sophisticated mathematics required to explain them has penned up those merits in ivory towers. That’s changing, as proponents tout the virtues of real options as a mind-set for decision-making . . . “The kinds of businesses companies go into today are difficult to go into with NPV,” says John Vaughan, vice president for business development
The Strategy Challenge
23
Box 1.5 (continued)
at M/A-COM, the Lowell, Massachusetts, based wireless products group of AMP Inc . . .. Net present value would have derailed this project long ago, Vaughan insists. “It would have been difficult to sell this business case, because of the high level of uncertainty,” he says. Real options analysis assembles diverse risks in a coherent fashion, Vaughan says, layer upon layer, like a papier-mâché creation. “It very much mimics the venture capitalist approach,” he says, “by timing expenditures to the maturity of the opportunity.” Handle with Care Real options “add richness and perspective I can’t get elsewhere,” says the oil industry executive. But like any metric that relies on judgment, he warns, real options must be used carefully. They are not tamper-proof. “Given enough volatility and time,” he says, “I can make an option a very big number.” Without solid, accurate measures of volatility, real options can lead companies astray. For evaluating an offshore oil lease, look at the history of oil-futures prices; for a petrochemical plant, look at historical futures and options contracts on margins . . . “I don’t think the value of great judgment or intuition is any less in using a more sophisticated model,” Bingham says. To the extent that real options analysis sheds more light on uncertainty, in his view, it provides a critical link between strategy and finance. Says Bingham: “Getting hold of real options will make a CFO more and more relevant and a valuable part of leadership.” In an uncertain world, that’s the sort of vision CFOs rely on. Reprinted with permission from CFO Magazine, website www.cfo.com © CFO Publishing LLC. Publication date: November 1999.
sometimes make wrong decisions with limited adverse consequences. In contrast, when several firms are active in the market, managers are under constant competitive pressure to make the right decisions all the time. Otherwise, the firm might go belly-up. In perfect competition the decisions of a single firm do not have a significant impact on others, and strategic interactions are again inconsequential. In reality, however, industries are rarely either purely monopolistic or perfectly competitive. In the real marketplace that is closer to oligopoly, firms typically respond to their rivals’ actions. This calls for an appropriate methodology, namely game theory.
24
Chapter 1
Over the last half century game theory has developed into a rigorous framework for assessing strategic alternatives.13 It helps managers formulate the right strategies and make the right decisions under competition. A recent article in CFO magazine epitomizes a renewed interest by companies in using game theory to aid decision-making (see box 1.6). The origins of game theory trace back to the 1900s when mathematicians got interested in studying various interactive games, such as chess and poker. The first comprehensive formulation of the concept of optimal Box 1.6 Game theory in business practice
More Companies Are Using Game Theory to Aid Decision-Making: How Well Does It Work in the Real World? Alan Rappeport, CFO Magazine When Microsoft announced its intention to acquire Yahoo last February, the software giant knew the struggling search firm would not come easily into the fold. But Microsoft had anticipated the eventual minuet of offer and counteroffer five months before its announcement, thanks to the powers of game theory. A mathematical method of analyzing game-playing strategies, game theory is catching on with corporate planners, enabling them to test their moves against the possible responses of their competitors. Its origins trace as far back as The Art of War, the unlikely management best seller penned 2,500 years ago by the Chinese general Sun Tzu. Mathematicians John von Neumann and Oskar Morgenstern adapted the method for economics in the 1940s, and game theory entered the academic mainstream in the 1970s, when economists like Thomas Schelling and Robert Aumann used it to study adverse selection and problems of asymmetric information. (Schelling and Aumann won Nobel Prizes in 2005 for their work.) Game theory can take many forms, but most companies use a simplified version that focuses executives on the mind-set of the competition. “The formal stuff quickly becomes very technical and less useful,” says Louis Thomas, a professor at the Wharton School of Business who teaches game theory. “It’s a matter of peeling it back to its bare essentials.” One popular way to teach the theory hinges on a situation called the “prisoner’s 13. Game theory is concerned with the actions of decision makers conscious that their actions affect those of rivals and that the actions of competitors, in turn, impact their own decisions. When many players can disregard strategic interactions as being inconsequential (perfect competition) or when a firm can reasonably ignore other parties’ actions (monopoly), standard optimization techniques suffice. Under imperfect competition such as in oligopoly, a limited number of firms with conflicting interests interact such that the actions of each can materially influence firm individual profits and values.
The Strategy Challenge
Box 1.6 (continued)
dilemma,” where the fate of two detainees depends on whether each snitches or stays silent about an alleged crime. Many companies are reluctant to talk about the specifics of how they use game theory, or even to admit whether they use it at all. But oil giant Chevron makes no bones about it. “Game theory is our secret strategic weapon,” says Frank Koch, a Chevron decision analyst. Koch has publicly discussed Chevron’s use of game theory to predict how foreign governments and competitors will react when the company embarks on international projects. “It reveals the win-win and gives you the ability to more easily play out where things might lead,” he says. Enter the Matrix Microsoft’s interest in game theory was piqued by the disclosure that IBM was using the method to better understand the motivations of its competitors—including Microsoft—when Linux, the open-source computer operating system, began to catch on. (Consultants note that companies often bone up on game theory when they find out that competitors are already using it.) For its Yahoo bid, Microsoft hired Open Options, a consultancy, to model the merger and plot a possible course for the transaction. Yahoo’s trepidation became clear from the outset. “We knew that they would not be particularly interested in the acquisition,” says Ken Headrick, product and marketing director of Microsoft’s Canadian online division, MSN. And indeed they weren’t; the bid ultimately failed and a subsequent partial acquisition offer was abandoned in June. Open Options wouldn’t disclose specifics of its work for Microsoft, but in client workshops it asks attendees to answer detailed questions about their goals for a project—for example, “Should we enter this market?” “Will we need to eat costs to establish market share?” “Will a price war ensue?” Then assumptions about the motives of other players, such as competitors and government regulators, are ranked and different scenarios developed. The goals of all players are given numerical values and charted on a matrix. The exercise is intended to show that there are more outcomes to a situation than most minds can comprehend, and to get managers thinking about competition and customers differently. “If you have four or five players, with four actions each might or might not take, that could lead to a million outcomes,” comments Tom Mitchell, CEO of Open Options. “And that’s a simple situation.” To simplify complex playing fields, Open Options uses algorithms to model what action a company should take—considering the likely actions of others—to attain its goals. The result replicates the so-called Nash
25
26
Chapter 1
Box 1.6 (continued)
equilibrium, first proposed by John Forbes Nash, the Nobel Prize winning mathematician portrayed in the movie A Beautiful Mind. In this optimal state, the theory goes, a player no longer has an incentive to change his position. As a tool, game theory can be useful in many areas of finance, particularly when decisions require both economic and strategic considerations. “CFOs welcome this because it takes into account financial inputs and blends them with nonfinancial inputs,” says Mitchell. Rational to a Fault? Some experts, however, question game theory’s usefulness in the real world. They say the theory is at odds with human nature because it assumes that all participants in a game will behave rationally. But as research in behavioral finance and economics has shown, common psychological biases can easily produce irrational decisions. Similarly John Horn, a consultant at McKinsey, argues that game theory gives people too much credit. “Game theory assumes rationally maximizing competitors who understand everything that you’re doing and what they can do,” says Horn. “That’s not how people actually behave.” (Activist investor Carl Icahn said Yahoo’s board “acted irrationally” in rejecting Microsoft’s bid.) McKinsey’s latest survey on competitive behavior found that companies tend to neglect upcoming moves by competitors, relying passively on sources such as the news and annual reports. And when they learn of new threats, they tend to react in the most obvious way, focusing on near-term metrics such as earnings and market share. Moreover finance executives have their own sets of metrics, and when favored indicators such as net present value clash with game theory models, choices become more complicated. “Sometimes [game theory] tells you things you don’t like,” says Koch. Game theory is still finding its place as a tool for companies, and its ultimate usefulness may depend on how quickly it moves from novelty to accepted practice. Practice in fact may be key. McKinsey takes that to heart with its “war game” scenarios, in which a company’s top managers play the roles of different parties in a simulation. In effect this boils game theory down to the schoolyard lesson that perfection comes through repetition. “Discipline is not a dirty word,” as basketball coach Pat Riley once said. Game theory is one way that companies can assess their options with more discipline. Reprinted with permission from CFO Magazine, website www.cfo.com © CFO Publishing LLC. Publication date: July 15, 2008.
The Strategy Challenge
27
strategies in a multiple-player setup came with The Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern (1944). More critical advancements were made in the early 1950s when John F. Nash Jr. provided a broad mathematical basis for the study of equilibria in strategic conflict situations (Nash 1950a, b, 1951).14 More recently game theory has been applied in many fields, including political science, international relations, military strategy, law, sociology, psychology, and biology. Game theory has revolutionized microeconomics and given a strong analytical basis for studying real market structures. As firm competitiveness involves interactions among many players (firms, suppliers, buyers, etc.), it also brought appealing insights into strategic management. Box 1.7 provides an overview of the basics of game theory by Avinash Dixit. An interview with Professor Dixit concerning the interconnection between real options and game theory and his pedagogical approach is given in box 1.8. To perform strategic analysis, one needs to reduce a complex multiplayer problem into a simpler analytical structure that captures the essence of the conflict situation. As discussed later, conducting such an analysis involves a clear depiction of the “rules of the game,” namely (1) identifying the players, (2) describing their available alternative choices, (3) specifying the information structure of the game, (4) determining the payoff values attached to each possible strategy choice, and (5) specifying the order or sequence of the play.15 From a specified game structure, one may derive useful predictions on how rivals are likely to react (equilibrium strategies) in a given environment. A key question commonly arises: how should managers view these models? Should they interpret them in a literal or in a metaphorical sense? There is no clear-cut answer, but the metaphorical interpretation is generally accepted as more appropriate. One of the underlying premises of standard game theory is the presumed rationality of economic agents.16 This assumption is not always consistent with real-world behavioral phenomena, so excessive mathematical rigor may limit the 14. Before John F. Nash’s work, the focus of game theory was mostly on zero-sum games. Nash’s (1950b) equilibrium concept applies to a large set of problems beyond zero-sum games. Myerson (1999) provides a comprehensive analysis of how the Nash equilibrium concept shaped economic theory. 15. The order of play may affect both the possible actions players can select from and the information they possess at the time they make their decisions. 16. Defining rationality and optimality in a given strategic setting is one of the core objectives of game theory. This has an impact on the choice of the game-theoretic solution concept. Nash equilibrium makes behavioral assumptions beyond common knowledge of rationality.
28
Chapter 1
Box 1.7 Overview of game theory basics
Avinash K. Dixit, John J. K. Sherrerd ’52 University Professor of Economics, Princeton University Game theory studies interactive decision-making, where the outcome for each participant or “player” depends on the actions of all. If you are a player in such a game, when choosing your course of action or “strategy” you must take into account the choices of others. But in thinking about their choices, you must recognize that they are thinking about yours, and in turn trying to take into account your thinking about their thinking, and so on. It would seem that such thinking about thinking must be so complex and subtle that its successful practice must remain an arcane art. Indeed some aspects such as figuring out the true motives of rivals and recognizing complex patterns do often resist logical analysis. But many aspects of strategy can be studied and systematized into a science—game theory. The Nash Equilibrium The theory constructs a notion of “equilibrium” to which the complex chain of thinking about thinking could converge. Then the strategies of all players would be mutually consistent in the sense that each would be choosing his or her best response to the choices of the others. For such a theory to be useful, the equilibrium it posits should exist. Nash used novel mathematical techniques to prove the existence of equilibrium in a very general class of games. This paved the way for applications. Biologists have even used the notion of Nash equilibrium to formulate the idea of evolutionary stability. Here are a few examples to convey some ideas of game theory and the breadth of its scope. The Prisoner’s Dilemma In Joseph Heller’s novel Catch-22, allied victory in World War II is a forgone conclusion, and Yossarian does not want to be among the last ones to die. His commanding officer points out, “But suppose everyone on our side felt that way?” Yossarian replies, “Then I’d certainly be a dammed fool to feel any other way, wouldn’t I?” Every general reader has heard of the prisoner’s dilemma. The police interrogate two suspects separately, and suggest to each that he or she should fink on the other and turn state’s evidence. “If the other does not fink, then you can cut a good deal for yourself by giving evidence against the other: if the other finks and you hold out, the court will treat you especially harshly. Thus no matter what the other does, it is better for you to fink than not to fink—finking is your uniformly best or ‘dominant’ strategy.” This is the case whether the two are actually guilty, as in some
The Strategy Challenge
Box 1.7 (continued)
episodes of NYPD Blue, or innocent, as in the firm L.A. Confidential. Of course, when both fink, they both fare worse than they would have if both had held out; but that outcome, though jointly desirable for them, collapses in the face of their separate temptations to fink. Yossarian’s dilemma is just a multi-person version of this. His death is not going to make any significant difference to the prospects of victory, and he is personally better off alive than dead. So avoiding death is his dominant strategy. John Nash played an important role in interpreting the first experimental study of the prisoner’s dilemma, which was conducted at the Rand Corporation in 1950. Real-World Dilemmas Once you recognize the general idea, you will see such dilemmas everywhere. Competing stores who undercut each other’s prices when both would have done better if both had kept their prices high are victims of the dilemma. (But in this instance consumers benefit from the lower prices when sellers fink on each other.) The same concept explains why it is difficult to raise voluntary contributions, or to get people to volunteer enough time for worthwhile public causes. How might such dilemmas be resolved? If the relationship of the player is repeated over a long time horizon, then the prospect of future cooperation may keep them from finking; this is the well-known tit-for-tat strategy. A “large” player who suffers disproportionately more from complete finking may act cooperatively even when the small is finking. Thus Saudi Arabia acts as a swing producer in OPEC, cutting its output to keep prices high when others produce more, and the United States bears a disproportionate share of the costs of its military alliances. Finally, if the group as a whole will do better in its external relations if it enjoys internal cooperation, then the process of biological or social selection may generate instincts or social norms that support cooperation and punish cheating. The innate sense of fairness and justice that is observed among human subjects in many laboratory experiments on game theory may have such an origin. Mixing Moves In football, when an offense faces a third down with a yard to go, a run up the middle is the usual or “percentage” play. But an occasional long pass in such a situation is important to keep the defense honest. Similarly a penalty kicker in soccer who kicks exclusively to the goalie’s right, or a server in tennis who goes exclusively to the receiver’s forehand, will fare poorly because the opponent will anticipate and counter the action. In such situations it is essential to mix one’s moves randomly so that on any one occasion the action is unpredictable.
29
30
Chapter 1
Box 1.7 (continued)
Mixing is most important in games where the players’ interests are strictly opposed, and this happens most frequently in sports. Indeed recent empirical studies of serving in tennis grand slam finals, and penalty kicks in European soccer leagues, have found the behavior consistent with the theory. Commitments Greater freedom of action seems obviously desirable. But in games of bargaining, that need not be true because freedom to act can simply become freedom to concede to the other’s demands. Committing yourself to a firm final offer leaves the other party the last chance to avoid a mutually disastrous breakdown, and this can get you a better deal. But a mere verbal declaration of firmness may not be credible. Devising actions to make one’s commitment credible is one of the finer acts in the realm of strategic games. Members of a labor union send their leaders into wagebargaining with firm instructions or mandates that tie their hands, thereby making it credible that they will not accept a lower offer. The executive branch of the US government engaged in international negotiations on trade or related matters can credibly take a firm stance by pointing out that the Congress would not ratify anything less. And a child is more likely to get the sweet or toy it wants if it is crying too loudly to hear your reasoned explanations of why it should not have it. Thomas Schelling pioneered the study of credible commitments, and other more complex “strategic moves” like threats and promises. This has found many applications in diplomacy and war, which, as military strategist Karl von Clausewitz told us long ago, are two sides of the same strategic coin. Information and Incentives Suppose that you have just graduated with a major in computer science and have an idea for a totally new “killer app” that will integrate PCs, call phones, and TV sets to create a new medium. The profit potential is immense. You go to venture capitalists for finance to develop and market your idea. How do they know that the potential is as high as you claim it to be? The idea is too new for them to judge it independently. You have no track record, and you might be a complete charlatan who will use the money to live high for a few years and then disappear. One way for them to test your own belief in your idea is to see how much of your own money you are willing to risk in the project. Anyone can talk a good game; if you are willing to put enough of your money where your mouth is, that is a credible signal of your own true valuation of your idea. This is a game where the players have different information; you know the true potential of your idea much better than does your prospective
The Strategy Challenge
Box 1.7 (continued)
financier. In such games, actions that reveal or conceal information play crucial roles. The field of “information economics” has clarified many previously puzzling features of corporate governance and industrial organization, and has proved equally useful in political science, studies of contract and tort law, and even biology. The award of the Nobel Memorial Prize in 2001 to its pioneers, George Akerlof, Michael Spence, and Joseph Stiglitz, testifies to its importance. What has enabled information economics to burgeon in the last twenty years is the parallel development of concepts and techniques in game theory. Aligning Interests, Avoiding Enrons A related application in business economics is the design of incentive schemes. Modern corporations are owned by numerous shareholders who do not personally supervise the operations of the companies. How can they make sure that the workers and managers will make the appropriate efforts to maximize shareholder value? They can hire supervisors to watch over workers, and managers to watch over supervisors. But all such monitoring is imperfect: the time on the job is easily monitored, but the quality of effort is very difficult to observe and judge. And there remains the problem of who will watch over the upper-level management. Hence the importance of compensation schemes that align the interests of the workers and managers with those of the shareholders. Game theory and information economics have given us valuable insights into these issues. Of course, we do not have perfect solutions; for example, we are just discovering how top management can manipulate and distort the performance measures to increase their own compensation while hurting shareholders and workers alike. This is a game where shareholders and the government need to find and use better counterstrategies. From Intuition to Prediction While reading these examples, you probably thought that many of the lessons of game theory are obvious. If you have had some experience of playing similar games, you have probably intuited good strategies for them. What game theory does is to unify and systemize such intuitions. Then the general principles extend the intuitions across many related situations, and the calculation of good strategies for new games is simplified. It is no bad thing if an idea seems obvious when it is properly formulated and explained; on the contrary, a science or theory that takes simple ideas and brings out their full power and scope is all the more valuable for that.
31
32
Chapter 1
Box 1.8 Interview with Avinash K. Dixit
1. You have helped establish and popularize both real options and game theory as separate disciplines. How do you see the interconnection or interplay among the two? The real options concept emphasizes the value of flexibility, whereas an irreversible commitment has value in many situations of strategic competition. Analyzing the two together enables us to understand when one prevails over the other, or more generally, the trade-off between the two. This is clearly an important research program. 2. In your teaching of game theory at Princeton you rely a lot on stories, movies, literature, sports, games, and other engaging tools to motivate your students. Can you elaborate on your view or approach? Undergraduate students are rightly skeptical of abstract theory, and demand evidence of its relevance before they will spend their time and effort on studying theory. Game theory is fortunate in having so many compelling and entertaining examples readily available. Using examples to bring out theoretical concepts is similar to the case method used in most business schools. But MBA students are narrowly focused on business and moneymaking. Undergraduates have richer and more varied lives; therefore examples from sports, games, literature, and movies appeal to them. 3. What other current or future areas of research in economic sciences do you find interesting? Connections between economics and other social sciences are enriching them all. Economists are becoming aware of aspects of human behavior
The Strategy Challenge
33
Box 1.8 (continued)
that differ from selfish rationality assumed in most traditional economic theory; sociologists, political scientists, and even psychologists and anthropologists are learning the value of economists’ conceptual framework of choice and equilibrium and of the issues of endogeneity and identification in empirical work. I find this confluence of the social sciences interesting and exciting. I don’t expect complete reintegration of fields that separated more than a century ago; the benefits of specialization remain. But I do expect much closer communication and collaboration that will benefit research in all these fields.
applicability of game theory in certain real-world situations. A metaphorical interpretation of game-theoretic models can nonetheless hold significant value. Game theory can generally be used to deduce principles and insights from simplified models of reality. Simpler models are generally more prescriptive. Oftentimes, when game theory is applied in more complex situations, it results in no outcome or in multiple equilibria. In such cases complex modeling may lose its predictive ability.17 One objective of microeconomic modeling is to simulate qualitatively the type of environment being studied. Useful insights into an issue or behavior of practical relevance can be then deduced. A simple game-theoretic framework has several advantages for strategic management.18 First, it provides an audit track that enables researchers and practitioners to go back to basic premises. Management should formulate the basic assumptions explicitly and consider whether they are of practical relevance. Second, it offers a methodology that is conducive to rigorous analysis and can help derive novel insights, which might be counterintuitive in some cases. Such insights may hardly stem from a “boxes-and-arrows” conceptual framework.19 Finally, it helps bring discipline by enforcing a common language that enables researchers and managers to compare results and refine earlier models.20 In view of such potential extensions, game theory holds out considerable promise for 17. See Grant (2005, p. 111). 18. This discussion follows Saloner (1991, pp. 120–25, 127). 19. Saloner (1991) includes Porter’s (1980) five-forces framework among these conceptual frameworks for strategic management. A game-theoretic refinement of Porter’s (1980) framework is offered by Brandenburg and Nalebuff (1996). 20. Some microeconomic models are quite tractable for studying new problems. Cournot and Bertrand duopoly models discussed in chapter 3 form the basis for many industrial organization setups which are often much more complex. For instance, the commitment theory addressed in chapter 4 can be understood in light of these two pillar models.
34
Chapter 1
studying human interactions. This explains the success of game theory particularly in economics and strategic management. The following three fields have greatly benefited from game-theoretic modeling:21 Industrial organization This field focuses on strategic interactions arising in the external environment of the firm, addressing issues such as competitive interactions in oligopolies, first- and second-mover advantages, firm entry and exit decisions, strategic commitment, reputation, signaling and information asymmetries among different players in an industry. •
Organization theory This field focuses on the firm’s internal or organizational aspects such as vertical and horizontal scope and conflicting incentives inside an organization (e.g., optimal compensation schemes).22
•
Interaction between the internal and external environment of the firm This area addresses issues at their interface like optimal incentive schemes in oligopolistic market structures,23 organizational design to achieve competitive advantage, cooperation versus competition in R&D.24 •
A good understanding of the competitive environment will thus enable managers to ascertain the strategic implications of their actions in the marketplace and determine how they should behave. A normative role for the strategic management literature is to provide a broad qualitative understanding of such strategic interactions and give qualitative prescriptions for managerial action.25 Although game theory has witnessed rapid developments since the 1950s, its use for practical strategic management purposes has remained limited so far.26 Nevertheless, some managers already incorporate game-theoretic thinking into their planning. 21. This discussion follows Saloner (1991, pp. 119–20). 22. Theories of the firm attempt to explain why firms exist and operate as they do. They include property-rights theory, incentive-system theory, rent-seeking theory, adaptation theory, and contract theory. 23. Ferschtman and Judd (1987), for example, argue that in case of product market competition, a firm has an incentive to design incentive schemes in a way that would not be optimal for a stand-alone organization. In their model, managers have an incentive to maximize output in a quantity competition setting, which makes the firm better off since the rival interprets the incentive contract as a commitment. This exemplifies the possible use of industrial organization thinking to better the understanding of firms’ organizational design. 24. D’Apremont and Jacquemin (1988) analyze the effect of R&D spillovers on the incentive to cooperate or compete during the R&D stage and the market competition stage. 25. See Saloner (1991, pp. 107–31). 26. In politics, game theory has been used to analyze the 1962 Cuban missile crisis, President Reagan’s 1982 tax cut, and certain public auctions.
The Strategy Challenge
35
1.4 An Integrative Approach to Strategy Both corporate finance and game theory provide useful insights for strategic management. As discussed by Jean Tirole in box 1.9, the interface between finance and game theory enables attaining a better understanding on a number of firm- or market-related issues. Viewed separately, however, these approaches have limited applicability. Integrating these approaches in a consistent manner is at the core of the option games approach. Standard real options analysis overcomes many of the drawbacks of the NPV approach but neglects other aspects. When management assesses its real options, it must determine whether the benefits resulting from the exercise of its options are fully appropriable. Kester (1984) distinguishes two categories of real options depending on whether the benefits are proprietary or shared. If management has an exclusive exercise right, retaining all potential benefits for itself, the investment opportunity is a proprietary option.27 When the firm is not in a position to appropriate all of the project’s benefits for itself but rivals share the same opportunity, it is a shared option.28 In this case, the presence of market contenders introduces strategic externalities (positive or negative) that can significantly affect the value and optimal exercise strategy of the firms’ real options. The value loss resulting from strategic interactions is seen as a competitive value erosion. Standard or naïve real options analysis typically assumes a proprietary or monopolistic mind-set, ignoring such shared options.29 A firm here formulates its investment decisions in isolation, disregarding interactive competition. 27. Rivals’ investment decisions have no material impact on project values or optimal strategies. For instance, a monopolist protected by significant entry barriers faces such a situation. Proprietary options are also encountered when a firm is granted an infinitely lived patent on a product that has no close substitutes or when it has unique know-how of a technological process. 28. Shared options include the opportunity to launch a new product that is unprotected from the entry of close substitutes, or the opportunity to penetrate a newly deregulated market. 29. One reason why strategic interactions among option holders are not typically considered in standard real options analysis is that early on real options were seen as an extension of standard option-pricing theory to real investment situations. In capital markets, except in special cases like valuation of warrants, strategic interactions among option holders rarely affect the asset or the option values. Certain continuous-time real option models attempt to account for market and competitive uncertainty in an exogenous manner, such as through a higher dividend yield or a jump process. These models represent an improvement over standard models developed with a monopolistic mind-set, but fall short of adequately accounting for the endogenous nature of strategic interactions in an oligopolistic setting. Trigeorgis (1991) discusses continuous-time real options models involving strategic uncertainty exogenously.
36
Chapter 1
Box 1.9 Interview with Jean Tirole
1. You have contributed greatly to extending game theory for the analysis of economic problems. What are the merits of this mathematical discipline for economic analysis? Which other social sciences do you believe can benefit from the use of game theory? Game theory aims at describing and predicting behaviors in environments in which actors are interdependent and have potentially conflicting objectives. It deepens our understanding of when the quest for specific goals may lead to inefficiencies and of how players choose actions with an eye on changing other actors’ incentives. As such, game theory applies to all social sciences and beyond. The most obvious applications, besides economics, include political sciences, sociology, law, and psychology. Psychology might look like an outlier as it usually focuses on the individual, but it is not. Experimental evidence confirms the old notion that we “play games with ourselves.” These can be represented as games among successive incarnations of the self. Biologists use game theory to understand mutualism between species, inefficient signals, or fights. Computer scientists also take a keen interest in game theory. Part of the appeal of game theory is that it accommodates diverse objective functions, which enables us to conceptualize the behavior of different actors, from consumers to politicians, from firms to suborganisms. Game theory more and more integrates behavioral approaches. Mainstream game theory focuses on optimal strategies given the strategic interdependences and the actors’ limited information and various constraints. This rational choice approach has served social sciences well by identifying the key strategic features of conflict situations. At the same time, limited cognition and various
The Strategy Challenge
Box 1.9 (continued)
behavioral biases are being increasingly incorporated into our thinking about strategic interactions, extending the reach of game theory beyond purely rational choice. Finally, experimental economists have been testing our equilibrium concepts and behavioral predictions, and empiricists use game theory to put more structure on their estimation strategies. 2. Your work on industrial organization has helped popularize this important discipline and extend its areas of application. Do you think industrial organization will become increasingly more useful for managerial practice and understanding or predicting of market developments? Yes. Game theory and its applications to industrial organization have made their way into business books and have affected managerial practice. For example, concepts developed in industrial organization are used in deliberations on how to design new platforms and get all sides on board. Game theory is taught to MBAs and strategy textbooks now incorporate game-theoretic thinking. Game-theoretic analyses have become a language for antitrust practitioners to conceptualize impacts of behaviors on market outcomes. Empirical work on estimating demand and strategic choices of price and non–price competition also make substantial use of game-theoretic industrial organization. 3. Do you see a connection between industrial organization and corporate finance? In what ways? Can game theory help reshape corporate finance as it has reshaped standard microeconomics? There is indeed a strong connection between industrial organization and finance. I am really happy that your book “cross-breeds” options theory and industrial organization and connects it to business, as this is an area of very fruitful cross-fertilization. Not only do finance and industrial organization share common tools (e.g., economics of incentives, game theory), they also interface in many areas. For example, it is hard to fully understand predation or entry into industries without understanding financial constraints and therefore corporate finance. Conversely, the industrial organization of finance and banking is a hot topic on our research agenda. Game theory has already made its way into various subfields of corporate finance: takeover strategies, liquidity hoarding, expectations of refinancing and bailouts, bank runs, issues of securities under asymmetric information, and conglomerate strategies are just a few examples. Many areas of corporate finance have benefited significantly from importing ideas coming from game theory.
37
38
Chapter 1
Table 1.2 Comparison of main advantages and drawbacks of standard stand-alone approaches Approach
Advantages
Drawbacks
Standard NPV
Easy to use; convincing logic; widely used; easy to communicate
Assumes precommitment to a given plan of action, often treating investment as a one-time decision (“invest now or never”); ignores flexibility to adapt to unexpected market developments or strategic interactions
Real options
Incorporates market uncertainty and managerial flexibility; recognizes that investment decisions can be delayed, staged, or adjusted under certain future contingencies
Typically applied to the valuation of a monopolist or proprietary option; ignores (endogenous) competitive interactions
Game theory
Incorporates competitive reactions endogenously; considers different player payoffs
Typically disregards market uncertainty involving stochastic variables
Game theory has been generally applied to studying strategic interactions in settings involving steady or deterministically changing states, where players could accurately predict the evolution of the external environment. Standard game theory falls short of explaining the firm’s incentive to stay flexible to react to unexpected developments. Under uncertainty this prescription of standard game theory is inadequate.30 The main advantages and drawbacks of each stand-alone approach (standard NPV, standard real options analysis, and game theory) are summarized in table 1.2. Many real-world problems, however, require a simultaneous assessment of both market (exogenous) as well as competitive (endogenous) uncertainty. Stand-alone NPV, real options analysis, and game theory alone fail in providing the necessary tool kit. The NPV paradigm deals with static situations where firms make now-or-never decisions or precommit to a certain plan of action. Real options analysis allows for 30. Different forms of uncertainty are considered in game theory. For instance, some solution concepts (e.g., Bayesian and perfect Bayesian equilibrium) are designed to address problems involving information uncertainty. This form of uncertainty is not equivalent to what we consider here. In stochastic environments, payoffs may be affected by exogenous factors or shocks, whose future values are not known with certainty but follow a known probability law. The appendix of the book provides a discussion of such stochastic processes.
The Strategy Challenge
39
Table 1.3 Classification of decision situations and relevant theories Decision theory (no strategic interaction)
Game theory (strategic interaction)
Net present value (DCF) Chapter 1
Static industrial organization Chapter 3
Deterministic
Resource extraction/ forest economics Chapter 9
Dynamic industrial organization Chapters 4, 11, 12
Stochastic
Real options analysis Chapters 5, 9, appendix
Option games Chapter 6 onward
Static
Dynamic
dynamic decision-making in situations where firms face exogenous stochastic uncertainty.31 Static industrial organization (IO) has limited applicability to situations involving simultaneous games where firms are ignorant of both past and future actions and payoffs.32 Dynamic industrial organization analysis permits a long-term perspective but assumes steady state or a deterministic evolution of the market environment.33 We here discuss an integrated approach employed to help overcome the shortcomings of stand-alone approaches, analyzing key value drivers concurrently. Option games are meant to capture dynamic strategic interactions in stochastic environments. Table 1.3 positions the option games approach within the traditional decision and game-theory paradigms.34 We indicate in which chapters each approach is most relevant in the book. The importance of incorporating options analysis and game theory is confirmed by the number of Nobel Prizes awarded in related fields. A 31. Real options analysis provides many applications for dynamic programming. The term “dynamic programming” was originally used by Bellman (1957) to describe a recursive process for solving dynamic problems. This method can be extended to stochastic environments. Stochastic dynamic programming or stochastic control is discussed by Harrison (1985), Dixit (1993), and Stokey (2008), with applications in economics and finance. 32. Static industrial organization rests on static game theory with the related notion of, for example, Nash or Bayesian Nash equilibria. See Osborne (2004) for an introduction. 33. Fudenberg and Tirole (1986) present a number of dynamic models of oligopoly. This field rests on dynamic game theory. It involves the use of “dynamic” solution concepts such as subgame perfect Nash, perfect Bayesian, or sequential equilibrium. A subfield is differential games that study dynamic strategic interactions in settings where an industry state evolves according to a differential equation. See Dockner et al. (2000) for an introduction to differential games. 34. Option games share some aspects with stochastic timing and differential games.
40
Chapter 1
Table 1.4 Selected Nobel Prizes awarded in Economic Sciences Year
Nobel Prize winner(s)
Noted contribution
2007
L. Hurwicz, E. S. Maskin, R. B. Myerson
For laying the foundations of mechanism design and contract theory
2005
R. J. Aumann, T. C. Schelling
For enhancing our understanding of conflict and cooperation through game theory analysis
2001
G. A. Akerlof, A. M. Spence, J. E. Stiglitz
For analyzing markets with asymmetric information
1997
R. C. Merton, M. S. Scholes
For developing the option pricing method to value derivatives (and thereby real options)
1994
J. C. Harsanyi, J. F. Nash Jr., R. Selten
For their analysis of equilibria in the theory of noncooperative games
1990
H. M. Markowitz, M. H. Miller, W. F. Sharpe
For their pioneering work in the theory of financial economics
1982
G. J. Stigler
For his studies of industrial structures, functioning of markets, and causes and effects of public regulation
1981
J. Tobin
For his analysis of financial markets, expenditure decisions, employment, production, and prices
1978
H. A. Simon
For his research into the decisionmaking process within economic organizations
1975
L. V. Kantorovich, T. C. Koopmans
For their contributions to the theory of optimum allocation of resources
1970
P. A. Samuelson
For developing dynamic economic theory and raising the rigor of analysis in economics
Source: Nobel Prize committee website.
selected list of Nobel Prize awards in economic sciences is shown in table 1.4. Real options analysis is a natural extension of major breakthrough developments in financial economics to real investments. It builds on the seminal works of Paul Samuelson, Robert C. Merton, Fischer Black, and Myron Scholes. Concurrently the analysis of industrial organization has been greatly facilitated by developments in game theory. Von Neumann, Morgenstern, and Nash have made significant early contributions to game theory. Selten, Harsanyi, Schelling, and Aumann also earned Nobel
The Strategy Challenge
41
Prizes for refinements to the theory.35 Option games, being at the intersection of option and game theories, benefited from the cumulative developments in these subfields of economic sciences. Today option games represent a powerful strategic management tool that can guide practical managerial decisions in a competitive context, as discussed by Ferreira, Kar, and Trigeorgis (2009). It enables a more complete quantification of market opportunities while assessing the sensitivity of strategic decisions to exogenous variables (e.g., demand volatility, costs) and competitive interactions. 1.5
Overview and Organization of the Book
The book is organized in three parts. Part I, “Strategy, Games, and Options,” presents the three building blocks or prerequisite fields for the option games approach. Chapter 2, “Strategic Management and Competitive Advantage,” reviews the main strategic management paradigms used to analyze or explain a firm’s performance in creating value for shareholders. We describe industry and competitive analysis and discuss how to create sustainable competitive advantage in an industry utilizing generic competitive strategies. Chapters 3 and 4 on “Market Structure Games” introduce game theory principles and industrial organization concepts providing economic foundations for strategic management. Chapter 3, focusing on “Static Approaches,” discusses benchmark cases where firms interact in one-time situations. Quantity and price competition are discussed in detail. Chapter 4, focusing on “Dynamic Approaches,” supplements the previous analysis by allowing firms to interact in the marketplace over many periods, attempting in the long term to shape the market in their own advantage or collaborating with rivals for mutual benefit. Chapter 5 on “Uncertainty, Flexibility, and Real Options” discusses the strategyformulation challenges facing the firm when the underlying market is uncertain. Motivated by various sources of uncertainty electricity utilities face today, we discuss how real options analysis can be used to analyze such situations, value strategic options, and optimally chose among them. We also briefly discuss discrete-time and continuous-time tools for the pricing of embedded real options. We ignore here the fact 35. Akerlof, Spence, Stiglitz, Hurwicz, Maskin, and Myerson won the Nobel Prize for insightful applications of game theory for the understanding of incentives in social groups (e.g., industrial organization, contract theory).
42
Chapter 1
that many firms may face counteracting business opportunities affected by rival behavior. Part II, “Option Games: Discrete-Time Analysis,” fleshes out in more detail in discrete time the integration of real options with game theory and industrial organization and explains how to capture the flexibility and strategic-interaction aspects of real investment situations. Chapter 6 presents core issues in option games analysis, namely optimal investment timing under uncertainty and competition and the trade-off between commitment and flexibility. We provide a number of examples to illustrate the discrete-time option games approach. Chapter 7, “Option to Invest,” rigorously sets the premise for analyzing option games in discrete time, building upon models developed in chapter 3. Chapter 8, “Innovation Investment in Two-Stage Games,” discusses at length the trade-off between commitment and flexibility in sequential investment settings. The focus, here, is on two-stage competition models where real options analysis tools are combined with industry organization insights. The two-stage analysis provides guidance into how and when strategic investments enhance value creation or are detrimental to the firm. We examine appropriate investment strategy applications in different settings, such as R&D and advertising. Part III, entitled “Option Games: Continuous-Time Models,” extends the analysis of option games by use of continuous-time modeling techniques. Chapter 9, “Investment and Expansion Option: Monopoly,” introduces the methodology employed throughout part III and sets the benchmark case of a monopolist firm. Two categories of options are discussed, the option to invest in a new market and the option to expand an existing market. Chapter 10, “Oligopoly: Simultaneous Investment,” extends the analysis to simultaneous investment oligopoly markets. Chapter 11, “Leadership and Early-Mover Advantage,” discusses the appeal of having a competitive advantage to turn the investment-timing game into one’s own advantage. Chapter 12, “Preemption versus Cooperation in a Duopoly,” deals with preemptive investments and the possibility of tacit collusion among firms, delaying investment until a later date. Chapter 13, “Extensions and Other Applications,” provides a short overview of important contributions on various subjects and other applications discussed in the literature. The appendix that follows discusses the basics of stochastic processes and provides a compendium of tools in stochastic calculus and control for the more analytically minded reader. To smooth out the exposition in the text, part III occasionally refers to this appendix when a derivation is more involved.
The Strategy Challenge
43
Conclusion In this introductory chapter we discussed key changes firms have faced over the past decades. We discussed the development and changes in a challenging business environment and the evolution of strategy, and examined to which extent the two pillar approaches underlying this book, namely game theory and real options analysis, can be rigorous and relevant for analyzing and understanding business strategies. We concluded with the need to combine both into an integrative option games approach. Selected References Grant (2005) discusses the role of strategy in corporate performance, stressing the need for sound strategy formulation based on consistent principles. Myers (1984) discusses the gap between financial theory and its practical implementation in corporate strategy, highlighting the differential insights corporate finance can add to strategy. Saloner (1991) and Rasmussen (2005) discuss the usefulness of game theory for strategic management, emphasizing its prescriptive value in competitive settings involving strategic interactions. Grant, Robert M. 2005. Contemporary Strategy Analysis, 5th ed. Malden, MA: Blackwell. Myers, Stewart C. 1984. Finance theory and financial strategy. Interfaces 14 (1): 126–37. Rasmussen, Eric. 2005. Games and Information: An Introduction to Game Theory. Oxford: Blackwell. Saloner, Garth. 1991. Modeling, game theory, and strategic management. Strategic Management Journal 12 (Winter): 119–36.
I
STRATEGY, GAMES, AND OPTIONS
2
Strategic Management and Competitive Advantage
Managing an enterprise in an uncertain competitive environment is not an easy task. Strategic management attempts to explain why some firms are more successful than others in the marketplace. At the core of strategy is a dilemma between flexibility and commitment. Flexibility to adapt strategy and operations is clearly valuable when the environment changes unexpectedly. An early investment commitment may yet have strategic value because it can influence the behavior of rivals in equilibrium, potentially creating a future competitive advantage for the firm. The flexibility perspective partly draws on the resource-based view of the firm and core-competence arguments: a firm should invest in resources and competencies that give it a distinctive ability to pursue a set of market opportunities. During the 1990s this view became a dominant paradigm in strategic management. It has also helped spark further developments in what is referred to as the “knowledge-based” view of the firm. The commitment view has been firmly anchored in industrial organization. In recent years competitive advantage has become rather temporary because industries and competition within industries change continually. Firms make tremendous efforts to sustain competitive advantage and protect their future growth options from duplication efforts by rivals. Whether competitive advantage can be sustained in the long term partly depends on mechanisms put in place by the firm to renew and protect its resource position and capabilities. In section 2.1 we provide an overview of some of the prevailing strategic management concepts and theories. We discuss in section 2.2 several approaches used in practice that help provide a deeper understanding of a given industry. We then examine, in section 2.3, the sources of competitive advantage and their sustainability as an industry evolves.
48
2.1
Chapter 2
Strategic Management Paradigms
Various paradigms in strategic management approach the underlying sources of firm value creation from distinct viewpoints. Categorized in figure 2.1 are the main strategic management approaches. Many of these managerial perspectives trace their roots to primary economic disciplines (microeconomics, organization theory, finance). Behind many of them lies the notion that competitive advantage is a function of the firm’s position, resources, and capabilities compared to those of its rivals, the opportunities these resources and capabilities create in a dynamic environment, and the firms’ adaptive capability to respond to market changes. It is commonplace to distinguish between approaches with an external perspective from those with an internal firm view. The former consider competitive advantage and value creation through the eyes of an external observer, focusing on external forces, opportunities, and threats in the external environment. The latter focus on internal forces within the firm, viewing value creation from in-house combinations of expertise, resources, and capabilities. These perspectives consider competitive advantage as dependent on unique, firm-specific resources and capabilities that enable the firm to create and exploit advantaged opportunities. Real options and option games lie at their intersection and can bring together these complementary perspectives. Real options are created by internal adaptive capabilities developed over time but may be affected by the actions of external parties. 2.1.1
External View of the Firm
Outside forces, such as firm’s rivals, suppliers, and customers, continually shape the external environment. External approaches view the sources of value creation as lying in market imperfections, synergies, or economies of scale. The industry and competitive analysis framework popularized by Michael Porter (1980) views strategy in terms of industry structure, entry deterrence, and strategic positioning. Key competitive variables include entry and exit barriers, as well as product differentiation and availability of information. Porter proposes to look at rivalry situations among suppliers of a product and analyze the impact of additional forces, such as the threat from substitute products and technology disruption, new market entry, and the bargaining power of suppliers and buyers. He emphasizes actions the firm should take to protect itself from these market forces and threats. Another external approach is that of strategic
Rumelt (1984) Wernerfelt (1984) Collins and Montgomery (1995)
Schelling (1960) Shapiro (1989) Ghemawat (1991) Dixit and Nalebuff (1991)
Dixit and Pindyck (1994) Trigeorgis (1996)
Real options
Dynamic capabilities/ core competencies
Prahalad and Hamel (1990) Teece, Pisano, and Shuen (1997)
Transaction costs
Property rights
Organization theory
Internal view of the firm
Resourcebased view
Agency theory
Strategic conflict
Game theory/ industrial organization
External view of the firm
Porter (1980)
Industry and competitive analysis
Structure conduct performance
Microeconomic theory
Grenadier (2000) Huisman (2001) Smit and Trigeorgis (2004)
Option games
Option pricing
Financial economics
Figure 2.1 Strategic management frameworks Rows 2 and 3 are related: economic theory (row 2) supports notions developed in strategic management (row 3) via formal models.
Representative authors
Strategic management
Economic theory
Broad field
Strategic Management and Competitive Advantage 49
50
Chapter 2
conflict (e.g., Shapiro 1989), which focuses on conflict behavior and views value creation as the result of strategic moves in a competitive environment. Game theory ideas are used to help management understand better the strategic interactions among rivals, predict rivals’ reactions, and determine the optimal competitive strategy. 2.1.2
Internal View of the Firm
The internal view of the firm traces its roots to The Theory of the Growth of the Firm by Edith Penrose (1959). This approach became known subsequently as the resource-based view of the firm in articles by Wernerfelt (1984), Rumelt (1984), Teece (1984), and others.1 Its distinguishing characteristic is that competitive advantage arises from within the firm. A firm becomes profitable not so much because it undertakes strategic investments that may deter entry or raise prices above long-run cost, but rather because it manages to achieve significantly lower costs or obtain markedly higher quality or product performance through internal mechanisms. Excess economic profits stem from imperfect markets for firmspecific intangible assets like distinctive competences, know-how, and capabilities. A more recent variant rests on corporate capabilities to adapt in environments of rapid technological change. The theory of “dynamic capabilities” proposed by Teece, Pisano, and Shuen (1997) views capabilities to adapt in a changing environment as resting on distinctive processes, shaped by the firm’s asset position and the evolutionary path it has adopted or inherited. Box 2.1 discusses the concept and process of strategy and their evolution in a changing and rapidly transformed competitive landscape. 2.2
Industry and Competitive Analysis
A key objective of strategic management is to help decision makers understand what leads to a firm’s success. Strategic management provides both explanation and direction. A useful strategy framework should address the following types of questions: Why are some firms more successful than others? Are there different paths to success? Can some firms be successful by adopting product innovation, and others by enhancing operational efficiency via process innovation? 1. According to Wernerfelt (1984), the resource-based view aims to understand the relationship between profitability and the different ways of managing resources over time. Resources are “those tangible and intangible assets which are tied semi-permanently to the firm” (p. 172).
Strategic Management and Competitive Advantage
Box 2.1 Strategy in a changing competitive environment
Changes in the Competitive Battlefield C. K. Prahalad, Financial Times Many of the concepts used in strategy were developed during the late 1970s and 1980s when underlying competitive conditions evolved within a well-understood model . . .. While the canvas available to today’s strategists is large and new, companies will need to understand global forces, react quickly, and innovate when defining their business models . . .. It is hardly surprising that the conceptual models and administrative processes used by managers often outlast their usefulness. It takes researchers time, after all, to identify new problems and emerging solutions before they can produce theories about them. Then there is the time lag between the development of these theories and their conversion into common business practice. Where management concepts are concerned, this time lag—often a decade—brings with it an interesting conundrum. In an era of rapid and disruptive change in the economic, political, social, regulatory, and technological environment do managers have to discard established and tested analytical tools equally as fast? How can they identify the ongoing relevance of concepts and tools in a changing environment? The Heritage of Strategy Concepts The most prevalent and widely used tools of strategy analysis are: strength weakness, opportunities, and threats (SWOT) analysis, industry structure analysis (five forces), value chain analysis, generic strategies, strategic group analysis, barriers to entry, and others of the genre . . .. The concepts and tools—many of them the staples of economists—were adopted and simplified for the use of managers. The formalization of these concepts was instrumental in pushing strategy development from the realm of “the intuitive genius of the founder or a top manager” to that of logical process. However, most of these concepts were developed during the late 1970s and the decade of the 1980s. During this period, underlying competitive conditions evolved but within a well-understood paradigm. A major competitive disruption during this period, certainly for US and European companies, was the spectacular success of Japanese manufacturing in industries as diverse as steel, consumer electronics, autos, and semiconductors. The sources of competitive advantage, during this decade, accrued to those who could wrest major efficiencies in operations through focus on quality, cycle time, reengineering, and team work. Operational efficiencies, within a relatively stable industry structure paradigm, became the focus. In fact this focus on wresting competitive advantage through operational efficiencies led some managers to believe that strategy was unimportant and management was all about implementation.
51
52
Chapter 2
Box 2.1 (continued)
The Emerging Competitive Landscape The decade of the 1990s has witnessed significant and discontinuous change in the competitive environment and an accelerating global trend to deregulate and privatize. Large and key industries like telecoms, power, water, health care, and financial services are being deregulated. Countries as diverse as India, Russia, Brazil, and China are at various stages of privatizing their public sectors. Technological convergence—such as that between chemical and electronic companies; computing, communications, components, and consumer electronics; food and pharmaceuticals; and cosmetics and pharmaceuticals—is disrupting traditional industry structures . . .. Ecological sensitivities and the emergence of nongovernmental organizations such as the green movement are also new dimensions of the competitive landscape. Are these discontinuities changing the very nature of the industry structure—the relationships between consumers, competitors, collaborators, and investors? Are they challenging the established competitive positions of incumbents and allowing new types of competitors and new bases for competition to emerge? We can identify a long list of discontinuities and examples to illustrate each one of them . . .. We need to acknowledge the signals (weak as they may be) of the emergence of a new competitive landscape where the rules of engagement may not be the same as they were during the decade of the 1980s. Strategists have to make the transition from asking the question: How do I position my company and gain advantage in a known game (a known industry structure)? Increasingly the relevant question is: How do I divine the contours of an evolving and changing industry structure and therefore the rules of engagement in a new and evolving game? Industries represent such a diversity of new, emerging, and evolving games. The rules of engagement are written as companies and managers experiment and adjust their approaches to competition. Strategy in a Discontinuous Competitive Landscape Strategists must start with a new mind-set. Traditional strategic planning processes emphasized resource allocation—which plants, what locations, what products, and sometimes what businesses—within an implicit business model. Disruptive changes challenge the business models. Four transformations will influence the business models and the work of strategists in the decades ahead: The strategic space available to companies will expand Consider, for example, the highly regulated power industry. All utilities once looked alike and their scope of operations was constrained by public utility commissions and government regulators. Because of deregulation, utilities can now determine their own strategic space. Today utilities have
•
Strategic Management and Competitive Advantage
Box 2.1 (continued)
a choice regarding the level of vertical integration: Do I need to be in power generation? Do I need to be in power transmission? Companies can unbundle assets and can also segment their businesses: Should we focus more on industrial or domestic consumers? They can decide their geographical scope: Should I become global, regional, national, or just remain local? And finally, they can change their business portfolio: Should I invest in water, telecoms, gas lines, services? The forces of change—deregulation, the emergence of large developing countries such as India, China, and Brazil as major business opportunities—provide a new playing field. Simultaneously forces of digitalization, the emergence of the Internet, and the convergence of technologies provide untold new opportunities for strategists. The canvas available to the strategist is large and new. One can paint the picture one wants. Business will be global Increasingly the distinction between local and global business will be narrowed. All businesses will have to be locally responsive and all businesses will be subject to the influences and standards of global players. Consider, for example, McDonald’s and Coca-Cola—held up as examples of truly global players unconstrained by local customers and national differences. In India, McDonald’s had to change its recipe to serve lamb (instead of beef) and vegetarian patties (a radical departure from its normal western fare). Coke had to recognize the power of “Thums Up,” a local cola (which Coke purchased) and promote that product. The need for local responsiveness, especially when global companies want to penetrate markets with different levels of consumer purchasing power, is very clear. On the other hand, Nirula’s, a local fast-food chain in India, was, in its own restaurants, forced to respond to the cleanliness and ambience of McDonald’s. This is a case of global standards being imposed on a local player. Global and local distinctions will remain in products and services. Globalization may have as much to do with standards—quality, service levels, safety, environmental concerns, protection of intellectual property, and talent management. Needless to say, globalization will force strategists to come to terms with multiple geographical locations, new standards, capacity for adaptation to local needs, multiple cultures, and collaboration across national and regional boundaries in everything from manufacturing, product development, global account management, and logistics.
•
Speed will be a critical element Given the nature of competitive changes, speed of reaction will be a critical element of strategy. At a minimum it will challenge the yearly planning cycle. For example, consider the traditional strategic planning process in a
•
53
54
Chapter 2
Box 2.1 (continued)
large company. The process of strategy discussion and commitments typically starts in October. It identifies the strategic issues for the next calendar year and three to four years hence. What is the use of such a process in an Internet-based start up? Speed of reaction, not tied to a rigid corporate calendar is of the essence. Strategy must be a topic of discussion and debate all the time not just during the planning sessions—strategy making and thinking cannot be a “corporate rain dance” during October! Speed is also an element in how fast a company learns new technologies and integrates them with the old. As all traditional companies are confronted with disruptive changes, the capacity to learn and act fast is increasingly a major source of competitive advantage. Innovation is the new source of competitive advantage Innovation was always a source of competitive advantage. However, the concept of innovation was tied to product and process innovations. In many large companies, the innovation process is still called the “product creation process.” Reducing cycle time, increasing modularity, tracking sales from new products introduced during the last two years as a percentage of total sales, and global product launches were the hallmarks of an innovative company. Increasingly the focus of innovation has to shift toward innovation in business models. For example, how does an auctionbased pricing market (e.g., airlines, hotels) in an industry with excess capacity change the business model? How do you think about resources available to the company for product development when customers become co-developers of the product or service? Should we have an expanded notion of resource availability? What impact does mass customization or, more importantly, personalization of products and services have on the total logistics chain? Business innovations are crucial in a competitive landscape subject to disruptive changes.
•
Strategy in the Next Millennium Given the dramatic changes taking place in the competitive landscape, I believe that both the concept of strategy and the process of strategy making will change. Older approaches will not suffice. Managers will have to start with two clear premises. First, they can influence the competitive environment. Strategy is not about positioning the company in a given industry space but increasingly one of influencing, shaping and creating it. What managers do matters in how industries evolve. This is not just about the reactions of large, well-endowed companies. Smaller companies can also have an impact on industry evolution . . .. Second, it is not possible to influence the evolving industry environment if one does not start with a point of view about how the world can be, not how to improve what is available but how radically to alter it. Imagining a new competitive space
Strategic Management and Competitive Advantage
Box 2.1 (continued)
and acting to influence the migration toward that future is critical. Strategy is therefore not an extrapolation of the current situation but an exercise in “imagining and then folding the future in.” This process needs a different starting point. This is about providing a strategic direction—a point of view—and identifying, at best, the major milestones on the way. There is no attempt to be precise on product plans, or budgets. Knowing the broad contours of the future is not as difficult as people normally assume. For example, we know with great uncertainty the demographic composition of every country. We can recognize the trends—the desire for mobility, access to information, the spread of the web, and the increasing dependence of all countries on global trade. The problem is not information about the future but insights about how these trends will transform industries and what new opportunities will emerge. While a broad strategic direction (or strategic intent and strategic architecture) is critical to the process, it is equally important to recognize that dramatic changes in the environment suggest managers must act and be tactical about navigating their way around new obstacles and unforeseen circumstances. Tactical changes are difficult if there is no overarching point of view. The need constantly to adjust resource configuration as competitive conditions change is becoming recognized. A critical part of being strategic is the ability quickly to adjust and adapt within a given strategic direction. This may be described as “inventing new games within a sandbox,” the sandbox being the broad strategic direction. The most dramatic change in the process of strategy making is the breakdown in the traditional strategy hierarchy—top managers develop strategy and middle managers implement it. By its very nature discontinuous change in the competitive environment is creating a whole new dynamic. People who are close to the new technologies, competitors, and customers appear as managers in the middle. They have the information, urgency, and motivation to act. They are also the ones who have direct control over people and physical resources. Top managers, in an era of discontinuous change, are rather removed from the new and emerging competitive reality. . . . Middle managers must take more responsibility for developing a strategic direction and, more important, in making decentralized decisions consistent with the broad direction of the company. The involvement of middle managers is a critical element of the strategy process. Finally, creating the future is a task that involves more than the traditional stand-alone company. Managers have to make alliances and collaborate with suppliers, partners, and often competitors to develop new standards, infrastructure, or new operating systems. Alliances and networks are an integral part of the total process. This requirement is so well understood that it is hardly worth elaborating here. Resources available
55
56
Chapter 2
Box 2.1 (continued)
to the company are dramatically enhanced through alliances and networks. The New View of Strategy The emerging view of strategy contrasts dramatically with the traditional view . . .. The shift in emphasis in the concept of strategy and the process of strategy making is dramatic. It is clear the disruptive forces that have wrought this change are accelerating. It is time for managers to abandon the comfort of the traditional, and tried and tested, tools and concepts and embrace the new. Disruptive competitive changes will challenge the status quo. Those who take up the challenge and proactively change will create the future. The markets will decide the drivers, passengers, and the rate of “roadkill” soon enough. Reprinted from Financial Times. Publication date: October 4, 1999.
Industry and market attractiveness
Revenue position compared to rivals
Cost position compared to rivals
Firm profitability Firm’s relative competitive positioning in the industry
Figure 2.2 Drivers of firm profitability From Besanko et al. (2004, p. 360)
Figure 2.2 summarizes the drivers of firm profitability according to Besanko et al. (2004). The first driver determines whether a firm operates in an attractive market or industry, as can be ascertained via detailed industry analysis. Profitability does not only vary across industries but also across firms within a given industry, requiring a closer look at the revenue or cost position of the firm relative to its competitors. Analyzing the firm’s environment involves taking a close look at a range of factors, some of which may be beyond the firm’s control (e.g., macroeconomic factors) as well as at industry-specific factors. We examine below how to analyze the macroeconomic environment and subsequently examine industry-specific factors.
Strategic Management and Competitive Advantage
2.2.1
57
Macroeconomic Analysis
The firm’s macroeconomic environment can have a critical impact on industry attractiveness. One way suggested to analyze the external environment is the PEST framework (standing for politics, economics, social culture, and technology). Politics (e.g., environmental legislation, antitrust rulings, tax policies, employment laws, trade restrictions, tariffs) may influence the profitability and viability of the overall industry, as well as specific firms within it. For multinational corporations (MNCs), assessing the impact of such political factors can be involved as MNCs have to constantly monitor governmental stability, monitor import and export regulations, and be abreast of local business legislations.
•
Economics can have a serious impact on the profitability of an industry or firm. The unemployment level, the relative value of the domestic versus foreign currencies, inflation, growth, and productivity can influence the health of the economy, by way of consumer demand or confidence. These economic factors determine the growth potential. A poor economic situation, such as the recent financial crisis, may lead to reduced spending by consumers. A firm must carefully monitor these factors and devise appropriate strategies to ride out an unfavorable economic environment or take advantage of opportunities arising from an expanding economy. Multinationality, in particular, enables a firm to shift operations among several countries, taking advantage of opportunities or reducing risks as relative labor costs, exchange rates, tax policies, and the like, change.
•
Social-cultural factors, such as the proportion of women in the workforce, health and fitness trends, or the growth in discretionary spending by the young, can also have a significant impact. A firm should monitor these trends to ensure that its products and services meet changing consumer needs. Moreover, as the firm expands into new markets or countries, differences in purchasing behavior due to social and cultural idiosyncrasies must be taken into account.
•
Technological changes have been unprecedented in recent decades in terms of incremental improvements and technological disruptions. Today one can travel faster, communicate instantly globally, and produce in more efficient ways than ever before. New industries have emerged (e.g., cellular phones and dot-coms), while others have entirely disappeared (e.g., typewriters or argentic photo cameras). Businesses
•
58
Chapter 2
that thrived in the past have often taken advantage of emerging technologies in other industries to serve their customers better or cheaper. 2.2.2
Industry Analysis: Structure–Conduct–Performance Paradigm
A thorough industry and microeconomic analysis must complement the analysis of the macroeconomic environment. Two countries with similar macroeconomic environments may be quite different with respect to their microeconomic profiles. For example, France and Germany are roughly similar in terms of macroeconomic features, but many industries are organized quite differently in the two countries (e.g., the banking system or the waste management industry). Microeconomic analysis enables a better understanding of the overall attractiveness of a particular market and the achievable profitability of the typical firm within that industry. A well-known industry analysis framework is the “structure–conduct– performance” (SCP) paradigm.2 At its core this paradigm assumes a causal link from market structure to firm conduct and performance: market structure determines firm conduct, which in turn determines industry and firm performance. This also works in the reverse direction, since firms may pursue strategies that can alter the market structure (e.g., M&A activities). Government intervention and basic demand and supply conditions may also influence the components discussed above. Market Structure In perfect competition, many firms (facing no entry or exit barriers) populate the market. Moreover clients have a perfect flow of information. Firms offer homogeneous products and behave as price takers. In the long run a competitive industry will supply a good at a price that reflects the marginal cost of the resources required to manufacture that product. On the other extreme, in an industry characterized by a monopoly structure, there are high entry and exit barriers (e.g., large fixed costs), and the customer base is relatively large and homogeneous. A monopolist can earn excess profits stemming from market power as reflected in its ability to set a price higher than the marginal cost of production. Market structure, as proxied by the number and market power of firms in the industry, is an important driver of industry 2. The SCP paradigm was developed by the “Harvard School,” including Joe Bain and Edward Mason, based on empirical observations.
Strategic Management and Competitive Advantage
59
profitability. The fewer the number of producers in the market, the greater their ability to wield market power and earn excess profits. The structure and bargaining power of suppliers and customers may also influence whether a firm exercises market power. This “extended rivalry” can put significant pressure on the firm. Firm Conduct in the Industry Conduct refers to whether a firm actually exercises its market power to earn excess profits, whereas market structure refers to whether market power is structurally possible in the industry. In addition to individual exercise of market power, firms may collude (explicitly or tacitly) in an oligopolistic industry to sustain a higher price and earn excess profits.3 The ability to exercise market power is influenced by strategic investments, such as engaging in advertisement campaigns or investing heavily in research and development, preventing potential rivals from market entry. Industry Performance The performance of an industry is based on its profitability as well as its static and dynamic efficiency. Excess profits earned by incumbent firms imply that the given industry is not perfectly competitive as some firms wield market power. A secure incumbent may have little incentive to improve its production processes.4 Although a consolidated industry can attain higher static efficiency resulting from larger production scale, the technology employed may not be the most efficient, with firms investing less in R&D compared to a highly competitive industry. In this sense there may be a “cost” to society from consolidated industries since they tend to be less dynamically efficient than a highly competitive industry. This issue has raised a big debate among economists with no clear consensus emerging on whether monopoly and the existence of patents is beneficial or harmful in terms of encouraging innovation.5 2.2.3
Porter’s Industry and Competitive (Five-Forces) Analysis
The industry analysis above provides a benchmark for the profitability of the “average” firm in an industry. A complementary approach to the industry analysis above is Michael Porter’s (1980) “five-forces” 3. Usually a cartel attempts to set a price equal to what a monopolist would charge as cartel members are attempting to maximize joint profits. The stability of a cartel is another matter. 4. A widely known remark on monopolistic industries is that of Hicks (1935, p. 8): “the best of all monopoly profits is a quiet life.” 5. See Tirole (1988, ch. 10) for a comprehensive economic analysis of the incentives to conduct R&D in oligopolistic industry structures.
60
Chapter 2
Potential entrants Threat of new entrants
Competitors Bargaining power of customers
Bargaining power of suppliers
Suppliers
Customers Rivalry among existing firms Threat of substitute products or services
Substitutes
Figure 2.3 Porter’s “five-forces” industry and competitive analysis From Porter (1980)
framework. Since the early 1980s, it has become a well-known paradigm used both in academe and in practice for analyzing industry performance. According to Porter (1980), the attractiveness of an industry depends on two kinds of strategic interactions: Interactions along the “value chain” These relationships, depicted along the horizontal axis in figure 2.3, involve the relative bargaining power of different parties along the value chain, from suppliers to manufacturers and distributors, to end customers. Extended rivalry This includes the internal rivalry within a particular industry (nature and degree of intra-industry competition) as well as the threat posed to the firm from external forces, such as potential entrants and the threat of substitute products or services. These “extended-rivalry” interactions are illustrated along the vertical axis in the figure. Porter categorizes the relevant economic factors into five groups or forces (hence, the “five-forces” analysis). He proposes a thorough assessment of (1) the impact of these factors on the intensity of competition within the industry or internal rivalry, (2) the threat of substitute products or services, (3) the threat of new firms entering the market, (4)
Strategic Management and Competitive Advantage
61
the bargaining power of suppliers, and (5) customers. These forces are in turn affected by industry structure and other relevant variables, like entry and exit barriers, product differentiation and availability of information.6 We look at these forces in detail next. Internal Rivalry Internal rivalry is a central piece of Porter’s analysis. It refers to competitive actions taken by each firm to gain market share within the industry. A means to assess the intensity of competition within an industry is to use a concentration ratio. Industrial economists and antitrust authorities have long attempted to find a quantitative measure of the intensity of rivalry using various concentration ratios. A common feature is that they are based on the market shares of the firms already active in the industry.7 Two concentration indexes are most commonly used to measure internal rivalry within an industry: (1) the cumulative market share of the k biggest firms, Ck, and (2) the Herfindhal–Hirschman index, developed by Herfindhal (1950) and Hirschman (1945, 1964), commonly referred to as HHI.8 Cumulative Market Share of the k Biggest Firms (Ck ) Let si denote the market share of firm i in an industry consisting of n active (incumbent) firms. A simple proxy of the concentration in a industry with n active firms is the cumulative market share of the k biggest firms (k ≤ n), that is, k
Ck ≡ ∑ si .
(2.1)
i =1
The market shares of the few “big” players are generally available in market reports. This concentration ratio has a major drawback: it fails to capture heterogeneity among the largest firms. For this reason industrial economists and antitrust authorities generally prefer alternative concentration measures, such as the Herfindhal–Hirschman index. This is discussed in example 2.1 below. 6. Although conceptually very useful, Porter’s (1980) framework does not give a clear prescription as to whether to invest in a given industry. Its primary benefit is that it helps frame an industry and identify key forces affecting market attractiveness. 7. These concentration ratios fail to capture whether external parties can easily enter these markets. 8. Tirole (1988) provides an alternative to these concentration indexes, namely the entropy index that involves a logarithmic function of the market shares. Encoua and Jacquemin (1980) describe desirable properties a concentration index should satisfy and assert that the HHI and entropy indexes are better suited to analyze industry concentration. Here we only discuss the Ck and HHI indexes due to their relative simplicity.
62
Chapter 2
Herfindhal–Hirschman Index (HHI) The HHI index has the merit of combining information about all firms in the market, not just the five (or k ) biggest firms. The Herfindhal– Hirschman index is given by n
HHI ≡ ∑ si ².
(2.2)
i =1
From a practical viewpoint, it is more difficult to gather information (market shares) on all firms operating in a given industry. Example 2.1 Concentration Indexes Consider the market share distribution of five firms in the three different industry situations described in table 2.1. The last two columns give the values of C 4 and HHI in each case. The industry in case 3 is clearly more concentrated than in case 2, which in turn is more concentrated than in case 1, as the market shares are less uniformly distributed. Using the C4 index, one cannot distinguish the difference in concentration within the industry in case 3 or 2, as the index is equal to 88 percent in both cases. The C4 index does not capture the fact that in case 3 a single firm is dominant with a 50 percent market share, compared to case 2 where the three biggest firms have comparable power. The HHI does a better job since it properly captures this difference, giving a higher value in case 3 relative to case 2. As summarized in figure 2.4, concentration indexes are used by economists and antitrust authorities to identify and differentiate among different market structures. A monopoly is generally characterized by only one seller and very high barriers to entry and exit. An example, from the diamond business, is DeBeers, which has exclusive access to scarce Table 2.1 Concentration indexes based on the first three (C3 ), four (C4 ), or all firms in an industry Case
Market share distribution
1 2 3
1
s1 /5 ¼ ½
s2 /5 ¼ ⅛
1
s3 1 /5 ¼ ⅛
Concentration index s4 1 /5 ⅛ ⅛
s5 1 /5 ⅛ ⅛
C4 80% 88% 88%
HHI 2,000 2,188 3,125
Note: By convention, the HHI is often given as 10,000 times the HHI number given by the definition in equation (2.2).
Strategic Management and Competitive Advantage
Ck(%) HHI
63
Perfect competition
Monopolistic competition
Oligopoly
Dominant firm
Monopoly
0
0 < C4 < 40
40 ≤ C4 < 60
60 ≤ C1 < 90
C1 ≥ 90
HHI < 1,000
1,000 ≤ HHI < 1,800
HHI ≥ 1,800
Figure 2.4 Classification of market structures based on different concentration index ranges
resources giving it a (quasi-) monopoly position due to high barriers to market entry. A monopoly is characterized by C1 ≥ 90 percent. In an industry with a dominant firm and some fringe competitors, the dominant firm can typically ignore strategic interactions with the smaller rivals. Barriers to entry and exit are fairly high. Apple and its iPod® have a dominant position in the portable music industry: despite smaller competitors, Apple has built an uncontestable entry barrier thanks to its unique brand name. Firm dominance is characterized by 60% ≤ C1 < 90% (and HHI ≥ 1, 800). An oligopoly is characterized by few competing firms with 40% ≤ C 4 < 60%. A classic case is the duopoly involving Airbus and Boeing in the airframe industry. Barriers to entry due to technological expertise or huge sunk capital costs are generally very high. National quality standards may also raise entry barriers for foreign competitors and explain oligopoly situations.9 Monopolistic/differentiated competition is characterized by many suppliers with heterogeneous products appealing to different customer or market segments. A good example is the luxury goods industry where distinct brands lure different customer groups (youth, fashion followers, etc.). Product differentiation makes it possible for firms to price products above the marginal cost even if many firms compete in the marketplace.10 Differentiated competition is characterized by 0 ≤ C4 < 40 percent. Perfect competition involves a homogeneous product (commodity) with no single firm having significant market power to influence the price-setting process. The agricultural sector, for example corn production, is considered a good approximation to a perfectly competitive industry. Typically HHI is below 1, 000. 9. A case in point is the French pipeline and valve industry. In France, valves for public water management pipes turn counterclockwise, whereas in most other European countries valves turn clockwise. For this reason only manufacturers that meet French standards are active in France, mostly French companies. 10. In monopolistic competition free entry of new brands leads to zero economic profit with gains from pricing over marginal costs exactly offsetting fixed cost.
64
Chapter 2
One explanation for the existence of imperfect competition lies with the large fixed costs incurred by incumbent firms: if the market is not sufficiently large, only a limited number of firms can afford incurring these high fixed costs. Even when the market-clearing price exceeds marginal production costs, no external party enters since it cannot recoup its large fixed costs. Threat of Substitutes In assessing the threat of substitute products, a key prerequisite is to determine what the relevant product market is and define the relevant substitute products. Are train and plane substitutes in the transportation market? To travel from France to Cyprus, the train is certainly not an option. However, from Paris to London the train is a valuable option thanks to the Eurotunnel.11 Many economists and antitrust authorities define the relevant market as the smallest set of products for which a firm, should it become dominant, would find it profitable to raise prices significantly (and permanently).12 Once the relevant market is defined, the threat of close substitutes can be assessed. The extent to which a company might be affected by substitute products depends on several factors, including the propensity of buyers to substitute, switching costs, the value added by the company’s product or service in the clients’ perception, as well as the price-performance characteristics of substitute offerings. Potential Entrants Another key force affecting firm performance is the threat of entry. New entrants pose a threat to incumbent firms as higher rivalry generally leads to lower profit margins (negative externality). How easy or difficult it is for a potential entrant to penetrate a market depends on entry barriers.13 Entry barriers may be structural (exogenous) or strategic (endogenous). An example of structural entry barriers is when the incumbent is protected by a favorable government policy or other administrative barriers (e.g., property rights,14 state, market or environmental regulation). 11. This travel option has become more attractive especially after September 11 since it reduces substantially the time to check in and out. 12. To determine the relevant product market, economists utilize various measurement tools, such as cross-price elasticity of demand, price correlation analysis, and shock analysis. 13. Bain (1956) has extensively analyzed entry barriers. A barrier to entry is a mechanism that allows incumbents to make economic profits without threat of entry by competition. 14. Examples include patents, copyrights, and licenses. The property right problem for a social planner hinges on the trade-off between erecting entry barriers (which is not socially optimal) and giving firms incentives to invest in R&D.
Strategic Management and Competitive Advantage
65
Structural barriers may also stem from other economic phenomena, such as fixed entry costs, economies of scale, scope, or learning, access to scarce resources,15 reputation, network effects,16 product differentiation advantages, process innovation, and vertical integration. Strategic entry barriers involve actions taken by incumbents to deter the entrance of new competitors into the market, for example, by manipulating prices before (limit pricing) or after entrance (predatory pricing), by building excess capacity, or by launching aggressive advertising campaigns to create brand loyalty. They may also create a new brand to capture a previously unsatisfied customer segment (product proliferation). We elaborate on corporate strategies to deter entry later in chapter 4. Bain (1956) identifies three kinds of behavior by incumbents in the face of an entry threat. Entry is blockaded if the incumbent is well protected by insurmountable structural barriers to entry and exit so that it continues to enjoy incumbency profits. The incumbent can ignore the threat of entry so that strategic interactions play a minor role in this case. Entry is deterred if the incumbent is not exogenously protected and behaves strategically to make it unprofitable for new competitors to enter. For instance, by massively investing in automated production processes and reducing its production costs (a strategic first-stage investment), a firm may ensure that the rival’s post-entry profits are driven close to zero. This kind of deterrence strategy may be extremely expensive to pursue, but nonetheless strategically justified. Entry is accommodated when the incumbent finds it preferable to allow entry than to erect costly barriers. A strategy of entry accommodation is not tantamount to a passive stance toward one’s rivals: the incumbent can still build up an early competitive advantage (e.g., via excess capacity or strong brand image). Bargaining Power of Suppliers and Customers Both suppliers and customers can extract profits from manufacturers depending on who influences the price-setting process when the manufacturer buys or sells. The firm’s ability to influence or set prices depends on a number of factors: The concentration and market power of customers and suppliers. If the customer base is small (e.g., B-to-B clients) but suppliers are numerous, •
15. A case in point is Nutella. The firm has an exclusive right to acquire a given species of nuts, so no entrant can imitate Nutella’s unique taste. 16. The combination “PC + MS DOS” won the computer war against “Apple Mac OS” partly because IBM had a less restrictive licensing policy than Apple.
66
Chapter 2
customers will wield more bargaining power. L’Oréal, one of the major cosmetic companies worldwide, puts significant pressure on its packaging services suppliers, which have to toe the line. •
The price elasticity of demand for the product (inputs or outputs).
•
Customer and supplier switching costs (purchase from another party).
The ability of customers to backward integrate or of suppliers to forward integrate. •
• The relation specificity of the firms’ assets (specific to clients or suppliers).
2.3
Creating and Sustaining Competitive Advantage
The profitability of a firm depends both on industrywide characteristics (e.g., competitive pressures, market power, bargaining power) as well as on firm-specific attributes. We already discussed the main strategic management frameworks for assessing industry attractiveness. We next focus on firm-specific factors that might help explain why certain firms in a given industry are more successful than the “average” firm considered in industry analysis. We review the “generic strategies” proposed by Michael Porter (1980), namely the incentive to be a cost leader, a differentiation leader, or focused on a specific customer segment. To understand these concepts from a microeconomic viewpoint, it is necessary to first address the notion of value creation and competitive advantage.17 2.3.1 Value Creation To earn profits in excess of the industry average, a firm must strive to be superior to its competitors in the industry. A key to superior performance is creating more value for customers than one’s rivals by exploiting some competitive advantage. Firms’ strategies aim to create such comparative advantages. To assess the value created by a firm, we need to go back to basic microeconomics. For each product there is a maximum value the consumer is willing to pay. This maximal value (“willingness to pay” or “consumer value”) determines whether the customer purchases the product. If the price asked for the good exceeds the customer’s willingness to pay, the customer will reject the product. If the price is lower, the customer will purchase it, “earning” the difference (between the 17. For a more detailed analysis of how firms can create competitive advantage, refer to Besanko et al. (2004, ch. 11) and Grant (2005, chs. 8 and 9).
Strategic Management and Competitive Advantage
67
customer value and the product price) as consumer surplus or utility. If p denotes the price and u the consumer’s willingness to pay (utility), the consumer surplus is represented by u − p if p ≤ u, and 0 otherwise. If the product is homogeneous, meaning the products offered by rivals are considered perfectly identical, a rational consumer will purchase from the lowest price supplier. For instance, if a consumer sees no significant difference among airline carriers and does not care much about small differences in the time schedules, she would choose to fly with a low-cost airline like Ryanair. We must also consider the incentive of a given firm to sell in the marketplace. This incentive is captured by the producer surplus or economic profit, and represents the bottom-line criterion for many managerial decisions. The value created by the producer is the difference between the price at which the firm sells the good, p, and its unit cost of producing it, c.18 The total economic value created through such an exchange in the marketplace is the difference between the utility the product brings to the consumer and the amount it costs to be produced, namely u − c. A portion of this value is captured by the consumer in the form of consumer surplus, u − p, and the remaining part is earned by the producer as economic profit, p − c. That is, Total value created = consumer surplus + producer surplus u−c = + (u − p) ( p − c)
(2.3)
The relation above is depicted in figure 2.5. A necessary condition for market exchange to take place is that the value (utility) the product represents for the consumer (u) exceeds the cost of producing it (c). In this case both the consumer and the producer gain. In equilibrium the producer does not set the price arbitrarily; this choice is closely related to the consumer price elasticity of demand, the production cost, the nature and degree of competition, as well as the size of the customer base. In a perfectly competitive market all economic value created by the product offering is captured by the consumer and competing firms make no economic profit. In order to be economically profitable, firms need to find ways to deviate from perfect competition. A firm has a competitive advantage when it is able to deliver more economic value than its rivals. 18. Included in c are the labor costs, input prices, and cost of capital per unit of the product. The profit and value measures we discuss here are net of the opportunity cost of capital. The term used for profits in this case is “economic profit.” A financial translation of this economic concept is economic value added (EVA).
68
Chapter 2
Consumer value u Consumer surplus (u−p) Price p Producer surplus (p− c)
Total economic value u− c
Cost c
Figure 2.5 Total value created consisting of consumer surplus plus producer surplus
In reality, if consumers are not identical, a given product may represent a higher utility for one consumer than for another. Distinct market segments can be identified in which consumers (with uniform preferences) are more willing to accept one particular offering versus another, namely the one for which their consumer surplus (u − p) is the highest. This basic economic principle underlies market segmentation. To create higher economic value, firms pay considerable attention to what drives customer value and production costs. The following factors typically drive the customer’s willingness to pay: The appeal of physical characteristics and the perceived fitness of the product (e.g., the size of furniture may be an important criterion if one’s flat is only 20 square meters or 200 square feet). •
The quality of services associated with the product (the price premium one may be willing to pay for a night at Sofitel in NYC rather than the Best Western Hotel is linked to the perceived services one receives rather than the quality of the bed). •
Brand name (Apple®’s brand name creates a unique competitive advantage for the iPhone® in the now-commoditized mobile telephony market). •
•
Perception by customers.
Strategic Management and Competitive Advantage
69
Firm infrastructure (e.g., finance, accounting, legal) Human resource management
Support activities
Technology development Procurement
Primary activities
Inbound logistics
Production
Outbound logistics
Marketing and sales
Services
Main activities
Figure 2.6 Porter’s value chain From Porter (1980)
The following factors typically drive production costs: Drivers related to the size of the firm (economies of scale and scope, capacity utilization and bargaining power). •
•
Experience of the firm (learning-curve effects).
Factors related to organizational structure (organization of transactions, agency efficiency, vertical chain). •
•
Other costs (lower input prices, production in a low labor cost country).19
To understand how value is created along the vertical chain, Porter (1980) proposes a conceptual framework (shown in figure 2.6) involving the organization of value-creating activities referred to as the value chain. Porter’s value chain essentially divides the organization into a series of value-creating activities that can be broadly classified as supportive or primary. Regardless of whether an activity belongs in the first or the second category, it can potentially contribute to creating more economic value either by increasing the value perceived by the consumer or by reducing the cost of producing it. Primary activities are involved with the physical creation of the product or development of the service until it reaches the end customer. Inbound logistics, production or operations, outbound logistics, marketing and sales, and services are typical primary activities. Additional activities support these primary activities by providing procurement and technology services, human resources management, and various firmwide functions such as finance, accounting, and 19. For more details on benefit and cost drivers, see Besanko et al. (2004, pp. 411–18).
70
Chapter 2
legal services. Increased value added may also be a result of these firmwide functions. The organization as a whole is embedded in a larger stream of activities that include suppliers, distributors, and buyers’ value chains, which together with the firm’s value chain form the so-called value system. These activities are all interrelated, so events in one of them may affect the company’s overall strategy basis. The notions of value creation and value chain are essential for understanding the “generic competitive strategies” proposed by Porter (1980). 2.3.2
Generic Competitive Strategies
A generic competitive strategy refers to how a firm positions itself to compete in the marketplace. Porter (1980) identifies three generic strategies—cost leadership, differentiation, and focus strategy. The choice of one strategy over another partly depends on the size of the market the firm wants to cover. When covering a broad market, firms can mainly pursue two generic strategies: cost leadership or differentiation. In homogeneous goods markets, cost leadership can play a central role since customers primarily decide based on the price. In a market where customers prefer customized products, a benefit leader or differentiated firm that offers a perceived superior product may obtain a stronger competitive advantage. A third strategic alternative is to specialize in a narrow customer segment, namely develop a niche, following a focus strategy. Cost Leadership In homogeneous goods markets, cost leadership consists in offering similar products as rivals but at lower price. This strategy typically involves producing larger quantities and appealing to a broader market (broad scope). It is more likely to succeed when customers are sensitive to prices, as measured by the price elasticity of demand. A costleadership strategy is advisable when products are commodity-like or customer services are hard to differentiate. Cost advantage can result from economies of scale, scope, or learning-curve effects. Economies of scale offer unit-cost savings that increase with the level of output: the average production cost of a single product decreases with the number of units produced. Fixed costs here play a critical role: when volume rises, the fixed-cost component per unit declines. Such savings may have a material impact on the equilibrium market structure. If fixed costs are large, only a limited number of firms can profitably operate in the market: the price markup over the marginal cost needs to be sufficiently large to justify spending the fixed costs by the incumbents. Economies of scope
Strategic Management and Competitive Advantage
71
correspond to cost savings gained by operating several product lines or businesses: the production of good A reduces the production cost of product B. Learning-curve effects are related to the experience and know-how firms cumulate over time when they produce a given product or provide a certain service. The classic BCG matrix originated from work related to the learning-curve effect.20 Cost leadership can also result from improved process efficiencies, increased bargaining power with suppliers, higher capacity utilization (especially when fixed costs are high), lean organizational structure, better compensation systems, or location advantages (manufacturing in low-cost countries). Firms employ several approaches to achieve cost leadership: cost leadership under benefit parity, cost leadership under benefit proximity, and product redesign. In case of benefit parity, the cost leader offers a product identical to the products offered by competitors but the cost of producing it is significantly lower. In case of benefit proximity, the cost of producing the good is lower but the consumer perceives the product to be of lower quality; here the increase in consumer surplus due to the lower price offsets the quality decrease. Alternatively, a firm may offer a product to consumers that is qualitatively different from competitors’ offerings (product redesign). Whether achieving cost leadership enhances firm value also depends on the size of the initial investment. Differentiation Strategy Consumer preferences in the marketplace may not be homogeneous. Within the same market some customers may have preferences for specific product features and others for other features. A differentiation strategy enables a firm to create more economic value than its rivals by offering higher consumer value than other products supplied in the marketplace. In exchange for this higher consumer surplus, a consumer may be willing to pay a price premium. A differentiation strategy may encompass the whole value chain. This strategy is more appealing when price elasticity is low or when cost advantages are limited. Traditionally one distinguishes two kinds of differentiation. In case of horizontal differentiation, product differentiation can be achieved thanks to new combinations of product characteristics (e.g., MP3-player for mobile telephone handsets), new distribution or sales outlets (e.g., online shopping for people living on the fast lane), better marketing differentiation (lenovo® laptop, mainly focused on corporate customers), 20. The BCG matrix paradigm asserts that a conglomerate should finance promising “stars” with excess cash generated by “cash cows.” By so doing, the “stars” commence production early on and accumulate experience ahead of competitors, leveraging on learning-curve effects.
72
Chapter 2
or better complementarities owing to network effects (e.g., Blu-ray players on Sony’s PlayStation3®).21 Vertical differentiation is achieved when all perceive the product as being of higher quality. Customers without budget constraints would be willing to pay a premium for it. Again, three cases may be distinguished here. In case of cost parity, the cost of producing the good remains unchanged, but the differentiated product is perceived as being of higher quality by a given customer segment. In case of cost proximity, the differentiated product implies higher production costs (than the standard product), but consumers appreciate the higher quality and willingly pay a price premium that compensates for these higher costs. Product redesign consists in offering a product with new characteristics that appeal to new or existing customers. Focus Strategy Alternatively, a firm can devise a focus strategy and tailor its products and services to the requirements of a specific customer group. In doing so, the firm creates higher economic value for this specific segment. One type of focused strategy is to be a local player or appeal to a given population group (e.g., Mecca Cola® as an alternative to CocaCola® and Pepsi® for Muslim consumers). A key advantage of a focused strategy is that the targeted market may not be large enough to accommodate many producers, enabling the focused firm to enjoy a quasi-monopolistic position within its segment. 2.3.3
Sustaining Competitive Advantage
It is said that history repeats itself in cycles. Many once-leading firms have been dethroned abruptly for not being able to protect and sustain their once-formidable competitive advantage. Imitators and new entrants with superior technologies can quickly erode competitive advantages that have taken years to build. Firms that persistently outperform their peers are those able to sustain or renew their competitive advantage over the long run. Sustainability of competitive advantage invariably depends on the dynamics of the market. In a market with low entry and exit barriers, it is more likely that a firm will enter when it sees a window of opportunity. To avoid this, an incumbent can erect entry barriers. Just as there are various mechanisms to protect the profitability of an industry (e.g., erection of entry and exit barriers), there exist mechanisms within an industry to protect a firm’s competitive advantage from rivals’ 21. See Besanko et al. (2004, p. 415).
Strategic Management and Competitive Advantage
73
imitation. A firm’s ability to create and sustain a competitive advantage depends on its firm-specific resources and the distinctive capabilities arising from these resources. To keep competitors from duplicating its competitive advantage, the firm should constantly strive to create or enhance asymmetries by acquiring and managing distinctive resources and capabilities that cannot be readily duplicated by would-be imitators. Heterogeneity among firms is the cornerstone of the resource-based view of the firm, emphasizing firm specificity and uniqueness. Imitation can only be precluded if there is heterogeneity and imperfect transferability of key resources. Besides the scarcity and immobility of unique resources, firms can erect isolating mechanisms to prevent rivals from internally developing similar resources. Isolating mechanisms fall into two main categories: (1) barriers to imitation (e.g., property rights or exclusive access to scarce resources) and (2) early-mover advantages, such as learning-curve effects and brand-name building. When a firm cannot acquire distinctive key resources, it has to build them up over time. In its history of investment and commitment, a firm accumulates skills, assets, and resources involving path dependencies. The experience, relationships, and reputation a firm has built over time enable it to leverage its resources and capabilities and represent sources of uniqueness. It is the exploitation of firm-specific resources and capabilities in a dynamic way that enables a firm to enjoy higher (excess) profit flows. Apple®, frequently ranked as one of the most famous brands in the world, has successfully leveraged its brand image to sustain its profitability over time. Conclusion In this chapter we provided a brief overview of the main paradigms and issues in strategic management, focusing on how prevalent frameworks view the key drivers of market attractiveness and firm profitability. We elaborated on market structure and discussed how limited access to a market and the existence of entry barriers can enhance a firm’s profitability. We described Porter’s five-forces paradigm and how it can help structure market analysis. We also discussed how, within a given industry, a firm can build competitive advantage through production efficiency (cost leadership), branding (differentiation leadership), or a focus strategy. Finally, we discussed the importance of sustaining competitive advantage dynamically.
74
Chapter 2
Selected References Bain (1956) examines barriers to market entrance in detail. Porter’s (1980) seminal work on industry and competitive analysis is a cornerstone for understanding the art of strategy and competitive advantage. Besanko et al. (2004) provide an easy-to-read economic perspective on strategy. Bain, Joe S. 1956. Barriers to New Competition. Cambridge: Harvard University Press. Besanko, David, David Dranove, Mark Shanley, and Scott Schaefer. 2004. Economics of Strategy, 3rd ed. New York: Wiley. Porter, Michael E. 1980. Competitive Strategy. London: Macmillan.
3
Market Structure Games: Static Approaches
Studying industrial organization is useful to deduce managerial insights to help explain how firms should behave strategically when faced with competition. In this chapter and the following one, we review some basic principles and models in this area, discuss industry structures, and examine information asymmetry, commitment, and collaboration. Basic ideas developed in these chapters serve as building blocks in subsequent discussions. In this chapter we deal mainly with static models that help explain the modus vivendi in competitive situations when firms focus on the short-run impact of their decisions. We discuss simple economic models that characterize optimal firm behavior under different industry structures. Chapter 4 extends the discussion to include long-term, dynamic strategy formulation, helping explain phenomena such as restraining one’s own freedom (commitment) or collaboration among rival firms. This chapter is organized as follows. Section 3.1 discusses the benchmark case of a monopolist, developing the basic building blocks for subsequent models. We then turn to oligopolistic situations where firms have enough market power to influence the decisions of rivals. Such analysis requires the use of game-theoretic tools. Section 3.2 introduces static models of duopoly, presenting first the case of Bertrand price competition and then discussing the classic Cournot quantity duopoly model. Section 3.3 extends the standard Cournot quantity competition analysis to accommodate a larger number of firms in oligopoly, obtaining the market equilibrium in perfect competition as a polar case. Going beyond earlier models that involved complete information, section 3.4 explores the impact of incomplete information on market structure in a duopoly.
76
3.1
Chapter 3
Monopoly
In monopoly entry barriers are typically sufficiently high to shield the incumbent firm from competitive entry (blockaded entry). Customers take price as given and cannot influence the price-setting process. Monopoly may naturally arise when demand is not sufficient or fixed costs are too high to accommodate other incumbents (natural monopoly) or when regulation prohibits further market entry (e.g., patents).1 In western Europe the electricity market used to be considered a national natural monopoly because of the prohibitive fixed costs. Price setting in a competitive market leads to lower prices, making it difficult or impossible for more electricity utilities to make a profit once large fixed costs are considered. The equilibrium market structure critically depends on such fixed costs. Economies of scale and scope are thus one of the main drivers of industry structures (Viner 1932). When large-scale production plants are needed (e.g., nuclear power plants), a monopoly is economically justified and may be socially preferable.2 In this chapter we simplify and ignore fixed production costs, focusing instead on the relationship between the market-clearing price and marginal production costs.3 In perfect competition a firm takes the market price as given and produces until the marginal cost of an additional unit is just below the market price. In contrast, a monopolist is a price setter. Consider a monopolist facing (inverse) demand function p (⋅) and variable production cost C (Q), as a function of the quantity Q supplied in the marketplace. Given a downward-sloping demand (∂p ∂Q < 0), the monopolist faces a trade-off between price and quantity. Setting a higher price p implies earning a higher profit margin but selling a lower quantity. Inversely, if the monopolist sells an additional unit of output, it moves down the (inverse) market demand curve, suffering a (marginal) price reduction. This trade-off is linked to marginal revenues. The monopolist’s profit function is concave in its own quantity, Q,
π (Q) = R (Q) − C (Q), 1. A natural monopoly may exist when a firm can make excess economic profits when operating alone, while a duopolist cannot. If π (i) indicates the equilibrium profit of a firm in an industry with i incumbent(s), π (2) < 0 < π (1) holds for natural monopoly. 2. Today, following deregulation, the electricity market is sufficiently mature to accommodate more suppliers. 3. Under certain conditions we show that firms can make excess economic profits (gross of fixed costs). Considering fixed costs might invalidate some of these results.
Market Structure Games: Static
77
where total revenues are given by R (Q) = p (Q) × Q. To earn maximum profit, the firm must choose to produce that output, Q *, that equates its marginal cost, MC (Q) ≡ C ′ (Q), to its marginal revenue, MR (Q) ≡ R ′ (Q).4 This principle, MR (Q *) = MC (Q *), holds whatever the industry structure and the assumed profit function. In perfect competition, the marginal revenue equals the price (since the output decision of an individual firm does not affect the price-setting process, p = MC in equilibrium). In monopoly, since the firm’s output decision influences the market-clearing price and ∂p ∂Q < 0, the firm loses revenue on already produced output when it decides to produce more. Box 3.1 and figure 3.1 describe common types of demand functions. Consider the linear (inverse) demand function p (Q) = a − bQ
(3.1)
and a linear cost function C (Q) = cQ with c < a, b > 0. In this case the marginal revenue is MR (Q) = R ′ (Q) = a − 2bQ and the marginal cost is MC (Q) = C ′ (Q) = c. In monopoly we thus have a − 2bQM = c. The equilibrium quantity produced by the monopolist is QM =
a−c . 2b
(3.2)
The equilibrium price, corresponding to point E′ in figure 3.2 (determined by substituting equation 3.2 for QM into the inverse demand function 3.1) is pM =
a+c a−c = c+ 2 2
(> c ) .
(3.3)
From the equilibrium quantity and price, equations (3.2) and (3.3), the equilibrium profit for the monopolist is 4. The marginal benefit (revenue) is MR (Q) ≡ R′ (Q) = p (Q) +
∂p (Q) × Q. ∂Q
The profit function is concave so the first-order condition is both sufficient and necessary for a maximum output (Q *) to obtain. The first-order derivative of the profit function is ∂π ∂p (Q) = p(Q) − C ′(Q) + (Q) × Q . ∂Q ∂Q The first two terms yield the profitability of an extra unit of output (i.e., the difference between the price and marginal cost), while the third term recognizes that an increase in output (implying a decrease in ∂p ∂Q < 0 ) affects the profitability of units already produced.
78
Chapter 3
Box 3.1 Common demand functions
Industry structure models rely on certain assumptions. One key assumption relates to the (inverse) demand function used to determine marketclearing prices and firm profits. We assume that firms can observe customer demand. There are several deterministic inverse demand functions. The most widely used are the following: The linear demand function, p(Q) = a − bQ, where p (Q) is the marketclearing price, Q the total quantity produced by all firms in the industry, b > 0 , and a is the demand intercept. Figure 3.1a depicts this linear demand function. Here p(·) is downward sloping (with slope − b < 0 ), indicating that for an increased industry output ( Q) the market-clearing price ( p (Q)) declines. This property holds for most markets (with notable exception the luxury market, where a high price may signal a more exclusive product). One limitation, however, is that for the price to be (or remain) positive, total industry output must be limited to a certain range (if Q > a b, the price is negative). • The isoelastic demand function, p(Q) = 1 (Q + W ), where W is a positive constant. This curvi-linear demand is depicted in figure 3.1b. Here •
Price (p)
Price (p)
a
p(Q) =
p(Q) = a−bQ
1 Q+W
Slope − b 0
a /b
0
Quantity (Q)
Quantity (Q)
(a)
(b)
Price (p)
Price (p)
p(Q) = Q−1 ⁄ ep p(Q) = a × exp(−e p Q) 0
(c)
Quantity (Q)
0
Quantity (Q)
(d)
Figure 3.1 Different (inverse) demand functions (a) Linear demand; (b) isoelastic demand; (c) exponential demand; (d) constantelasticity demand
Market Structure Games: Static
79
Box 3.1 (continued)
whatever the total industry output Q, the market-clearing price remains positive. • The exponential demand function, p(Q) = a exp ( − ε p × Q), where ε p is the price elasticity of demand. This is illustrated in figure 3.1c. This steeply declining demand function has the property of excluding negative prices even for very high quantity levels and allowing a limited price for low output. −1 • The constant-elasticity demand function, p (Q) = Q ε p . This demand function is often used because of its relative simplicity. It is depicted in figure 3.1d. A condition on the price elasticity parameter ε p is often imposed to obtain nice mathematical properties. Since the linear (inverse) demand function is the simplest and most widely used, many industrial organization models rely on it to obtain simple expressions for equilibrium quantities, prices, and profits.
Price (p)
a Equilibrium price
pM =
E'
a+c 2
E
c
Marginal cost (c) Demand function
p(Q) = a−bQ
Marginal revenue
MR(Q) = a−2bQ
−2b
0
Equilibrium quantity
QM =
a− c 2b
Figure 3.2 Equilibrium price and quantity in a monopoly
−b
Quantity (Q)
80
Chapter 3
πM =
(a − c ) ² 4b
.
(3.4)
As confirmed in figure 3.2, the monopolist firm maximizes its profit by selecting the output that makes its marginal revenue, MR (Q), just equal to its marginal cost, c, as represented by the intersection point E. Inverse Elasticity Markup Rule or Lerner Index Lerner (1934) complements the discussion on price setting by a monopolist by adopting an approach based on the price elasticity of demand, ε p. This elasticity measure corresponds to the percentage decrease in quantity sold due to a 1 percent increase in price, all other things equal. It is given by
H p (Q ) ≡ −
∂Q Q pQ . =− ∂p p ∂p ∂Q
(3.5)
From the profit-maximizing condition, a markup formula measuring the firm profit margin in equilibrium obtains as5 L≡
pM − c 1 = . εp pM
(3.6)
This markup rule, commonly known as the Lerner index, provides a practical rule of thumb for pricing a product in a monopoly. It asserts that the profit margin received by a monopolist in equilibrium, L, is inversely proportional to the price elasticity of demand, ε p ≡ ε p(QM ). If customers are highly sensitive to a price increase (i.e., ε p is high) and would refrain from purchasing the product in case of a price increase, the firm’s profit margin L will be low, since ∂L ∂ε p < 0. In contrast, if the price elasticity of demand is low such that customers are hardly sensitive to the price increase, the monopolist can set a very high price ( pM ) and still enjoy a high profit margin (L). The price distortion is larger when customers reduce their demand only slightly in response to an increased price. Table 3.1 gives an indication of price-elasticity ranges. 5. We can rewrite the marginal revenue in note 4 based on the price-elasticity formula (3.5), obtaining MR (Q) = p +
∂p (Q) × Q = ∂Q
⎛ 1 ⎞ Q ∂p ⎛ ⎞ p⎜1 + (Q)⎟ = p ⎜ 1 − . ⎝ ⎠ ⎝ ε p (Q) ⎟⎠ p ∂Q
Expression (3.6) obtains from the first-order condition in the special case of a linear cost function. If demand is linear as in (3.1), it obtains from (3.3) that L = (a − c ) (a + c ) and ε p = (a + c ) (a − c ), giving L ≡ 1 e p.
Market Structure Games: Static
81
Table 3.1 Range of price elasticity of demand Perfectly elastic
εp → ∞
Elastic
1 < εp < ∞
Unit elastic
εp = 1
Inelastic
0 < εp < 1
Perfectly inelastic
εp = 0
Example 3.1 Market Equilibrium in Monopoly Assume a linear demand as in equation (3.1) with parameters a = 10 and b = 1; that is, p (Q) = 10 − Q. The marginal cost is constant, c = 1, and the profit function is π (Q) = ( p (Q) − 1) × Q. In this case equations (3.2) to (3.6) give a − c 10 − 1 a + c 10 + 1 (a − c ) = = 4.5 , pM = = = 5.5 , π M = = 20.25, 4b 2b 2 2 2 2
QM =
e p (QM ) = −
pM / Q M 5.5 = − ( −1) = 1.22 , 4.5 ∂p / ∂Q
and L=
pM − c 5.5 − 1 4.5 ⎛ 1 ⎞ = = = . pM 5.5 5.5 ⎜⎝ ε p ⎟⎠
Figure 3.3 illustrates the price-setting trade-off (higher profit margin vs. lower sales) that occurs in this situation and the optimal price markup using the Lerner index. 3.2
Duopoly
A duopoly is characterized by competition among two firms in an industry. The analysis of duopoly or oligopoly situations requires a clear depiction of the influence of each firm on the other firms in the industry. An appropriate tool kit is offered by game theory that gives prediction about the likely outcome of such strategic interactions. A game has a certain structure, rules, and characteristics as discussed in box 3.2. The tools borrowed from game theory, used throughout the book, are sometimes criticized for being based on the strong assumption of rationality by all agents. In box 3.3 Reinhard Selten addresses
82
Chapter 3
Demand function, marginal revenue
Profit 25
12
5.5−1 1 L≡ ≈ 5.5 1.22
a =10 10
πM = 20.25 20
8 Equilibrium price
pM = 5.5
E'
6
Demand function
15
Profit function
p(Q)=10−Q
10 4 Marginal revenue
5
MR(Q)=10−2Q
2
E
c=1
−1
0 0
2
4 Equilibrium quantity
6
8
QM = 4.5
0 10
Quantity (Q)
Figure 3.3 Trade-off and optimal price markup for a monopolist The demand function is p (Q) = 10 − Q and marginal cost is constant ( c = 1).
Box 3.2 “Rules of the game”
The players These are the individuals, firms, entities, or actors who make decisions. In games under exogenous uncertainty, a player’s actions depend not only on the strategies played but also on external events, called “states of the world.”a Alternative actions and strategies Each time players are called upon to “play” (possibly only once), they face different alternative actions they can choose from. The collection of alternative actions at a given stage is called the action set. It is either discrete (e.g., involving choices whether or not to enter a market) or continuous (e.g., a decision on the output to supply or the size of the production capacity expansion). A strategy is a contingent a. Occasionally so-called pseudoplayers, such as nature, are used to account for or explain outside exogenous factors, such as R&D success or demand realization. Nature selects the state of the world at random regardless of the players’ actions. The probability distribution of nature’s moves is a key element of certain games, especially in option games modeling demand uncertainty.
Market Structure Games: Static
Box 3.2 (continued)
plan of actions indicating which action to take at each and every stage or state.b Information set Players condition their actions on the information they possess. An information set consists of all relevant information available to a player at the time of a decision.c Over time players generally collect more information. A key question is whether players can react to information revealed over time or if they stay committed.d Payoff structure Each strategy combination, also called strategy profile, results in a specified payoff value for each player. In equilibrium, each player pursues a strategy that maximizes its expected well-being. In a business context, ignoring agency problems, this corresponds to managers acting to maximize shareholder value. Order (sequence) of decisions In a simultaneous game, all players make their decisions at the same time so that no player observes other players’ actions before making its own decision.e If one player makes its decision after the other, having observed the earlier actions, we face a sequential or dynamic game. In such games, “time” is interpreted in terms of decision time, not necessarily real time.f b. At the start of the game, each player determines, as part of a contingent rule, what to do at each subsequent decision node, conditional on information available then. A strategy prescribes action choices at decision nodes that might not be reached during the actual (equilibrium) evolution of the game (i.e., decision nodes off the equilibrium path). A strategy profile encompasses the strategies pursued by all the players. The distinction between actions in one-stage problems and strategies as a contingent plan of actions in dynamic problems is essential to the understanding of dynamic games. c. One often distinguishes various types of information structure, such as perfect, incomplete, or imperfect information. Under perfect information, decision makers know the previous moves over the play of the game. Under incomplete information, players do not know the exact payoffs received by rivals. Such games are typically transformed into games of imperfect information by assuming that players have probabilistic information (beliefs) about some characteristics (types) of their rivals (Harsanyi transformation). d. In dynamic games, strategies that depend on calendar time but not on previous plays are called open-loop. Strategies that take account of previous plays as well are closed-loop. This distinction can substantially affect the resulting equilibrium outcome. We come back to this distinction later when discussing commitment and games of timing. e. When competing firms face such a problem under perfect information, each is aware that there is another player that is similarly aware of the potential choices of the former and the impact of its decisions on their payoffs (common knowledge). f. A two-period game where the second player faces information asymmetry concerning the move of the first player is tantamount to a simultaneous game.
83
84
Chapter 3
this issue and suggests how to refine the standard approach by incorporating behavioral considerations. There are two archetypical economic models of duopoly competition, Cournot quantity competition and Bertrand price competition. These two basic models serve to illustrate how competitive advantage can result from a better cost position or from product differentiation. They thus provide an economic foundation to Porter’s (1980) generic business strategies and enable an economic study of strategic management issues via option games. Cournot (1838) first introduced the quantity competition model. The original treatise did not explicitly rely on game theory, but Cournot (1838) roughly anticipated the equilibrium concept developed by Nash (1950) over a century later. A half century after Cournot presented his analysis of quantity competition, Bertrand (1883) criticized the model’s fundamental premise, arguing that in the real world firms do not compete in quantity but in prices. The basic Cournot model essentially assumes that each individual firm sets the quantity it wishes to provide to the market, and once all delivered quantities are aggregated, the market (acting as a “representative auctioneer”) determines the market-clearing price given the total quantity supplied by producers and the demand sought by consumers. In contrast, rather than assuming that the market price is exogenously determined, Bertrand posited that individual incumbent firms directly set their prices. The theory of industrial organization has since largely relied upon these two cornerstone models. Apart from the early criticisms of these models, economists have interpreted (for reasons explained later) Bertrand price competition as a short-run, tactical approach, while Cournot quantity competition is thought to involve long-term capacity commitments. For this reason we first present the basic Bertrand model where identical firms compete in price over homogeneous products. This model leads to what is called the Bertrand paradox, describing a situation where, due to competitive pressures, duopolists make no excess profits at all (a fortiori if fixed costs are material). Subsequently, we discuss a refinement allowing firms to produce differentiated products (differentiated Bertrand model). This extended model gives interesting insights for understanding the incentive of firms to differentiate their product offerings from those of rivals, avoiding cutthroat competition. We next consider the basic Cournot model of duopoly where firms compete in quantity
Market Structure Games: Static
Box 3.3 Interview with Reinhard Selten, Nobel Laureate in Economics (1994)
1. Your work on game theory refined existing solution concepts to select equilibria more in line with intuitive prediction. Do you think there is room for heuristics in economic analysis? My work on equilibrium refinement was guided by rational game theory and intuitions based on this approach. I think that rational game theory has to be complemented by a descriptive approach. This leaves room for heuristics but of a different kind. These heuristics involve plausible assumptions about nonoptimizing decision procedures that are within the boundaries of human cognitive abilities. 2. You are a pioneer of experimental economics. Do you believe that experimental economics has revealed limited usefulness or relevance of mathematical modeling in economic analysis? Experimental economics is very important for the development of a behavioral approach of decision and game theory. Mathematical methods are also needed for that purpose, but they are different from those used in the mainstream of economic theory. They might involve the analysis of dynamic systems, for example, learning processes and stationary concepts replacing game equilibrium. 3. Game theory generally hinges on the assumption of rationality by all players. What if people do not react rationally? Do you believe that the use of rational game theory in social sciences is necessary or appropriate? Rational game theory assumes common knowledge of the rationality of all players. When rationality is defined in terms of Bayesian decision
85
86
Chapter 3
Box 3.3 (continued)
theory, human behavior is not rational in this sense but it is not irrational. Therefore it is necessary to build a theory of bounded rationality. However, this task is far from being completed, and as long as we do not have a good substitute, rational game analysis may still be valuable because it reveals the strategic structure of a problem and may serve as a benchmark for experimental economics. We must be very skeptical, however, about the descriptive validity of rational decision and game theory.
facing the same production cost and subsequently extend the analysis to allow for (variable) cost asymmetry. 3.2.1
Bertrand Price Competition
Here, to analyze strategic interactions based on the Bertrand model of price competition, we distinguish between two cases, depending on whether firms offer identical products or not. Standard Bertrand Model Consider first a market where two symmetric firms compete over a homogeneous product, have no capacity constraint and can supply whatever quantity is required. Firms decide what price to set, and customers decide to purchase the product if the set price is lower than the value they attribute to the product (their willingness to pay). As the products offered by the rival firms are not distinguishable (they are perfect substitutes), customers have an incentive to purchase from the firm with the lowest price. Suppose that firm i sets a price pi. The best response for firm j is to set a price pj just lower than its rival’s, namely pj = pi − ε, where ε (> 0) is small, as long as its profit margin is nonnegative. Similarly firm i will then consider selling its product at a somewhat lower price pi − 2ε (< pj ) if this price is still higher than (or equal to) its marginal cost of production. Firm j will likely follow suit, and so on and on. Eventually, the rival duopolists will reduce the price they set all the way down to the marginal cost of production (assumed identical for both firms at a constant level c), at which point they stop further pointless price reduction. Consequently the duopolists will make no excess economic profit, a result analogous to the outcome found in perfectly competitive markets.
Market Structure Games: Static
87
Thus, according to the standard Bertrand model of price competition, there is no need for a large number of players to be active in an industry to create the economic conditions most beneficial to customers (i.e., perfect competition). Two firms competing in price over an undifferentiated product suffice to create a situation involving no excess economic profit for any firm and the highest possible consumer surplus. This outcome has been coined the “Bertrand paradox” in industrial organization since it challenges common business sense. One may wonder why firms bother to enter the market if they make no economic profit once they enter. A firm typically incurs a fixed cost upon entry. If a firm already operates, the other firm will not invest, however small the fixed entry cost; the market is thus likely to yield a monopoly. This standard Bertrand model rests on strong assumptions that can be relaxed but derives its appeal by illustrating cutthroat competition among a few firms. Porter’s business strategies are essentially meant to circumvent such undesirable outcome, allowing for firms to earn excess profits. To achieve this, firms compete over dimensions other than price. Differentiated Bertrand Model One noted business strategy is for firms to differentiate their product offerings. This is the differentiation strategy proposed by Porter (1980). Economists can justify this strategy thanks to the differentiated Bertrand model. Following Gibbons (1992), suppose that two firms, i and j, produce a differentiated product while facing symmetric (linear) cost6 Ci (qi ) = cqi, where qi is the quantity produced by firm i, with constant marginal cost of production c. The (modified) linear inverse market demand function for each differentiated good (allowing to charge a different price by firm i, pi) is given by pi (qi , q j ) = a − b ( qi + sq j ),
(3.1′)
where a > c ≥ 0, b > 0, and parameter s ∈ [ 0, 1) represents the substitution effect between the two differentiated product offerings.7 Products are unrelated if s = 0; here each firm can disregard the rival’s price decision since it has no impact on its own, with demand function (3.1′) reducing to the linear demand in (3.1) faced by a monopolist. If s approaches 1, 6. We formulate the demand function somewhat differently than Gibbons (1992). 7. The substitution effect captures the price change of one product for a unit change in the supply of its substitute product.
88
Chapter 3
products are undifferentiated or perfect substitutes; equation (3.1′) then reduces to the traditional linear demand faced by duopolists in the homogeneous-product case. Note that here products are horizontally differentiated, whereby the characteristics of a differentiated product appeal to a certain customer base with particular taste.8 In the case above, by inverting (3.1′), one gets the demand function9 qi ( pi , pj ) =
a (1 − s ) − pi + spj . b (1 − s 2 )
(3.7)
Firms select their prices pi , pj (≥ 0 ) simultaneously not knowing the rival’s price decision. The Nash equilibrium prices under Bertrand competition ( piB , pBj ) are such that each firm’s price choice is the best response to the other’s optimal price decision (see related box 3.4): ⎧ π i ( piB , pBj ) ≥ π i ( pi , pBj ) , ∀pi ≥ 0, ⎨ B B B ⎩π j ( pi , pj ) ≥ π j ( pi , pj ) , ∀pj ≥ 0. In the continuous case the first-order profit maximizing condition for a Nash equilibrium is a(1 − s) − 2 pi + spj + c ∂π i = 0. ( pi , pj ) = b (1 − s 2 ) ∂pi Firm i’s best-reply or reaction function is piB ( pj ) =
a (1 − s ) + c s + pj. 2 2
(3.8)
Solving the system of two equations (first-order conditions for firms i and j) with two unknowns ( pi and pj ) results in the following equilibrium prices and quantities: 1− s ⎧ B B B ⎪⎪ p = pi = pj = c + 2 − s (a − c ) ( > c ) , ⎨ a−c ⎪ q B = qiB = q Bj = . b(1 + s)(2 − s) ⎪⎩
(3.9)
8. In this case there are no commonly agreed best features for the product, just individual preferences. Products are not qualitatively ranked on a scale where customers desire the top-quality products but cannot afford them due to budget constraints. This category of differentiated products (Ferrari vs. a standard car) relates to vertical differentiation. Horizontal differentiation refers to situations where customers have taste preferences among a pool of products with comparable quality standards. 9. The resulting profit function is (twice) differentiable and concave, as can be seen from ∂ 2π i 2 =− < 0. ∂pi 2 b (1 − s 2 )
Box 3.4 Solution concepts and Nash equilibrium
Once model assumptions are laid out, one can solve a game-theoretic model using a so-called solution concept.a A solution concept is a methodology for predicting players’ behavior intended to determine the decisions (actions or strategies) that maximize each player’s payoff.b The rationality of each player is typically accepted as a common knowledge; namely each player is aware of the rationality of the other players and acts accordingly.c To obtain stronger predictions about a game outcome, one may impose assumptions beyond common knowledge of rationality.d Here equilibrium strategy profiles must form a Nash equilibrium. Consider n players. Let a i (∈ Ai ) denote firm i ’s pure strategic action (and Ai its strategy set). By convention, a −i represents the strategies played by all other players except i . When firm i chooses strategy a i and her rivals a −i , firm i receives payoff p i (a i , a − i ). A Nash equilibrium is a set of decisions—strategy profile—such that no player can do better by unilaterally changing their decision. A strategy profile (a i*,a − i*) forms a Nash equilibrium if, for any player i, i = 1, …, n,e p i (a i*, a − i*) ≥ p i (a i , a − i*)
∀a i ∈ Ai .
Equivalently, each firm i, i = 1, . . ., n, is faced with the following profitoptimization problem: max p (a i , a − i*). a i ∈Ai
We can interpret the above in terms of best-reply or reaction functions. Let R(a − i ) denote firm i ’s best response to her rivals’ strategies a −i . In Nash equilibrium each player formulates her best response to the other players’ optimal decision; that is, a i * ∈ R(a − i*). Depending on the game specification, such as the order of the play or the available information, the solution concept used may be more stringent as discussed in chapter 4. a. We do not intend here to provide a mathematical account of game theory. Readers should refer to the readings suggested at the end of this chapter for a more formal discussion of game theory. b. We are being vague on the optimality notion. While in problems involving a single decision maker optimality has an unambiguous meaning, in multiplayer decision settings “optimality” is not a well-defined concept. Its understanding is closely related to the solution concept chosen. c. The rationality assumption imposes an important limitation in situations where pride and irrationality play a role. However, building up a reputation as being irrational or unpredictable can also make strategic sense: One can turn such reputation to its advantage by altering opponents’ beliefs. Reagan’s foreign policy toward the Soviet Union might be interpreted in this light. Similarly a firm that has a reputation to wage war with any contestant imposes a credible threat on potential entrants who might think twice before entering. d. Rationalizability, introduced by Bernheim (1984) and Pearce (1984), is considered a fundamental solution concept. Based on the weak assumption that payoffs and players’ rationality are common knowledge, it predicts that a player will not play a strategy that is not a best response to some beliefs about her opponents’ strategies. By iteration, we can narrow down the set of strategies that could be reasonably played (so-called rationalizable strategies). By design, rationalizability makes very weak predictions: the set of rationalizable strategies can be large since it contains all strategy profiles that cannot be excluded based on the assumption of common knowledge of rationality. Nash’s (1950b) equilibrium concept is usually preferred for being more restrictive. e. We consider, here, pure strategies. An equivalent definition exists for mixed strategies, namely convex combinations of pure strategies. By employing mixed strategies, one ensures that (at least) one Nash equilibrium exists (Nash 1950b).
90
Chapter 3
Thus, in differentiated Bertrand–Nash equilibrium firms set a price, pB, strictly higher than the marginal cost of production, c, earning excess profits. This contrasts to the previous standard Bertrand case involving perfect substitutes (homogeneous products). Moreover, in equilibrium, prices for both differentiated products are equal ( piB = pBj ); this results from the fact that products are horizontally differentiated and that there is (by assumption) no quality premium for one of the products over the other. Finally, the equilibrium price decreases with the degree of substitutability s (∂pB ∂s = − (a − c ) ( 2 − s ) < 0). From (3.9) firm profits are
π B = π iB = π Bj =
1− s ⎛ a − c⎞ ⎜ ⎟ b (1 + s ) ⎝ 2 − s ⎠
2
(> 0) .
(3.10)
Thus, for products that are close to being perfect substitutes (s → 1), the excess profits for the duopolists become zero, a result equivalent to the outcome obtained in the standard Bertrand price competition case. Clearly, firms have an incentive to differentiate their product offerings to soften price competition, departing from the undesirable Bertrand paradox where no firm makes excess profits. This is in line with most marketing and strategic management practices.10 Example 3.2 Differentiated Price Competition Assume the linear market demand function of equation (3.1′) with parameters a = 24, b = 2 3, s = 1 2 and constant variable production cost c = 3. From (3.7) the demand functions are given by ⎧ qi ( pi , pj ) = 24 − 2 pi + pj , ⎨ ⎩q j ( pi , pj ) = 24 − 2 pj + pi . From equation (3.8), firm i’s reaction function is piB ( pj ) = 7.5 +
1 p j. 4
Firm j’s reaction function is obtained symmetrically. In (differentiated) Bertrand price competition, reaction functions are upward-sloping. In Nash equilibrium, equilibrium prices, quantities, and profits, obtained from equations (3.9) and (3.10), are pB = 10, q B = 14, and π B = 98, respectively. This situation is illustrated in figure 3.4. 10. For an economic discussion of the advisable degree of differentiation, refer to Tirole (1988, pp. 286–87).
Market Structure Games: Static
91
Price by firm j ( pj ) 20
Firm i’s reaction function
piB(pj )
15
10
E
Firm j’s reaction function
pjB( pi)
5
0 0
5
10
15
20
Price by firm i (pi) Figure 3.4 Upward-sloping reaction functions in differentiated Bertrand competition a = 24, b = 2 3, s = 1 2 , and c = 3
The differentiated Bertrand model above is fairly descriptive of many real-world rivalry situations in the short term. This model underscores that competition is not just about price but that additional parameters may come into play, such as heterogeneous tastes among customers. The main alternative to price competition is quantity competition represented by the Cournot model.11 Although Bertrand price competition seems more descriptive of certain real-world situations in the short run, Kreps and Scheinkman (1983) suggest that the implicit assumption of a “market auctioneer” in the Cournot model is not necessary. Cournot 11. In Cournot quantity competition, producers simultaneously and independently make production quantity decisions. The output is brought to the market and a “market auctioneer” sets the market-clearing price. In (differentiated) Bertrand price competition, producers simultaneously and independently set prices and there is no need for a price-setting party.
92
Chapter 3
outcomes may also result from a two-stage competition game where duopolists first make a capacity choice, and once these capacity choices become common information, firms set prices as in Bertrand price competition under capacity constraints.12 The two-stage model of Kreps and Scheinkman (1983) results in Cournot-like outcomes and may be more realistic than strict Bertrand price competition in situations involving long-term investments and constrained capacities. For this reason capacity (quantity) is often thought of as a long-term strategic variable, while price is a short-run, tactical action variable. Most of the models discussed in subsequent chapters deal with long-horizon investment problems and therefore build upon the Cournot quantity setting. 3.2.2
Cournot Quantity Competition
Cournot’s (1838) classic quantity competition model characterizes industries in which firms set production schedules in advance and cannot alter them in the short run. The price-setting process is driven by the capacity or quantity chosen by the active firms in the industry.13 Firms produce a homogeneous good. We discuss next two variants of the Cournot duopoly model. We consider first the situation where firms have symmetric costs, and then relax the symmetric cost assumption. A comparison of these two models helps illustrate why firms have an incentive to be cost leader in quantity competition involving a homogeneous good. Cost Symmetry Consider two identical firms (i and j) that face the same, constant unit variable production cost c (≥ 0 ). The linear (inverse) demand function, driven by the total quantity supplied in the market Q ( = qi + q j ), is given by p(Q) = a − bQ,
(3.1)
with a > c and b > 0. Firms’ strategies consist in selecting an output that maximizes profit.14 Equivalently, one can assume that they maximize net 12. From this perspective we can consider the (equilibrium) profit functions in Cournot competition as reduced-form profit functions in which later price competition has been subsumed. Kreps and Scheinkman (1983) show this property in the case where firms face a concave demand function and cannot satisfy all demand according to the “efficientrationing rule.” Investment in new capacity units must be costly for this result to hold. 13. The ex ante chosen production schedules are hard to reverse, so firms cannot influence the market-clearing price-setting process in the short-run. 14. An important assumption of the Cournot model is that firms invest simultaneously and therefore do not observe the strategy chosen by their rivals. This is a case of complete information in a simultaneous game. The appropriate solution concept is the “simple” Nash equilibrium.
Market Structure Games: Static
93
present value (NPV) where value is given by the perpetuity of profits (π k , where k is the risk-adjusted discount rate).15 Firm i’s profit, resulting from the action profile ( qi , q j ), is given by16 p i ( qi , q j ) = [ p (Q) − c ] qi.
(3.11)
As in the monopoly case there is a trade-off between increasing the quantity supplied (qi) and receiving a lower price (and profit margin) because of the upsurge in total industry quantity. This time, however, the firm’s own output choice is not the only factor influencing the pricesetting process; the rival influences it as well. The Nash equilibrium outputs ( qiC , qCj ) are such that each firm’s quantity choice is the best response to the other’s optimal quantity decision. Taking the rival’s quantity choice as given, the first-order condition for firm i’s profit maximization (∂π i ∂qi = 0) yields a − 2bqiC − bq j = c,
(3.12)
or qiC (q j ) =
1⎛a−c − q j ⎞⎟ . ⎜ ⎠ 2⎝ b
(3.13)
Firm j’s first-order profit maximizing condition is obtained symmetrically. If one of the firms does not produce (i.e., if q j = 0), the sole active firm i will supply in equilibrium QM = (a − c ) 2b, as in monopoly. In quantity competition, the reaction functions of duopolists given by (3.13) are downward sloping (i.e., decreasing in rival’s capacity-setting action), as depicted in figure 3.5. The Nash equilibrium outputs can be determined by solving the system of the two equations (3.12) (for firms i and j) with two unknowns (qiC and qCj ) or by substituting firm i’s reaction function from (3.13) into firm j’s (and reciprocally). The equilibrium is found at the intersection (point E) of the two reaction functions: qiC ≡ qiC (qCj ( qiC )) =
1⎛a−c 1⎛a−c − ⎜ − qiC ⎞⎟ ⎞⎟ . ⎜ ⎠⎠ 2⎝ b 2⎝ b
Since symmetric firms presumably produce the same output, the Cournot–Nash equilibrium output by each firm is 15. We assume that firms settle in steady state and that there is no (expected) growth for the underlying profit flow π . 16. The profit function π i (⋅, ⋅) is concave and twice continuously differentiable in qi.
94
Chapter 3
Quantity supplied by firm j (qj)
( 0; (a−c )/ b)
Firm i’s reaction function
( 0; ( a−c ) / 2b) (qiC ; qjC ) E Firm j’s reaction function
(( a−c ) / 2b; 0 )
(( a−c )/ b; 0 ) Quantity supplied by firm i (qi)
Figure 3.5 Downward-sloping reaction functions in (symmetric) Cournot quantity competition
qC = qiC = qCj =
a−c . 3b
(3.14)
The total industry output then is QC = qiC + qCj =
2 ⎛ a − c⎞ ⎜ ⎟. 3⎝ b ⎠
(3.15)
Two observations are of particular interest. First, in Cournot duopoly each individual firm produces less than does a monopolist firm: qC ≤ QM
⎛ 1 a − c ≤ 1 a − c⎞. ⎜⎝ ⎟ 3 b 2 b ⎠
Second, firms collectively produce more than does a monopolist: QC ≥ QM
⎛ 2 a − c ≥ 1 a − c⎞ . ⎜⎝ ⎟ 3 b 2 b ⎠
Consequently, given the downward-sloping demand (∂p ∂Q < 0), the market-clearing price in Cournot duopoly is lower than in monopoly.
Market Structure Games: Static
95
One can readily deduce the equilibrium price and profit. The equilibrium market-clearing price in Cournot duopoly, pC, obtained by substituting the equilibrium quantity of equation (3.15) into demand equation (3.1), is pC = c +
a−c 3
(> c ) .
(3.16)
The equilibrium profit for firm i ( j) is
π C = π iC = π Cj =
(a − c )2 9b
.
(3.17)
Due to the lower individual output and lower market-clearing price, a Cournot duopolist earns lower profits than a monopolist (π iC ≤ π iM ). From a social-welfare viewpoint, Cournot duopoly is better than monopoly as the total quantity supplied is higher, the equilibrium marketclearing price lower, and the profit or producer surplus lower.17 What would happen if the duopolists could collaborate to improve their joint profits? Suppose that firms could (tacitly) collude, choosing to maximize their joint profit instead of their individual profits. In this case the symmetric duopolists would select the optimal cumulated quantity, Q, and then divide up the higher joint-profit pie. The optimal total industry output selected by the cartel would be the monopoly quantity, QM. Each firm could, for example, produce half of it and earn half of the monopoly rent. Since π M 2 ≥ π iC, a collusive agreement seems preferable at first sight. This strategy profile is not stable, however. The contract ruling the cartel is not self-enforceable because each firm has an incentive to cheat, increasing the quantity it supplies to benefit from a higher price.18 Firms would increase their output until the Cournot–Nash equilibrium output ((a − c ) 3b ; (a − c ) 3b) is reached. This is the only stable equilibrium in this simultaneous quantity game. Collusion is not likely 17. This efficiency result is based on the premise that fixed costs are immaterial. The presence of material fixed costs might substantially alter this result, since a natural monopoly might turn out to be socially optimal. 18. To demonstrate the instability of the collaborative outcome, consider first the optimal reaction of the deviating party (e.g., firm i). Substituting half the monopoly quantity given in (3.2) into firm i’s reaction function in (3.13), the best reply obtains qiC (Q M 2 ) = 3 (a − c ) 8b . The resulting market-clearing price is p = c + 3 (a − c ) 8 . The profit for the deviating party is higher than half the monopoly profit, creating an incentive to deviate from the cartel agreement:
πD =
9 πM ⎛ πM ⎞ ⎜> ⎟. 8 2 ⎝ 2 ⎠
96
Chapter 3
to occur since each firm has an incentive to deviate, being pulled as in a prisoner’s dilemma to the inferior Nash equilibrium outcome. Collusion will thus not occur in such a static one-shot duopoly game. This ultimately benefits consumers who can purchase the product at a lower price.19 Cost Asymmetry Suppose now that the two firms have different marginal costs ci ≠ c j, with firm i’s cost function given by Ci (qi ) = ci qi , ci ≥ 0. If ci < c j , firm i produces the (homogeneous) good more efficiently than firm j, enjoying a cost-leader advantage. Assuming the same (inverse) demand function as before, firm i’s profit function is p i (Q) = ( p (Q) − ci ) qi. Due to strategic interaction, firm i’s quantity choice ultimately depends on its own cost ci as well as on its rival’s cost c j. The cost differential, c j − ci (≠ 0 ), does matter. From the first-order profit-maximizing condition, firm i’s reaction function is qiC (q j ) =
1 ⎛ a − ci − q j ⎞⎟ . ⎜ ⎠ 2⎝ b
(3.18)
Substituting the reaction functions (into each other), firm i’s equilibrium quantity is20 qiC =
a − 2ci + c j . 3b
(3.19)
In equilibrium, firm i produces more when its rival is cost disadvantaged or the latter’s marginal production cost is increased (∂qiC ∂c j > 0). The resulting industry equilibrium price is pC =
a + ci + c j . 3
(3.20)
Firm i’s resulting equilibrium profit is
π = C i
(a − 2ci + c j )2 9b
.
(3.21)
Useful insights can be deduced from the latter expression. The cost leader (here firm i) earns higher profits in the market than its less efficient rival. This provides an economic rationale for the cost leadership strategy proposed by Porter (1980). As the firm’s profit decreases in its 19. We discuss later how (tacit) collusion can sustain itself as stable industry equilibrium in certain repeated games. 20. The formulas for firm j are analogous, meaning one can obtain firm j’s quantity by substituting j for i and i for j in the expression above.
Market Structure Games: Static
97
own cost (∂π iC ∂ci < 0), the cost leader would further benefit from an improved cost position. An alternative, indirect tactic to achieve cost leadership is to increase the rival’s cost (∂π iC ∂c j > 0), for example, by limiting its access to scarce resources it needs. 3.2.3
Strategic Substitutes versus Complements
As noted earlier, reaction functions may be downward sloping (as in the Cournot quantity competition model) or upward sloping (as in differentiated Bertrand price competition). This distinction between these two kinds of reactions is at the core of the notion of strategic substitutes versus strategic complements introduced by Bulow, Geanakoplos, and Klemperer (1985). The notions of strategic substitutes and complements are meant to capture how competitors are expected to react when a firm changes its strategic decision variables, such as price or quantity. This distinction is informative on whether a firm reacts to its rivals’ strategic actions in a reciprocating or in a contrarian way. The notion of commitment—analyzed extensively in industrial organization—rests on these types of reaction functions. When reaction functions are downward sloping, the actions are strategic substitutes. Let α i ∈ Ai be firm i’s strategic action variable (with Ai its action set) and Ri (α j ) its best reply to rival action αj.21 The general form of the equilibrium in case of strategic substitutes is depicted in figure 3.6. In figure 3.6a, a particular case of interest is the reaction function in Cournot quantity competition. Assuming a linear (inverse) demand function as in equation (3.1) and a linear cost function, Ci (qi ) = cqi with c constant, firm i’s reaction function is obtained in (3.13) as qiC (q j ) =
a−c 1 − qj. 2b 2
Since ∂qiC ∂q j < 0, if a Cournot duopolist increases its output, its rival will do the opposite by reducing it, a contrarian reaction. Cournot quantity competition is a game where actions are strategic substitutes. In case of strategic complements, competitive reactions are similar or reciprocating. The distinction again relates to the shape (slope) of the reaction function. When reaction functions are upward sloping, as in figure 3.6b, the firms’ actions are strategic complements or reciprocal. In the (differentiated) Bertrand model, we deal with strategic complements 21. We assume that the firms’ reaction functions are characterized by slopes of the same sign, meaning both are downward sloping or both upward sloping.
98
Chapter 3
aj
R i (a j) a j*
E
R j (a i )
a i*
ai
(a)
aj
R i (a j)
a j*
E'
R j (a i )
a i*
ai
(b) Figure 3.6 Downward and upward-sloping reaction functions compared: strategic substitutes versus complements (a) Strategic substitutes or contrarian reactions ( ∂Ri ∂α j < 0 ); (b) strategic complements or reciprocating reactions ( ∂Ri ∂α j > 0 )
since a reduction in price by a firm is an optimal response to its competitor’s price cut. If the inverse demand function is linear as in equation (3.1′), firm i’s reaction function is given by (3.8) above, namely piB ( pj ) =
a (1 − s ) + c s + pj . 2 2
Since ∂piB ∂pj ≥ 0, when a Bertrand duopolist decreases its price, its rival will follow suit and decrease its price as well, a reciprocating reaction. For perfect substitutes (s → 1), such reciprocating reactions can lead
Market Structure Games: Static
99
to the Bertrand paradox, where firms end up waging a fierce price war and make zero economic profits (as in perfect competition). Equilibrium outcomes in case of strategic substitutes vs. complements are illustrated as outcomes E and E ′ in figure 3.6. The slope of the reaction function matters. Whether actions are strategic substitutes or complements can greatly affect the optimal decisionmaking in such settings. Following Gal-Or (1985), when reaction functions are downward sloping (involving strategic substitutes or contrarian reactions), each firm has an incentive to take the lead, acting as a Stackelberg leader and enjoying a first-mover advantage. This can lead, however, to situations involving preemption as firms strive to seize this advantage ahead of competitors. By contrast, in case of strategic complements or reciprocating actions, the Stackelberg follower is better off, benefiting from a second-mover advantage. For instance, under price competition no one has an incentive to set its price first if the follower can undercut it later.22 This kind of strategic interaction could result in a war of attrition where firms compete to be the last to make a move, each firm doing its utmost not to be considered a coward (chicken game). 3.3
Oligopoly and Perfect Quantity Competition
In the previous sections we analyzed industry structure where only two firms are incumbent. Although duopoly situations exist (e.g., the competition between Boeing and Airbus in the aircraft manufacturing industry), there is often more than two players operating in a given industry. Numerous examples of such industries abound. A case in point is the automotive sector, with giants such as Volkswagen (including Audi, Porsche, and Seat), Toyota, Ford, BMW, Daimler, and GM. The economic analysis of such oligopolistic structures can provide interesting insights as well. The basic quantity duopoly setup analyzed by Cournot (1838) may be refined to consider more than two competitors. At first we analyze below an oligopoly with cost asymmetry. Subsequently we discuss the simpler case of oligopoly under cost symmetry (as a special case). We confirm that as the number of competitors substantially increases, the Cournot oligopoly outcome tends toward the perfect competition benchmark. This analysis is useful later in the analysis of option games in both discrete and continuous time. 22. A firm is better off to defer its decision and select its own price until after having full knowledge of the price charged by the leader.
100
Chapter 3
Assume n oligopolist firms competing in quantity over a homogeneous product. Each firm i faces a linear demand function as in equation (3.1) and marginal production cost ci. Without loss of generality, firms are ranked in cost advantage with firm 1 having the largest cost advantage or lowest cost c1. Firm i’s profit function is given by
π i (qi , Q− i ) = [ p (qi , Q− i ) − ci ] qi ,
i = 1, . . ., n,
where Q− i stands for the quantity produced collectively by all other suppliers except firm i, with Q = qi + Q− i . To obtain the Cournot–Nash equilibrium, one has to deduce the optimal production strategy profile (q1C , . . ., qnC ) such that each firm i, i = 1, . . ., n, maximizes profit p i ( qi , Q−Ci ) , considering other rivals’ choices as given. This leads to the first-order condition: MRi ( qiC , Q−Ci ) = qiC ×
∂p C C (qi , Q− i ) + p (qiC , Q−Ci ) = ci , ∂qi
i = 1, . . ., n. (3.22)
In the linear demand case, marginal revenue is MRi (qi , Q− i ) = a − 2bqi − bQ− i . In the general Cournot oligopoly with n asymmetric firms, we must solve the following system of n equations with n unknowns: ⎧ a − 2bq1C − b (QC − q1C ) = c1 , ⎪ ⎪⎪ C C C ⎨ a − 2bqi − b (Q − qi ) = ci , ⎪ ⎪ C ⎪⎩a − 2bqn − b (QC − qnC ) = cn . Summation leads to a total quantity for the entire market of n ⎞⎛a−c⎞ QC (n) = ⎛⎜ , ⎝ n + 1⎟⎠ ⎜⎝ b ⎟⎠
(3.23)
where c ≡ ∑ j = 1 c j n is the average (variable) production cost in the industry. Denote by c− i ≡ ∑ j ≠ i c j (n − 1) the average production cost for all other firms except i. Individual firm quantities are obtained by substituting the total industry quantity of (3.23) into each equation of the system above: n
Market Structure Games: Static
qiC (n) =
101
1 ⎛ a − nci + ( n − 1) c− i ⎞ ⎜ ⎟⎠ , n + 1⎝ b
i = 1, . . ., n .
(3.24)
The equilibrium price obtains from (3.1) and (3.23) as pC ( n) = c +
a−c n+1
(> c1 ).
(3.25)
Regardless of how many firms operate in the market, the most costadvantaged firm (absolute cost leader) always enjoys a price strictly higher than its variable cost c1.23 The resulting profit for firm i is p iC ( n) =
(a − nci + (n − 1) c− i )2
1
(n + 1)2
b
,
i = 1, . . ., n .
(3.26)
It can be seen that profits are increasing in the cost advantage. Moreover, a firm’s profitability depends on its production cost, its market share, and the price elasticity of demand.24 The special case of cost symmetry (with ci = c) has clear-cut insights. The equilibrium quantity, obtained from equation (3.24), is the same for each symmetric firm: qC ( n) =
1 ⎛ a − c⎞ ⎜ ⎟, n + 1⎝ b ⎠
i = 1, . . ., n.
(3.27)
The equilibrium price, resulting from equation (3.25), is given by pC (n) = c +
a−c n+1
( > c ).
(3.28)
The expression above suggests that even for a large oligopoly (n large), the equilibrium price margin, pC − c, remains positive. From (3.26), the profit for each identical oligopolist firm is
π C (n) =
1
(n + 1)2
( a − c )2 b
,
i = 1, . . ., n.
(3.29)
23. This holds as long as the demand intercept exceeds the average unit cost in the industry. 24. Let si ≡ qiC QC denote firm i’s (equilibrium) market share and recall the price elasticity of demand e p in equation (3.5). The first-order condition in (3.22) yields firm i’s Lerner index: Li ≡ ( pC − ci ) pC = − si ε p . This measure proxies for firm i’s profit margin and depends on ci , si , and ε p .
102
Chapter 3
In the special case when there is only one firm operating (n = 1), the previous monopoly results in equations (3.2) to (3.4) obtain. In duopoly (n = 2), we obtain the symmetric Cournot duopoly results of equations (3.14) to (3.17). As the number of active firms is greatly increased (n → ∞), the quantity produced by any one firm becomes negligible, the market-clearing price approaches marginal production cost, c, and the economic profit of an individual firm approaches zero. These outcomes confirm the well-known results in perfect competition: firms make no excess profits and set prices at marginal cost. The presence of fixed production or investment costs may affect the number of firms operating in the sector. 3.4
Market Structure under Incomplete Information
The standard Cournot model assumes that duopolists know perfectly the cost structure of their rivals; their profit-maximizing quantities are derived as a function of the known variable costs. This assumption might not hold in certain industry settings characterized by information asymmetry. Suppose that firm j does not know for sure firm i’s cost but that “nature” will reveal it with certain probability. For example, firm i may have invested in a new innovative process that could alter its cost structure if its R&D efforts succeed (with probability P). The rival’s cost can be either low (cL) with probability P or high (cH ) with probability 1 − P (cL < cH).25 That is, firm j has probabilistic beliefs about its rival’s type (cost). Suppose also that firm i can perfectly observe what “nature” decided concerning its own cost (e.g., the outcome of its own R&D efforts), as well as its rival’s cost (e.g., the rival uses the prevalent production technology). Firm j is aware of the information asymmetry in favor of firm i. Once firm i knows its own cost, the two firms choose simultaneously their capacity or output. Figure 3.7 depicts this situation. In selecting its optimal quantity, firm j no longer maximizes its deterministic profit function but instead maximizes its expected profit function, taking into account the uncertainty it faces concerning firm i’s type or cost. Firm j knows that if the low-cost outcome (cL) occurs (with probability P), firm i’s reaction function would be similar to equation (3.18) in the Cournot game: qiC ( q j , cL ) =
1 ⎛ a − cL − q j ⎞⎟ . ⎜⎝ ⎠ 2 b
25. Subscript L stands for low- and H for high-cost type.
(3.30)
Market Structure Games: Static
103
Nature
cL (low cost)
Firm i qi (cL ) = qL
cH (high cost)
Firm i qi (cH) = qH
Firm j
qj
Firm j
qj
Figure 3.7 Extensive form of Cournot competition under asymmetric information The dashed box indicates that firm j has two nodes in its information set and is unable to anticipate its rival’s quantity decision.
However, in case the high-cost outcome (cH ) occurs (with probability 1 − P), firm i’s reaction function is instead qiC ( q j , cH ) =
1 ⎛ a − cH − q j ⎞⎟ . ⎜ ⎠ 2⎝ b
(3.31)
Firm j’s expected profit reflects its belief (probabilistic distribution) about firm i’s possible production costs. It is given by26
π j ( q j , qL , qH ) ≡ E [π j (qi , qL , qH )] = P × π j ( q j , qL ) + (1 − P ) × π j ( q j , qH ) ,
(3.32)
where qL and qH stand for firm i’s quantity choice as a function of its low or high marginal cost. Firm j’s (Bayesian Nash) equilibrium strategy consists in selecting its output q j so as to maximize its above expected profit in (3.32), considering its rival’s optimal decision as given. From the first-order profit optimization condition (and substitution of equations 26. Firm j ’s profit function is differentiable and concave in its own strategic action q j ( ∂ 2π j ∂q j 2 < 0 since b > 0). The first-order condition is both necessary and sufficient for a maximum to obtain.
104
Chapter 3
(3.30) and (3.31) into firm j’s reaction function) firm j’s equilibrium quantity is27 qj * ≡
a − 2c j + ci , 3b
(3.33)
where ci = PcL + (1 − P ) cH is the mean (expected) value of firm i’s cost. This result is similar to the equilibrium outcome in Cournot quantity competition under complete information, except that here we utilize firm i’s expected cost (ci). Firm i faces no information asymmetry and may adapt the quantity it produces to its actual production cost realization (cL or cH ). But firm j cannot. Firm i’s equilibrium quantities, depending on nature’s move, are obtained by substituting firm j’s equilibrium quantity from (3.33) into the reaction functions (3.30) and (3.31). This gives ⎧ q * = qC q *, c = qC − 1 − P c − c ( H L) i ( j L) L ⎪ L 6b ⎨ ⎪qH * = qiC ( q j *, cH ) = qLC + P (cH − cL ) ⎩ 6b
(≤ qLC ) , ( ≥ qCH ) ,
(3.34)
where qLC = ( a − 2cL + c j ) 3b and qCH = ( a − 2cH + c j ) 3b are the asymmetric complete-information Cournot quantities for firm i depending on whether it has low or high cost. The equilibrium quantities for firm i are not the same as the ones derived for the standard Cournot model (under complete information), even though firm i has the same information as before; that is, it knows both its cost and its rival’s. The difference arises from the fact that firm j has an informational disadvantage and that firm i knows it. In the favorable case where firm i has lower cost cL, the total quantity supplied in the marketplace, Q (cL ), is higher under asymmetric information than under complete information. Indeed, from equations (3.33) and (3.34), we have Q (cL ) = q j * + qL* = QC (cL ) +
1− P ( c H − cL ) 6b
( ≥ QC (cL )),
(3.35)
27. The first-order derivative of firm j’s profit with respect to its own quantity (holding firm i’s quantity choices qL and qH fixed) is ∂p j ∂q j = a − 2bq j − bqi − c j , with qi ≡ PqL + (1 − P ) qH . From the first-order condition, qCj (qi ) =
1 ⎛ a − cj ⎞ − qi ⎟ . ⎜ ⎠ 2⎝ b
Equation (3.33) obtains from substituting firm i’s reaction functions (3.30) and (3.31) in the expression above.
Market Structure Games: Static
105
where QC (cL ) = qCj + qLC = ( 2a − c j − cL ) 3b is the total industry output in the complete-information case obtained by summing the quantities for firms i and j in equation (3.19). As the inverse demand function is downward sloping, the market-clearing price is lower in the asymmetricinformation case since Q(cL ) ≥ QC (cL ). Firm i would have been better off if its rival had known its cost.28 Due to the combined effect of lower price and lower quantity for firm i, the informed party (i) is worse off as a result of the rival’s information disadvantage in the favorable cost situation (cL).29 This rests on the fact that firm j forms a higher expectation on i’s cost (than the actual low cost cL) and consequently produces more compared to the situation where firm j actually knows the cost realization. Since rivals’ actions are strategic substitutes or contrarian, firm i will produce less as a best reply to firm j’s oversupply. In the opposite (unfavorable) case where firm i turns out to have a high production cost (cH ), the effects are reversed. Firm i produces more than under complete information since its rival, firm j, believes it has a lower average cost. The market-clearing price is higher, and the informed party makes larger excess profit.30 This underscores that an informed 28. Given the linear demand function of equation (3.1) and the total industry output in (3.35), one obtains the market-clearing price in the asymmetric-information case: p (Q (cL )) = pLC −
1− P ( c H − cL ) 6
(≤ pLC ),
where pLC = ( a + c j + cL ) 3 from equation (3.20). 29. Firm i’s equilibrium profit is p L = p i ( cL ) =
1 ⎡ ⎛ a + c j − 2 cL ⎞ 1 − P (cH − cL )⎤⎥ ⎜ ⎟⎠ − 3 6 b ⎢⎣⎝ ⎦
2
(≤ p LC ) .
The equilibrium profit in the complete-information Cournot case, π LC = (a + c j − 2cL ) 9b , comes from (3.21). 30. In this case total industry output is obtained from equations (3.33) and (3.34): 2
Q (cH ) = q j * + qH * = QC (cH ) −
P (cH − cL ) 6
(≤ QC (cH )) ,
where QC (cH ) = ( 2a − c j − cH ) 3b is the total industry output in the complete-information case. The equilibrium price in the asymmetric-information case is p (Q (cL )) = pHC +
P ( c H − cL ) 6
(≥ pHC )
with pLC = (a + c j + cH ) 3 . Firm i’s equilibrium profit is obtained from the above and equation (3.34) as
π H = π i ( cH ) =
1 ⎡ a − 2cH + c j P ⎤ + ( c H − cL ) ⎥ 3 6 b ⎣⎢ ⎦
2
(≥ π CH )
where the equilibrium profit of the high-cost firm, π CH = (a − 2cH + c j ) 9b, is obtained from equation (3.21). 2
106
Chapter 3
Table 3.2 Equilibrium outcomes under various industry structures A: Cost symmetry Industry structure
Firm i ’s quantity ( qi*)
Industry quantity (Q*)
Firm i’s profit
Monopoly
1 ⎛ a − c⎞ ⎜ ⎟ 2⎝ b ⎠
Cournot duopoly
1 ⎛ a − c⎞ ⎜ ⎟ 3⎝ b ⎠
1 ⎛ a − c⎞ ⎜ ⎟ 2⎝ b ⎠ 2 ⎛ a − c⎞ ⎜ ⎟ 3⎝ b ⎠
1 (a − c ) 4 b 2 1 (a − c ) 9 b
Stackelberg leadera
1 ⎛ a − c⎞ ⎜ ⎟ 2⎝ b ⎠
Stackelberg followera
1 ⎛ a − c⎞ ⎜ ⎟ 4⎝ b ⎠ 1 ⎛ a − c⎞ ⎜ ⎟ n + 1⎝ b ⎠
Cournot oligopoly ( n players) Bertrand duopoly (differentiated)
1
2
1 (a − c ) 4 b
2
3 ⎛ a − c⎞ ⎜ ⎟ 4⎝ b ⎠
1 (a − c ) 16 b 2 1 ⎛ a − c⎞ ⎜⎝ ⎟⎠ b n+1 2
n ⎛ a − c⎞ ⎜ ⎟ n + 1⎝ b ⎠ ⎛ a − c⎞
⎜ ⎟ (1 + s ) (2 − s) ⎝ b ⎠
2
⎛ a − c⎞
⎜ ⎟ (1 + s ) (2 − s) ⎝ b ⎠
⎛ ⎞ ( a − c )2 1 − s2 b ⎝⎜ (1 + s )2 ( 2 − s )2 ⎠⎟
B: Cost asymmetry Industry structure
Firm i ’s quantity ( qi*)
Industry quantity (Q*)
Firm i’s profit
Monopoly
1 ⎛ a − ci ⎞ ⎜ ⎟ 2⎝ b ⎠
1 ⎛ a − ci ⎞ ⎜ ⎟ 2⎝ b ⎠
1 (a − ci ) 4 b
Cournot duopoly
1 ⎛ a − 2ci + c j ⎞ ⎜ ⎟⎠ 3⎝ b 1 ⎛ a − 2ci + c j ⎞ ⎜ ⎟⎠ 2⎝ b 1 ⎛ a − 2ci + c j ⎞ ⎜ ⎟⎠ 4⎝ b 1 a − nci + (n − 1)c− i n+1 b
2a − ( ci + c j ) 3b
1 (a − 2ci + c j ) b 9 2 1 (a − 2ci + c j ) b 4 2 1 (a − 2ci + c j ) b 16
Stackelberg leadera Stackelberg followera Cournot oligopoly ( n players)
3 ⎛ a − ci ⎞ ⎜ ⎟ 4⎝ b ⎠ n ⎛a−c⎞ ⎜ ⎟ n + 1⎝ b ⎠
2
2
1 ⎛ a − nci + (n − 1)c− i ⎞ ⎜ ⎟⎠ b⎝ n+1
2
Note: p (Q) = a − bQ with Q = qi + q j ; s is the substitutability parameter in p (Q) = a − b ( qi + sq j ) ; the cost function is Ci (qi ) = cqi (symmetry) or Ci (qi ) = ci qi (asymmetry). c = ∑ nj =1 c j n and c− i = ∑ j ≠i c j (n − 1). a. The outcomes in case of the Stackelberg game are derived in chapter 4.
Market Structure Games: Static
107
party cannot always benefit from its informational advantage when strategic interactions come into play. Rivals form beliefs about the informed party’s cost type and may over- or under-react as a result of their informational disadvantage. These inaccurate beliefs can sometimes prove detrimental for the better-informed firm. Conclusion In this chapter we provided an overview of static market structure games. We first discussed the monopoly benchmark. We then gave applications illustrating how noncooperative game theory can provide powerful insights about real-world problems. We considered several static models involving price and quantity competition, and examined how such models motivate certain generic competitive strategies of being a cost leader or differentiating from one another. We analyzed the impact of the number of players in a given industry on an individual firm’s profit, as well as potential effects of asymmetric information on the industry structure. Several equilibrium outcomes discussed in this chapter are summarized in table 3.2, panels A and B, for cost symmetric and cost asymmetric firms, respectively. These tables may be useful for later reference. The next chapter extends this analysis to dynamic models of oligopoly, highlighting that, in the long term, a competitive stance such as commitment or collaboration may be both value-enhancing for the individual firms and sustainable as industry equilibrium. Selected References Osborne (2004) is a good introductory textbook on game theory. Tirole’s (1988) appendix provides a short, concise manual on noncooperative game theory. Averted readers might prefer the rigorous and more advanced treatment of game theory offered by Fudenberg and Tirole (1991). Besanko et al. (2004) provide a good overview of industrial organization issues focusing on the models’ strategic insights. Tirole (1988) is considered a key reading on industrial organization.
108
Chapter 3
Besanko, David, David Dranove, Mark Shanley, and Scott Schaefer. 2004. Economics of Strategy, 3rd ed. New York: Wiley. Fudenberg, Drew, and Jean Tirole. 1991. Game Theory. Cambridge: MIT Press. Osborne, Martin J. 2004. An Introduction to Game Theory. New York: Oxford University Press. Tirole, Jean. 1988. The Theory of Industrial Organization, Cambridge: MIT Press.
4
Market Structure Games: Dynamic Approaches
In chapter 3 we dealt with benchmark models of market structure from a static perspective. These static games allow predicting the short-run impact of a firm’s actions on its rivals. The current chapter extends this discussion to dynamic approaches. These allow the inclusion of long-term strategy formulations and discussion of phenomena that require more dynamic thinking such as commitment and collaboration. Dynamic games make explicit how today’s decisions may affect or induce distinct future strategic situations. For example, if one adopts today an aggressive stance toward a rival, this behavior might induce the rival to act aggressively in the future. When assessing the benefit the firm could gain from an aggressive stance, it has to figure out what is the potential long-term impact of its decision today. One way to do this is to “look forward and reason backward” (Dixit and Nalebuff 1991). This dynamic way of thinking consists in figuring out what will be the likely future reaction in the marketplace to today’s firm actions. Once this is understood, one can assess alternative actions based on the impact they may have in the future—possibly rejecting certain initiatives that appear beneficial today but may have a negative long-term impact. This forms the underlying logic behind backward induction and subgame perfection used in dynamic games under perfect information. These notions require that for every history (or subgame) players act optimally as part of Nash equilibrium and that they make their early decisions knowing that all future actions will be optimal given the current set of information. Based on these notions, we discuss below two streams of models dealing with multiplayer decision-making in multistage settings. In section 4.1 we elaborate on commitment and discuss how limiting one’s own flexibility might create strategic value for the committing firm, thereby contradicting standard real options thinking that suggests that flexibility is always of value. Subsequently, in section 4.2, we discuss
110
Chapter 4
situations when firms may find it beneficial to cooperate with their rivals and have no long-term incentive to “cheat” on them. 4.1
Commitment Strategy
Industrial organization and game theory have evolved to help analyze situations and concepts encountered in everyday life. Commitment is a core topic in several books and movies. A case in point is Dr. Strangelove or How I Learned to Stop Worrying and Love the Bomb (1964) by Stanley Kubrick. The movie depicts an imaginary setting of the Cold War in the aftermath of an unauthorized launch of nuclear weapons on the Soviet Union. US General Ripper (who “went a little funny in the head”) utilizes flaws in the US defensive system, deciding on his own to attack selected targets with hydrogen bombs. He does this in the hope that the US president will react by ordering an all-out attack, destroying all Soviet military bases to circumvent any retaliation. The president, however, reacts differently. He summons his senior officials to the War Room to formulate alternatives to the unauthorized attack. He decides to warn the Russians of the imminent US attack, but learns that the USSR has installed a deterrence device—the “Doomsday Machine”— that would be triggered automatically in case of a sneak US nuclear attack, with no possibility to be reversed. This automatic retaliation would destroy all human life. Astonished by the threat of this Doomsday device, the president summons the director of Weapons Research and Development, Dr. Strangelove, for advice: “How is it possible for this thing to be triggered automatically and at the same time be impossible to un-trigger?” the president asks. Dr. Strangelove replies: It is not only possible, it is essential. That is the whole idea of this machine. Deterrence is the art of producing in the mind of the enemy the fear to attack. Because of this automated decision-making process—which rules out human meddling—the Doomsday Machine is terrifying and simple to understand. It is completely credible. . . . The whole point of this Doomsday Machine is [however] lost if you keep it a secret.
The only flaw in the Soviet deterrence strategy was that General Ripper, when deciding to attack the Russians, was ignorant of the very existence of this deterrence device.1 1. Dixit and Nalebuff (1991) discuss a simple setting to underline the effectiveness of strategic commitment to deter nuclear warfare (pp. 128–31), and explain how the Doomsday Machine should have deterred sneak attacks if effectively communicated (pp. 155–56).
Market Structure Games: Dynamic
111
c
a
Firm j
Firm i
Firm j c
d
a
(4, 3)
(2, 4)*
b
(3, 2)
(1, 1)
Firm i
d
c
(4, 3)
(2, 4)
(3, 2)*
b Firm j d
a. Simultaneous game
(1, 1)
b. Sequential game
Figure 4.1 Payoffs in a simultaneous versus sequential game for strategic commitment The first element in (·, ·) corresponds to firm i‘s payoff, while the second denotes the rival’s payoff.
4.1.1
Concept of Commitment
Commitment relates to strategic moves. A strategic move is intended to alter the beliefs or actions of rivals to one’s own benefit by purposely limiting one’s own freedom of action (e.g., killing one’s options). The raison d’être of strategic moves counteracts a common belief held in the real options literature that it is preferable under uncertainty to always keep options open (e.g., see Dixit and Pindyck 1994). As is well known in the industrial organization literature, lack of freedom can have strategic value if it can change the rival’s expectations about one’s future response, turning it to one’s own advantage. One approach to considering strategic moves is to look at how firms can be better off by altering the rules of the game, such as by transforming a simultaneous game into a sequential one. Consider the simultaneous game under complete information described in panel a of figure 4.1. Firm i may choose between action a and b, and firm j between action c and d . Firm i has a dominant strategy to take action a since whatever firm j decides (c or d ), the payoff for firm i is always higher when choosing action a (4 > 3 and 2 > 1). The best response to firm i’s choosing action a is for firm j to choose action d (receiving 4 rather than 3). Given this,
112
Chapter 4
the Nash equilibrium (*) is the right-top situation, with equilibrium payoffs of 2 for firm i and 4 for firm j.2 An alternative strategy for firm i is to move ahead of firm j, influencing its subsequent reaction. In this way, firm i turns a simultaneous game into a sequential one. To deal with the resulting sequential game shown in panel b of figure 4.1, we need to refine the Nash equilibrium solution concept to a multistage setting. Nash’s contribution to game theory and refinements of the Nash equilibrium concept are discussed in box 4.1. Figure 4.2 summarizes four basic game theory solution concepts. The appropriate solution concept here is the subgame perfect Nash equilibrium that rules out cheap talk and empty threats by the first mover (e.g., having the possibility to un-trigger the Doomsday Machine). In this finite-horizon problem (two stages) the solution is obtained by backward induction along the game tree of figure 4.1b. Once firm i chooses action a in the first stage and firm j observes this, the latter’s optimal action in stage two is to choose action d since its payoff for the strategy profile ( a, d ) is higher than for (a, c ) as 4 > 3. Thus, if firm i pursues action a, it will receive a payoff of 2 provided that firm j behaves optimally in the next stage (choosing d to receive 4 rather than c receiving 3). However, if firm i chooses action b in the first stage, firm j will select c (receiving 2 rather than 1), and so firm i will then receive 3. Firm i is thus better off choosing action b in the first stage, receiving 3 rather than 2. Firm i’s equilibrium payoff in the sequential game of figure 4.1b is higher than the equilibrium payoff it would have received in the simultaneous game depicted in figure 4.1a. To acquire this advantage obtained in the sequential game, firm i can announce early on it will pursue strategy b, whatever the decision of its rival (e.g., no wavering by the Soviet Union following a sneak attack by the United States). To behave strategically, firm i must commit not to follow the static optimal action of the simultaneous game (which was action a). Such strategic commitment makes firm i better off, receiving 3 rather than 2. The discussion above provides an example of how a player can act strategically, changing the ex post subgames with its ex ante strategic decision. If firm i declares upfront it will pursue action b regardless of its rival’s subsequent action, it can change the rules of the game in its favor. But for such a move to have real commitment value, it must be, among other things, credible and observable. To be credible, such strategic 2. The Nash equilibrium (a, d ) consists of strategies that are rationalizable since they survive iterated removal of never-best responses. This equilibrium selection relies on very weak assumptions, namely common knowledge of rationality.
Market Structure Games: Dynamic
113
Box 4.1 Development of game theory and refined solution concepts
As far back as the early nineteenth century, beginning with Auguste Cournot in 1838, economists have developed methods for studying strategic interaction. But these methods focused on specific situations, and for a long time no overall method existed. The game-theoretic approach now offers a general toolbox for analyzing strategic interaction. Game Theory Whereas mathematical probability theory ensued from the study of pure gambling without strategic interaction, games such as chess and cards became the basis of game theory. The latter are characterized by strategic interaction in the sense that the players are individuals who think rationally. In the early 1900s mathematicians such as Zermelo, Borel, and von Neumann had already begun to study mathematical formulations of games. It was not until the economist Oskar Morgenstern met the mathematician John von Neumann in 1939 that a plan originated to develop game theory so that it could be used in economic analysis. The most important ideas set forth by von Neumann and Morgenstern in the present context may be found in their analysis of two-person zerosum games. In a zero-sum game, the gains of one player are equal to the losses of the other player. As early as 1928 von Neumann introduced the minimax solution for a two-person zero-sum game. According to the minimax solution, each player tries to maximize his gain in the outcome that is most disadvantageous to him (where the worst outcome is determined by his opponent’s choice of strategy). By means of such a strategy each player can guarantee himself a minimum gain. Of course, it is not certain that the players’ choices of strategy will be consistent with each other. von Neumann was able to show, however, that there is always a minimax solution, namely a consistent solution, if so-called mixed strategies are introduced. A mixed strategy is a probability distribution of a player’s available strategies, whereby a player is assumed to choose a certain “pure” strategy with some probability. John F. Nash In his dissertation Nash introduced the distinction between cooperative and noncooperative games. His most important contribution to the theory of noncooperative games was to formulate a universal solution concept with an arbitrary number of players and arbitrary preferences, that is, not solely for two-person zero-sum games. This solution concept later came to be called Nash equilibrium. In a Nash equilibrium all of the players’ expectations are fulfilled and their chosen strategies are optimal. Nash proposed two interpretations of the equilibrium concept: one based on
114
Chapter 4
Box 4.1 (continued)
rationality and the other on statistical populations. According to the rationalistic interpretation the players are perceived as rational, and they have complete information about the structure of the game, including all of the players’ preferences regarding possible outcomes, where this information is common knowledge. Since all players have complete information about each others’ strategic alternatives and preferences, they can also compute each others’ optimal choice of strategy for each set of expectations. If all the players expect the same Nash equilibrium, then there are no incentives for anyone to change his strategy. Nash’s second interpretation—in terms of statistical populations—is useful in so-called evolutionary games. This type of game has also been developed in biology in order to understand how the principles of natural selection operate in strategic interaction within and among species. Moreover Nash showed that for every game with a finite number of players, there exists an equilibrium in mixed strategies. Despite its usefulness there are problems associated with the concept of Nash equilibrium. If a game has several Nash equilibria, the equilibrium criterion cannot be used immediately to predict the outcome of the game. This has brought about the development of so-called refinements of the Nash equilibrium concept. Another problem is that when interpreted in terms of rationality, the equilibrium concept presupposes that each player has complete information about the other players’ situation. It was precisely these two problems that Selten and Harsanyi undertook to solve in their contributions. Reinhard Selten The problem of numerous noncooperative equilibria has generated a research program aimed at eliminating “uninteresting” Nash equilibria. The principal idea has been to use stronger conditions not only to reduce the number of possible equilibria, but also to avoid equilibria that are unreasonable in economic terms. By introducing the concept of subgame perfection, Selten (1965, 1975) provided the foundation for a systematic endeavor. An example might help to explain this concept. Imagine a monopoly market where a potential competitor is deterred by threats of a price war. This may well be a Nash equilibrium—if the competitor takes the threat seriously, then it is optimal to stay out of the market—and the threat is of no cost to the monopolist because it is not carried out. But the threat is not credible if the monopolist faces high costs in a price war. A potential competitor who realizes this will establish himself on the market and the monopolist, confronted with fait accompli, will not start a price war. This is also a Nash equilibrium. In addition, however, it fulfills Selten’s requirement of subgame perfection, which thus implies systematic
Market Structure Games: Dynamic
115
Box 4.1 (continued)
formalization of the requirement that only credible threats should be taken into account. Selten’s subgame perfection has direct significance in discussions of credibility in economic policy, the analysis of oligopoly, the economics of information, and so forth. It is the most fundamental refinement of Nash equilibrium. Nevertheless, there are situations where not even the requirement of subgame perfection is sufficient. This prompted Selten to introduce a further refinement, usually called the “trembling-hand” equilibrium. The analysis assumes that each player presupposes a small probability that a mistake will occur, that someone’s hand will tremble. A Nash equilibrium in a game is “trembling-hand perfect” if it is robust with respect to small probabilities of such mistakes. This and closely related concepts, such as sequential equilibrium (Kreps and Wilson 1982), have turned out to be very fruitful in several areas, including the theory of industrial organization and macroeconomic theory for economic policy. John C. Harsanyi In games with complete information all of the players know the other players’ preferences, whereas they wholly or partially lack this knowledge in games with incomplete information. Since the rationalistic interpretation of Nash equilibrium is based on the assumption that the players know each others’ preferences, no methods had been available for analyzing games with incomplete information, despite the fact that such games best reflect many strategic interactions in the real world. This situation changed radically in 1967–68 when John Harsanyi published three articles entitled Games with Incomplete Information Played by “Bayesian” Players. Harsanyi’s approach to games with incomplete information may be viewed as the foundation for nearly all economic analysis involving information, regardless of whether it is asymmetric, completely private, or public. Harsanyi postulated that every player is one of several “types,” where each type corresponds to a set of possible preferences for the player and a (subjective) probability distribution over the other players’ types. Every player in a game with incomplete information chooses a strategy for each of his types. Under a consistency requirement on the players’ probability distributions, Harsanyi showed that for every game with incomplete information, there is an equivalent game with complete information. In the jargon of game theory, he transformed games with incomplete information into games with imperfect information. Such games can be handled with standard methods. Source: Nobel Prize Committee Website.
• Determine stable (fixed) points among possible strategy profiles
• Eliminate dominated strategies
• Select dominant strategies
• Complete information
• Static game
• Simultaneous moves
• Avoid profitable one-stage deviations
• Go back to the beginning (backward induction)
• Determine Nash equilibria at each subgame
At date t, players know all moves before t –1
• Almost perfect information
Each player knows all actions taken previously
• Perfect information
• Dynamic game
• Players move sequentially
Subgame perfect equilibrium
• Players form expectation about the outcome of the game and act accordingly
Players have probabilistic beliefs about other players’ type
• Imperfect
Players do not know other players’ payoffs
• Incomplete
• Static game
• Simultaneous moves
Bayesian equilibrium
Beliefs are obtained from strategies and observed actions using Bayes’s rule
• Actions are optimal given the beliefs
• Mixed form of perfect and Bayesian equilibrium
Players have probabilistic beliefs about other players’ type
• Imperfect
Players do not know other players’ payoffs
• Incomplete
• Dynamic game
• Players move sequentially
Perfect Bayesian equilibrium
Figure 4.2 Main game theory solution concepts The subgame perfect, Bayesian, and perfect Bayesian equilibria are essentially refinements of Nash equilibrium. Other solution concepts include correlated equilibrium and sequential equilibrium.
Model use
Information set
Order of moves
Nash equilibrium
116 Chapter 4
Market Structure Games: Dynamic
117
commitments involve early decisions with a long-term impact that are costly or difficult to reverse (e.g., they involve substantial fixed or sunk costs).3 This is the “whole idea” of the Doomsday Machine that cannot be un-triggered once initiated. The automatic Soviet retaliation is suboptimal from the second-stage perspective (annihilation of all human life on earth) but has commitment value in a dynamic setting provided that the attacking party is aware of the deterrence device (which was not the case in Dr. Strangelove). Such strategic commitments differ from tactical decisions that can be easily reversed. According to Schelling (1960), for a strategic move to have commitment value it must be: Observable Rivals must be aware of the committing party’s strategic move before making their own decision. The Doomsday Machine could not impact on General Ripper’s decision since he was not aware of its existence. Understandable The commitment should affect the incentives of the opponent. The strategic move must be able to change the ex post choices. Credible A strategic decision has little commitment value if an announcement is perceived as a bluff. Credibility influences the rival’s estimation whether the committing party is willing to carry through what it has stated regardless of circumstances. Costly to reverse For a move to be credible, it must be hard, costly, or impossible to reverse once set in motion. This typically involves substantial sunk costs for the committing party.4 Credibility is crucial. Dixit and Nalebuff (1991) enumerate eight devices for achieving credibility (coined the “eightfold path to credibility”).5 These are summarized in table 4.1. Ex ante commitments can significantly alter ex post incentives, altogether affecting the outcome of strategic interactions in dynamic games. A classic case is when an incumbent can deter rival entry to protect its own market by building overcapacity (e.g., see Spence 1977, 1979, or Dixit 1980).6 When firms commit, they do not only anticipate the direct 3. If firm i were to announce it will pursue action b but later it may choose to implement alternative action a —that is optimal from a simultaneous-game perspective—its announcement will be seen as “cheap talk” and will be of little strategic value. 4. Sunk costs are significant when the ex post value of the investment outlay is significantly lower. In the case of sunk investment with low or no salvage value, there is effectively no option to abandon. This may be the case with relationship- or industry-specific assets. 5. See Dixit and Nalebuff (1991, pp. 142–67). 6. In the first stage, the incumbent can choose excessively high capacity (higher than the second-stage optimal capacity) to deter entry by potential entrants.
118
Chapter 4
Table 4.1 Paths to credible commitment Basic concept
Credibility device
Make it costly to break your commitment
(1) Establish and use a reputation (bluffing may be costly in terms of reputation if revealed; in repeated games, reputation is crucial and should be carefully cultivated). (2) Make contracts (agree on punishment if the announcement is not followed through).
Limit the options to reverse actions
(3) Cut off communication (e.g., seal off the base as General Ripper did). (4) Burn bridges behind you (deny yourself the opportunity to retreat or to reverse your action). (5) Leave the outcome beyond control (i.e., provide automatic response to your rivals’ action). This was the “whole idea” behind the Doomsday Machine.
Engage in a repeated relationship
(6) Move in small steps (build up a reputation of carrying through with your announcement via repeated relationships rather than one-time agreements).
Build credibility on others
(7) Develop credibility through teamwork (individual weaknesses can be resolved by forming groups, peer pressure) (8) Employ negotiating agents (agents have the permission to negotiate up to a point).
Source: Adapted from Dixit and Nalebuff (1991).
effect of the commitment (e.g., direct cost savings from investment) but also what will be the ex post strategic impact on rivals, called the strategic effect. Under uncertainty there is a trade-off between this positive strategic value of early commitment and the flexibility to wait to invest. Strategic commitment kills one’s option to wait, but it can make the firm better off due to strategic interactions. It is thus of critical importance to closely examine the trade-off between flexibility and commitment in an integrated framework under uncertainty (considered in chapter 7). 4.1.2 Taxonomy of Commitment Strategies Fudenberg and Tirole (1984) extend the theory on strategic commitment, introducing a new classifying scheme for business strategies.7 They 7. The following taxonomy is based on Tirole (1988), who complements Fudenberg and Tirole (1984) with elements from Bulow, Geanakoplos, and Klemperer (1985). The terminology “strategic substitutes” and “strategic complements” was not used in the original paper (of 1984). The names for the four main business strategies are unchanged. We collectively refer to this work as Fudenberg and Tirole (1984) thereafter, although parts are more directly based on Tirole (1988, pp. 323–28).
Market Structure Games: Dynamic
119
identify four main business strategies: top dog strategy, puppy dog ploy, lean and hungry look, and fat cat strategy. These are closely linked to the type (and sign) of the strategic effect brought about by the strategic commitment. This strategic effect ultimately depends on whether the (ex post) actions are strategic complements or substitutes, and whether the commitment makes the firm tough or soft.8 We discuss next a firm’s incentive to be tough or soft and present Fudenberg and Tirole’s taxonomy. Entry Strategies Standard competition models (e.g., Cournot, Bertrand) assume that the number of firms in an industry is given exogenously. In reality the number of firms may be endogenous and driven, for example, by the magnitude of fixed entry costs. If there are low or no barriers to entry and exit and incumbents make excess profits, other firms will contemplate entry to take a slice of the pie. In such a contestable market, economic profits will be forced down to zero. Excess profits may be sustainable if there exist significant barriers to entry and exit. Bain (1956) initiated the study of entry barriers, distinguishing three entry types: blockaded, deterred, and accommodated. Fudenberg and Tirole (1984) build on this framework to examine commitment strategies. The authors disregard the case of blockaded entry, since it is an exogenous state that cannot be altered by incumbents. They focus instead on entry-barrier erection strategies, specifically on deterred and accommodated entry. For simplicity, consider two players: firm i is the incumbent and firm j a would-be entrant. In the first stage, firm i may commit by incurring a sunk investment outlay, K i. In the second stage, both firms compete (deciding simultaneously) over tactical or short-term variables α i and α j (e.g., prices).9 Firm i’s profit p i ( K i , a i , a j ) depends on the investment commitment Ki and later action choices α i and α j.10 Under perfect information, the relevant solution concept is the subgame perfect Nash equilibrium. In subgame perfect equilibrium, firms’ second-stage actions, α i* ( K i ) and α j* ( K i ), must form a Nash equilibrium for commitment choice Ki. The first-stage strategic investment thus affects ex post equilibrium choices; that is, the second-stage actions are functions of the first-stage investment.11 Firm i can deter entry (entry 8. Smit and Trigeorgis (2001) use the terms “aggressive” versus “accommodating” instead of “tough” versus “soft.” 9. If the two firms choose their actions simultaneously, the outcome will be, for example, that of Cournot quantity or Bertrand price competition. 10. π i(⋅, ⋅, ⋅) and π j (⋅, ⋅, ⋅) are twice continuously differentiable with respect to α i and α j , and concave in one’s action. π i(⋅, ⋅, ⋅) is concave in K i . 11. α i* (⋅) and α j * (⋅) are differentiable in K i .
120
Chapter 4
deterrence) if its investment Ki prevents firm j from making profits in the second stage:
π j ( Ki , α i* ( Ki ) , α j * ( Ki )) ≤ 0. Firm i accommodates entry (entry accommodation) if, despite committing, it allows its rival to make profits:
π j ( Ki , α i* ( Ki ) , α j * ( Ki )) > 0. To analyze the strategic impact, we need to consider the total derivative (total effect) of firm i’s equilibrium profit, π i, with respect to the firststage strategic commitment, Ki, namely dp i ⎛ ∂p i ⎞ ⎛ ∂p i da i * ⎞ ⎛ ∂p i da j * ⎞ . =⎜ ⎟ +⎜ ⎟+ dKi ⎝ ∂Ki ⎠ ⎝ ∂a i dKi ⎠ ⎜⎝ ∂a j dKi ⎟⎠
(4.1)
The total derivative for firm j’s profit is obtained symmetrically. Business strategies may differ depending on whether entry is deterred or accommodated. Deterred Entry As noted, firm i’s commitment strategy is driven by its rival’s profit (π j). We must thus consider the total derivative of π j with respect to Ki to determine firm i’s optimal first-stage investment policy. Since in the second stage firm j will select its action α j optimally (∂π j ∂α j = 0), the third term in the total derivative of firm j’s profit—the symmetric version of equation (4.1) above—drops out. This leads to dπ j = dKi (total effect)
⎛ ∂π j ⎞ ⎛ ∂π j dα i * ⎞ ⎜⎝ ⎟ +⎜ ⎟. ∂Ki ⎠ ⎝ ∂α i dKi ⎠ (direct (strategic effect) effect)
(4.2)
Firm i’s first-period strategic investment, Ki, has several value effects. First, it has a direct impact on firm j’s profit value, ∂π j ∂Ki ; this is the direct effect. For instance, if firm i acquires all scarce resources in the first stage, firm j cannot operate and make any profit; this is a positive direct effect. In many cases, however, this effect is negligible. This is the case when firm i invests in a process innovation that does not improve firm j’s cost position (no spillover). The second term, ∂π j ∂α i × dα i* dKi , represents the strategic effect of the commitment. It results from firm i’s ex post behavioral change due to its own commitment (dα i* dKi ) and
Market Structure Games: Dynamic
121
from the impact of this behavioral change on firm j’s profit (∂π j ∂α i ). The total effect of the strategic investment is the sum of the direct and the strategic effects.12 To determine what commitment strategy to follow, we further need to discuss tough as opposed to soft commitment. These two concepts are meant to capture whether a commitment by one firm places its rival at an advantage (benefits them) or at a disadvantage (hurts them). Firm i makes a tough commitment if the rival, firm j, is hurt, meaning dπ j dKi < 0. Such an announcement is bad news for the competitor. In this case firm i should overinvest in the first stage to hurt its rival and deter entry.13 Fudenberg and Tirole (1984) coin this approach “top dog” strategy because it consists in “being big or strong, to look tough or aggressive.” On the contrary, an early investment is a soft commitment if the rival benefits from it, meaning if dπ j dKi > 0. If firm i commits or invests too much in the first stage (Ki is high), entry will hardly be deterred since π j will be increased. Firm i should then underinvest to deter entry, as part of a “lean and hungry look” strategy. Whether one of the two approaches is advisable also depends on the trade-off between the sunk investment commitment cost and the value increment resulting from the direct and strategic effects in equation (4.2). A general recommendation cannot be readily formulated. 12. Fudenberg and Tirole (1991, pp. 132–33) propose an alternative, more technical interpretation of equation (4.2) based on the notion of open-loop and closed-loop strategies. Open-loop strategies depend only on calendar time but not on the actions previously played in the dynamic game. Dynamic games where firms can only adopt open-loop strategies are in a way static since firms cannot react optimally to previous plays by rivals. Closed-loop strategies allow this since they take account of previous moves as well. In this setting, the key difference between these two notions depends on whether the first-stage strategic move by firm i is effectively communicated to firm j when the latter decides to act. The direct effect in equation (4.2) refers to the first-order optimality condition in the open-loop strategy case (open-loop equilibrium), whereas the second term (strategic effect) only exists if firms observe their rival’s first-stage strategic moves, that is, if they can devise closed-loop strategies. In Dr. Strangelove, the existence of the Doomsday Machine has no strategic effect since General Ripper was not aware of it; that is, he could not formulate a closed-loop strategy and act optimally (i.e., not attack the Russians) given this information. We come back to the notions of open-loop versus closed-loop strategies (and the corresponding equilibrium concepts) in later chapters. 13. The notion of “overinvestment” (and later of “underinvestment”) is defined with respect to the benchmark case where firms cannot formulate closed-loop strategies, namely where the strategic move is of no commitment value since firm j does not take its (secondstage) action based on the information conveyed by the commitment. The difference between the subgame perfect equilibrium outcome (in closed-loop strategies) and the Nash equilibrium (in open-loop strategies) is captured by the strategic effect. This term fully reflects the incentive to under- or overinvest.
122
Chapter 4
Accommodated Entry If deterring entry is too costly or infeasible, firm i may accommodate entry instead. This friendlier stance still leaves room for strategic behavior because firm i can make an early move that enhances its position in the (ex post) product market competition stage. Contrary to the case of entry deterrence, firm i considers here its own profit function (not its competitor’s) when it devises its business strategy. We thus look at the total derivative of firm i’s own profit (π i) with respect to its investment Ki, dπ i ⎛ ∂π i ⎞ ⎛ ∂π i dα i * ⎞ ⎛ ∂π i dα j * ⎞ =⎜ . ⎟+ ⎟ +⎜ dKi ⎝ ∂Ki ⎠ ⎝ ∂α i dKi ⎠ ⎜⎝ ∂α j dKi ⎟⎠ Since firm i selects action α i as part of a Nash equilibrium in the second stage, ∂π i ∂α i = 0 so the expression above simplifies to ⎛ ∂π dα j * ⎞ dπ i ⎛ ∂π ⎞ . = ⎜ i⎟ + ⎜ i ⎝ ⎠ ⎝ ∂α j dKi ⎟⎠ dKi ∂K i (total (direcct (strategic effect) effect) effect)
(4.3)
The first (right-hand) term in equation (4.3) is the direct effect of the investment on firm i’s own profit, ∂π i ∂Ki . This effect occurs even if the rival does not observe the strategic move. Since sequential strategic interaction has no impact on the direct effect, we set it aside as irrelevant from a strategic viewpoint. The last term, ∂π i ∂α j × dα j * dKi , is the strategic effect. If this is positive, firm i should overinvest to increase its total (gross) value. If this strategic effect is negative, the firm should underinvest instead. Thus the strategic effect provides guidance whether to over- or underinvest. Its sign depends on:14 14. Note that ∂π i dα j ∗ ⎛ ∂π i ∂α j ∗ ⎞ dα i ∗ . = ∂α j dKi ⎜⎝ ∂α j ∂α i ⎟⎠ dKi If the two reaction functions are both downward or both upward sloping, ⎛ ∂ π dα j * ⎞ ⎛ ∂α j * ⎞ ⎛ ∂ π j dα i * ⎞ . sign ⎜ i = sign ⎜ × sign ⎜ ⎝ ∂α i ⎠⎟ ⎝ ∂α i dKi ⎟⎠ ⎝ ∂α j dKi ⎟⎠ The last term, ∂α j * ∂α i , captures the effect of a change in firm i’s action α i on firm j’s best reply. Its sign depends on whether the actions are strategic complements (positive sign) or substitutes (negative). The first right-hand term is the strategic effect in (4.2) for the entrydeterrence case. Ignoring the direct effect, its sign depends on whether the firm faces tough (negative sign) or soft commitment (positive sign).
Market Structure Games: Dynamic
Strategic substitutes
(∂a * j
Tough investment
( dp
j
dKi < 0)
Soft investment
( dp
j
dKi > 0)
∂a i < 0)
123
Strategic complements
(∂a * j
∂a i > 0)
Positive strategic effect
Negative strategic effect
Negative strategic effect
Positive strategic effect
Figure 4.3 Sign of the strategic effect
1. whether firm i’s strategic commitment (Ki) hurts (tough investment) or benefits (soft investment) its rival firm j (see the sign of dπ j dKi ); 2. whether firms react to each other in a reciprocating (strategic complements or ∂D j* ∂D i > 0) or a contrarian (strategic substitutes or ∂D j* ∂D i < 0) manner. This analysis can be represented by the two-by-two matrix of figure 4.3. Consider a different situation involving two incumbents where firm i would like firm j to exit the market. Firm i would design its commitment strategy to hurt firm j, considering the first-order (total) derivative of its rival’s profit, dπ j dKi . This case is equivalent to the entry-deterrence case discussed above. Choosing Commitment Strategies Following our previous discussion, we can differentiate among four main business strategies. These rest on (1) whether the investment is intended to be tough or soft, and (2) whether firms behave in a contrarian (substitutes) or reciprocating (complements) way. The objective of the firm in each of the four strategies is to induce the rival to behave less aggressively. The four main business strategies are summarized in figure 4.4 in case of deterred entry (figure 4.4a) and of accommodated entry (figure 4.4b). The four business strategies are discussed next: Top dog strategy Two cases are distinguished. In the entry-deterrence case (figure 4.4a) this means overinvesting when the investment is tough to ensure that the rival will renounce entering the market (earning zero profit). In the accommodated-entry case (figure 4.4b), it means
124
Chapter 4
Tough investment
Top dog strategy
Soft investment
Lean and hungry look
(a) Strategic substitutes (Cournot quantity competition)
Strategic complements (Bertrand price competition)
Tough investment
Top dog strategy
Puppy dog ploy
Soft investment
Lean and hungry look
Fat cat strategy
(b)
Figure 4.4 Four main business strategies (a) Deterred entry; (b) accommodated entry. Adapted from Fudenberg and Tirole (1984).
overinvesting for tough commitment (dπ j dKi < 0) when second-stage actions are strategic substitutes (∂D j* ∂D i < 0) inducing rivals to back down. Lean and hungry look In the deterred-entry case (figure 4.4a), this means underinvesting to be soft or flexible (dπ j dKi > 0), ensuring that the rival stays out. In the accommodated-entry case (figure 4.4b), this business strategy is advisable if second-stage actions are strategic substitutes (∂D j* ∂D i < 0) and the investment makes firm i soft, cushioning the potentially negative strategic effect (see figure 4.3). Puppy dog ploy In the accommodated-entry case (figure 4.4b), if the investment makes firm i tough, hurting its rival (dπ j dKi < 0), the rival will be more aggressive in the second stage as actions are strategic complements (∂D j* ∂D i > 0). Firm i should then underinvest (stay flexible). Fat cat strategy In the accommodated-entry case (figure 4.4b), if second-stage actions are reciprocating or strategic complements
Market Structure Games: Dynamic
125
Strategic substitutes
Strategic complements
Tough investment
Submissive underdog
Mad dog
Soft investment
Suicidal Siberian
Weak kitten
Figure 4.5 Suboptimal business strategies observed in practice (accommodated entry) Adapted from Besanko et al. (2004)
(∂D j* ∂D i > 0), firm i should avoid being aggressive (dπ j dKi < 0), behaving as a “fat cat.” In the real world some companies sometimes follow suboptimal strategies. Besanko et al. (2004) extend the taxonomy above to include additional business strategies that have a harmful effect on the committing firm.15 They identify the following strategies, summarized in figure 4.5: Submissive underdog The firm underinvests to accommodate entry when its commitment is tough (dS j dKi < 0) and actions are strategic substitutes (∂D j* ∂D i < 0). This strategy is not advisable; the firm should be a “top dog” instead (overinvest). Suicidal Siberian Here the firm overinvests in case of strategic substitutes (∂D j* ∂D i < 0) even though its investment makes it soft (dπ j dKi > 0), instead of underinvesting to keep a “lean and hungry look.” Mad dog The firm overinvests in case of tough commitment (dπ j dKi < 0) even though actions are strategic complements (∂D j* ∂D i > 0). It would be better to be a clever, harmless “puppy dog,” avoiding the negative effect depicted in figure 4.3 (underinvestment). Weak kitten Here the firm underinvests in case of soft commitment (dπ j dKi > 0) when actions are strategic complements (∂α j ∂α i > 0). The “weak kitten” is not mature enough to recognize that it should put on more weight (overinvest), becoming a “fat cat.” 15. See Besanko et al. (2004, pp. 246–47).
126
Chapter 4
Commitment in Differentiated Bertrand and Cournot Competition Bertrand and Cournot competition are examples of games where actions are strategic complements and strategic substitutes, respectively. We illustrate next application of the four main business strategies in the context of these benchmark models. Bertrand Price Competition Differentiated Bertrand price competition involves reciprocating actions (strategic complements). If firm i decreases its price, firm j will respond by following suit, and vice versa. Consider firm i’s reaction function from equation (3.8): piB ( pj ) =
a (1 − s ) + c s + pj , 2 2
where s ∈[0, 1) is the degree of substitutability. We thus have ∂piB ∂pj ( = s 2 ) ≥ 0, confirming that price choices are strategic complements. Should firm i invest early in a new technology to attain reduced future production costs? Firm i could then commit to a price cut, being more aggressive toward its rival in the later product market stage. This tough commitment by firm i is detrimental to rival firm j (as dπ j dKi < 0). If firm i decides to charge a lower price in the second stage, the marketclearing price will spiral downward since the reaction functions are upward sloping. For a given level of the rival’s price pj , firm i’s price pi will be lower, with the reaction curve shifting to the left as depicted in figure 4.6a.16 Firm j is worse off ex post because it is obliged to reduce its own price, following a reciprocating reaction. This strategy is not advisable because the strategic move by firm i will backfire as the strategic effect (represented in the top-right in figure 4.3) is negative. Firm i should instead underinvest, maintaining higher prices, to avoid entering an intensified price war. The optimal business strategy here is to be a nice “puppy dog.” In contrast, if investment makes firm i soft (dπ j dKi > 0), the rival will be less aggressive in the second stage. For a given level of competitor price pj , firm i optimally charges a higher price pi as a result of this 16. The case before (without) investment is indexed “before,” whereas the case after investment commitment as “after.” The case “before” corresponds to the open-loop equilibrium where product-market decisions are taken in ignorance of the rival’s strategic move, whereas the case “after” refers to closed-loop equilibrium where firms know that their commitment is recognized in their rivals’ strategy formulation and firms maximize profits accordingly (subgame perfection).
Market Structure Games: Dynamic
127
pj
RiBEFORE(pj) RiAFTER(pj)
pjAFTER *
Rj (pi)
E
pjBEFORE * E'
piAFTER *
piBEFORE *
pi
(a)
pj
RiBEFORE(pj) RiBEFORE(pj)
E'
pjAFTER * pjBEFORE *
Rj (pi)
E
piBEFORE *
piAFTER *
(b) Figure 4.6 Tough versus soft commitment in differentiated Bertrand competition (a) Tough commitment (puppy dog); (b) soft commitment (fat cat srategy)
pi
128
Chapter 4
commitment with the reaction function shifting to the right. The original price, pj , however, is not on the reaction curve. To reach the Nash equilibrium, firm j charges a higher price than before. The two firms are better off due to this accommodating strategy. In this case firm i should overinvest becoming fatter (fat cat), amplifying the positive strategic effect (bottom-right in figure 4.3) as much as possible. This is illustrated in figure 4.6b. An application of “soft” advertising strategy to the German telecom market is discussed in box 4.2. Cournot Quantity Competition To illustrate the importance of tough versus soft commitment in case of strategic substitutes or contrarian reactions, consider a tough investment commitment such as an R&D investment in process innovation. This would enhance firm i’s cost advantage in the Cournot duopoly setting (section 3.2.2). By contrast, a soft commitment would worsen the cost differential in favor of the rival, firm j; this would be the case, for instance, if the firm announces the building up of new, fancy headquarters. The (inverse) market demand function is linear as per equation (3.1). The cost functions are also linear. We allow for distinct marginal production costs, ci and c j (ci , c j < a). As seen from equation (3.13), firm i’s reaction function in Cournot duopoly is qiC (q j ) =
1 ⎛ a − ci − q j ⎞⎟ . ⎜ 2⎝ b ⎠
(4.4)
Firm i’s reaction function qiC (⋅) is differentiable and decreasing in its own cost (∂qiC ∂ci = − 1 2b < 0), implying that for a cost increase (soft commitment) the reaction curve shifts to the left, whereas for a cost decrease (tough commitment) it shifts to the right. As seen in figure 4.7a, if firm i makes a tough commitment (curve shifts to the right), then no matter what output its rival produces it will produce more output (than it would without the commitment). Since quantities are strategic substitutes, firm j behaves in a “contrarian” way, producing less in equilibrium than it would have if this investment did not occur. Ex post profit is higher for firm i if it makes a tough commitment ex ante (without accounting for the cost involved in the first-stage investment). This investment has a positive strategic effect and firm i should overinvest as in a “top dog” strategy. By contrast, a soft commitment would lead firm i to produce less than it would otherwise. The reaction curve now shifts to the left and firm i produces less after the commitment, while firm j produces more. Firm
Market Structure Games: Dynamic
129
Box 4.2 European liberalization, “soft advertising” and the persistence of high prices in the German telecom market
Fudenberg and Tirole’s (1984) framework can provide powerful insights. Their framework is particularly useful to help explain how an industry evolves once liberalization of the market is enforced. In most European countries certain sectors (e.g., railway, electricity, post and telecommunications) have long been considered as natural monopolies. Governments have erected high entry barriers (blockaded entry), believing that competitive entry would be socially detrimental. Presumably there were not enough room for several firms in these markets to make positive profits or at least high enough profits to pay for the large fixed infrastructure costs. In the last two decades a revolution has occurred in Europe. Policy makers decided to enforce liberalization of these markets, believing that enhanced competition would result in lower prices and be more beneficial to European consumers. A case in point is the telephone industry in Germany where Deutsche Telekom, once a formidable monopolist, faces competitive entry from rival companies such as Vodafone, Telecom Italia (Alice), and other regional companies. Deutsche Telekom has been one of the world’s leading telecommunication and information-technology service providers, with an annual turnover of )60 bn a year. Although liberalization of the telecommunication sector has taken place many years ago, the German Federal Network Agency (“Bundesnetzagentur”) must still wonder why no significant price decreases and market share shifts have occurred in Germany up to now. This may be partly due to Deutsche Telekom’s heavy investment in advertising campaigns. Every year Deutsche Telekom channels nearly 15 percent of its revenues into ads. The telecommunication industry is typical of Bertrand price competition. Firms face no serious capacity constraints and the key purchasing criterion for many customers is the price. As it is difficult to differentiate among offerings in the telecommunication industry (with the exception of bundling for the iPhone), the advertising campaign of Deutsche Telekom was not meant to build a differentiation advantage. It rather promoted telecommunication services generally. As such, its ad campaigns have been beneficial to rivals as well. The massive general advertising investment made by Deutsche Telekom is soft (benefits its rivals) and rivals have been less aggressive in second-stage competition. Consequently, despite liberalization, prices for telecommunication services have not decreased significantly in Germany. Market shares have not declined dramatically either since customers do not find it worthwhile to incur switching costs if alternative offerings are not sufficiently better or cheaper. Still, even though competition is not yet that fierce, Deutsche Telekom has not taken full benefit since its advertising campaigns have been quite expensive.
130
Chapter 4
qj
RiBEFORE(qj) RiAFTER(qj)
qjBEFORE *
E
qjAFTER *
E' Rj (qi)
q iBEFORE *
qiAFTER *
qi
(a)
qj
RiAFTER(qj) RiBEFORE(qj)
qjAFTER *
E'
E
qjBEFORE *
qiAFTER *
qiBEFORE *
Rj (qi)
qi
(b) Figure 4.7 Tough versus soft commitment in Cournot quantity competition (a) Tough commitment (top dog strategy); (b) soft commitment (lean and hungry look strategy)
Market Structure Games: Dynamic
131
i’s investment is beneficial to firm j who is more aggressive in the product market stage. Firm i should refrain from committing and should thus underinvest. This “lean and hungry look” strategy is depicted in figure 4.7b. This is what the strategic effect in the case of tough versus soft commitment for strategic substitutes is about. There is a positive strategic effect when its strategic investment makes firm i tough. This may dominate even though the direct effect might be negative (e.g., due to sunk costs). When its investment makes the first-mover soft, there is a negative strategic effect and firm i should refrain from making this kind of investment. Box 4.3 describes entry accommodation in the Italian electricity market, previously dominated by state monopoly Enel. Overinvestment in capacity may also result in an alternative model, also famous in industrial organization. It is the duopoly model developed by Stackelberg (1934) where one of the firms makes an early move selecting its quantity (i.e., capacity) first, while the second firm selects its own quantity in view of the leader’s quantity choice. The following section develops the sequential model by Stackelberg and discusses in which circumstances it might be useful. 4.1.3
Sequential Stackelberg Game
Heinrich von Stackelberg (1934) proposed a dynamic duopoly model in which a firm (the leader L) moves first (for whatever reason) and its rival (the follower F ) follows suit. A key assumption is that the follower observes the leader’s choice before selecting its own output. The profit and cost functions are the same as used in Cournot quantity competition (section 3.2.2). The (inverse) demand function is linear as given by equation (3.1). Cost functions are also linear, allowing for distinct marginal costs cL and cF . In the second period, the follower chooses output qF (≥ 0) to maximize its own profit, given the leader’s observed quantity choice qL (≥ 0). The leader has no possibility to revise its production plan and installed capacity ex post (i.e., it is irrevocably committed to its announced capacity decision, qL). The subgame perfect Nash equilibrium of this sequential, finite-horizon game can be obtained by backward induction. The follower’s optimization problem is to select its output qF (≥ 0) to maximize its profit:17
π F ( qL , qF ) = [ p (Q) − cF ] qF . 17. The follower’s profit function is differentiable and concave in its own strategic variable, qF .
132
Chapter 4
Box 4.3 Entry accommodation in the Italian electricity market
As electric utilities are subject to serious capacity constraints in offering a homogeneous, nonstorable product, they effectively compete over capacity as in Cournot competition. Firms first decide on their installed capacity base (a long-term decision) and then compete in the short run in prices under capacity constraints. The Italian electric utility Enel is recently facing new challenges, having been a protected monopolist in the Italian marketplace for decades. Since July 2007 the Italian electricity market has opened up to foreign utilities in the wake of the European Commission enforcing liberalization across European electricity markets. In the current environment, traditional frameworks (e.g., SWOT, five-forces analysis, or generic strategy framework) offer little guidance for Enel executives about how to deal with the issues they face under uncertainty because they lack the dynamic perspective necessary to understand market-entry problems. Fudenberg and Tirole’s (1984) framework of business strategies can be helpful. The Italian electricity industry was previously blockaded due to high administrative and other entry barriers. Now Enel cannot rely on the Italian government to protect its home market from competitive forces since the government has to toe the line dictated by the European Commission. Even if Enel manages to deter competitive entry (deterred entry), DG Competition, the European body responsible for implementing and monitoring adherence to European antitrust law, may intervene. Enel has one main choice left, to accommodate entry. Of course, Enel may accommodate entry but still behave in a way that makes entry less profitable for potential entrants. In this industry, capacities are strategic substitutes in that if one firm adds capacity, the optimal reaction of rivals is not to raise capacities or revise their construction plans to accommodate less capacity. Being the sole electricity provider in the Italian market (until July 2007), Enel had the opportunity to make a “first-stage” strategic move to alter the “second-stage” competition game. Given that investing in new capacity was perceived as a tough initiative in this setting, Enel had the opportunity to “over-invest” in capacity over the years to discourage potential entrants from building new production units. Accommodation was likely a preferred strategy.
Market Structure Games: Dynamic
133
The follower’s reaction function (where superscript S stands for Stackelberg) is 1 a − cF qFS ( qL ) = ⎛ − qL ⎞ . ⎠ 2⎝ b The leader L knows that the follower will choose its output once it observes its own and will infer the follower’s reaction before determining its own optimal output. The leader will thus choose its quantity qL so as to maximize its profit:
π L(qL , qFS ( qL )) = [ p (qL + qFS (qL )) − cL ] qL. The resulting Stackelberg equilibrium quantities for the leader (L) and the follower (F ) are given by ⎧qS = a − 2cL + cF , ⎪ L 2b ⎨ ⎪qFS = a + 2cL − 3cF . ⎩ 4b
(4.5)
The Stackelberg equilibrium price, obtained by substituting the equilibrium quantity above in (3.1), is pS =
a + 2 c L + cF . 4
(4.6)
The profits for the leader (L) and the follower (F ) in subgame perfect equilibrium are ⎧ S ( a − 2cL + cF )2 , ⎪⎪π L = 8b ⎨ 2 ⎪π S = ( a + 2cL − 3cF ) . F ⎪⎩ 16b
(4.7)
In case of cost symmetry between the leader and the follower (cL = cF = c), the above equilibrium profit expressions simplify to ⎧ S ( a − c )2 ⎪⎪S L = 8b ⎨ 2 a 1 ⎪ S ( − c) S = = S LS ⎪⎩ F 16b 2
(> S C ),
(4.8)
(< S ), C
where π C = ( a − c ) 9b is the Cournot profit under cost symmetry given in equation (3.17). 2
134
Chapter 4
The leader in the above sequential Stackelberg game is better off than a symmetric Cournot duopolist (S LS > S C). The Stackelberg follower receives a lower profit than the single-period Cournot duopolist (S FS < S C ). Moreover the aggregate (total) quantity produced in the sequential symmetric Stackelberg game (3 4 × (a − c ) b) is higher than the industry output in symmetric Cournot duopoly (2 3 × (a − c ) b). Therefore, given the downward-sloping demand, the market-clearing price is lower in the sequential Stackelberg game. The leader could defer its output decision to the second period but is better off not to do so. The profit value of being a leader in the sequential Stackelberg game is higher than in the simultaneous wait-and-see case, even if the price is lower. Here the leader is not acting optimally from the second-stage static (Nash-equilibrium) perspective since its output is not a best response to the rival’s quantity in the second stage. From a dynamic perspective, the leader is actually better off, thanks to its commitment to a certain output. By contrast, the Stackelberg follower produces less than under symmetric Cournot competition. Since the market price is lower, the Stackelberg follower makes lower profits than in the Cournot case. The sequential Stackelberg model provides an example of first-mover advantage. In the sequential Stackelberg setting, the follower might have been better off ignoring the quantity chosen by the leader. Although the leader is better off communicating its output decision to the follower, it should be careful not to lose credibility because if the follower suspects “cheap talk,” it will choose its quantity as if no communication occurred, namely à la Cournot. The sequential Stackelberg game should thus be interpreted in light of commitment theory: the leader should follow a “top dog” strategy and overinvest in capacity, with investment costs being fully sunk. The sequential Stackelberg model is also useful to help assess the importance of information in multiperson games. In Stackelberg competition, the firm that knows its rival’s quantity decision (the follower) is worse off than a firm that ignores this information (Cournot case). Conversely, when one gains a competitive advantage by deciding first (e.g., regarding capacity choice or market entry), the less-informed party (i.e., the leader) is not necessarily worse off. This may justify an early commitment as a sound strategy for a firm even if not all information concerning the market development is known or predictable. But why should one firm have the possibility to commit and not the other? We discuss in chapter 12 the timely interplay that occurs when firms compete over early commitment (e.g., in the case of market entry).
Market Structure Games: Dynamic
4.2
135
Bargaining and Cooperation
So far we have discussed models where firms take a noncooperative stance toward their rivals, ignoring the possibility of more complex or repeated relationships based on both competition and collaboration. In reality, however, fierce competition is not the only modus vivendi adopted by firms in the marketplace. Firms often bargain or cooperate with other parties, including competitors. Antitrust authorities generally prohibit formal collaboration (explicit collusion) but may tolerate other forms (e.g., tacit collusion). Such cooperation between rival firms is not necessarily detrimental to customers. For example, customers may find it advantageous to be faced with only one technology standard owing to product externalities. An agreement on common technological norms (e.g., Blue ray) may be beneficial both to the cooperating firms and to the end consumers. Real-world competition calls for analytic models that can better explain this kind of complex strategic interactions observed in the marketplace. We discuss in turn bargaining and (tacit) collusion in repeated games.18 4.2.1
Bargaining
Bargaining problems are treated as dynamic games under complete or incomplete information. They are solved using solution concepts suited to a multistage setting (e.g., subgame perfection or perfect Bayesian equilibrium). Here we use subgame perfect equilibrium strategy profiles under perfect information. When reasoning backward, one needs to consider the time value of money (discounting) and the trade-off between reaching an agreement today or continuing bargaining. The “patience” of the bargaining parties is thus a key factor in negotiations. The bargaining process can be limited in time (finite horizon) or continue indefinitely until parties reach an agreement (infinite horizon). Consider first a simple example of bargaining to help identify the key drivers. A typical problem is how to split a pie among players. Ståhl (1972) discusses such a model for finite horizon, and Rubinstein (1982) extends it to infinite horizon.19 Suppose that two firms “bargain” over market shares in the marketplace. One of the two firms (the bargaining 18. We discuss bargaining and tacit collusion in sequence owing to some similar economic interpretations. We do not mean to suggest that the theory of repeated games is built upon bargaining games. In fact sustainability of cooperative behavior in infinitely repeated games can be established directly by using so-called grim-trigger strategies. 19. We here follow the treatment by Shaked and Sutton (1984) and Gibbons (1992).
136
Chapter 4
Nature
Leader
Follower
Leader
Follower
leader L) is allowed first to make a proposal to the follower (e.g., due to its technological edge or market power). Subsequently the follower (F ) may make a proposal as roles are reversed. The slice (as a percentage of the total market value) that accrues to the leader (L) is denoted by si where subscript i stands for firm i that makes the proposal; the follower (F ) receives the remaining slice, 1 − si. In the first period, the leader (L) proposes the following deal to the rival: the leader takes sL (%) of the pie (0 ≤ sL ≤ 1), with the follower (F ) receiving 1 − sL. The follower may either accept the proposed deal or refuse it. If F rejects the proposal, it may in turn make a new offer: the leader takes sF and the follower 1 − sF . The leader may accept it or not. If no agreement is reached after two negotiation rounds, an exogenously given settlement is applied: the leader receives s (%) and the follower 1 − s (0 ≤ s ≤ 1). The extensive form of this sequential bargaining game is depicted in figure 4.8. Over the bargaining process, firms have a certain degree of “impatience” captured by a common discounting factor δ (0 ≤ δ < 1). Note that δ ≡ 1 (1 + k ), where k (k > 0) is the appropriate discount rate. Discounting future payoffs at a higher discount rate gives the players an incentive to reach an agreement earlier. We can conjecture that the equilibrium slicing is
t jec
( s, 1 − s )
re
sF
t
Decision maker
(sF , 1 − sF )
accep
sL
pt acce
t ec rej
( sL , 1 − s L )
Leader
Follower
Follower
Leader
(Nature)
Decision time
1
2
3
4
5
Real time
1
2
3
Figure 4.8 Extensive form of the bargaining game under complete information Here ( si , 1 − si ) are the payoffs to the leader and the follower, respectively. Two time references are considered: the order of the play (decision time) and the real time at which agreements (or settlement) may occur. Discounting relates to the second dimension.
Market Structure Games: Dynamic
137
affected by the magnitude of the discount rate since a later ( 1) settlement has lower present value. In such a sequential game with perfect information and a finite horizon, the subgame perfect equilibrium is found backward. At decision time 4, the leader may either accept the follower’s proposal, receiving sF today, or reject it, receiving the exogenous amount s in the last period. This latter settlement is worth δ s today (at real time 2). The leader will accept the offer sF if sF ≥ δ s.20 What is the follower’s best continuation strategy from decision time 3 onward, when the leader acts optimally in the subsequent period? The follower (F ) faces this decision if it rejects the offer made by the (bargaining) leader previously. The follower may construct the offer (at decision time 3) in two alternative ways: Deal A The leader accepts the offer. In this case, the follower is better off offering the minimum acceptable level for the leader, namely sF * = δ s, instead of any higher share. The follower would then receive a slice of 1 − sF * = 1 − δ s (at real time 2). Deal B The leader rejects the offer. In this case, the follower receives 1 − s at the last stage, worth δ (1 − s ) today (at real time 2). The leader receives δ s (at real time 2). When selecting between the two alternative deals, the follower considers the relative value of 1 − δ s (deal A) versus δ (1 − s ) (deal B). For 0 ≤ δ < 1, we have 1 − δ s > δ (1 − s ). The optimal deal at decision time 3 is deal A, where follower F proposes δ s to its rival who accepts it. The follower would then earn 1 − δ s. One step earlier (at decision time 1), the leader may design its proposal in a similar manner: Deal C The follower accepts the offer. F then receives 1 − sL. Deal D The follower refuses the offer. The follower then proposes a new settlement. As determined above, L would then receive δ s at real time 2, which is worth δ 2 s at real time 1. F receives the present (real time 1) value of 1 − δ s, meaning δ(1 − δ s ). The follower will not accept the offer unless it receives a higher value than otherwise. In other words, firm F accepts if 1 − sL ≥ δ (1 − δ s ). The leader would optimally retain for itself the maximum acceptable amount, 20. We assume that if a firm is indifferent between the present values of the two different deals, it will select the proposal made first. This assumption enhances the model readability but it can be relaxed.
138
Chapter 4
which is sL * ≡ 1 − δ (1 − δ s ) = 1 − δ + δ 2 s (≥ δ 2 s ). Both parties will thus accept the equilibrium pie sharing ( sL*, 1 − sL*) at the outset. The three-period model above is rather simplistic and not descriptive of many real-world bargaining situations. In reality, although decision times are discrete, firms sometimes bargain over a longer period until an agreement is reached. In such a setting one can truncate the infinitehorizon problem, leveraging on the earlier three-period setup. Previously the final settlement ( s, 1 − s ) required the presence of a third party or arbiter in the bargaining process. Instead of ( s, 1 − s ) being exogenously given, suppose that this pie-sharing rule results from another similar three-period bargaining game. As a result in perfect equilibrium the bargaining leader’s payoff satisfies s* = 1 − δ + δ 2 s *; hence s* = 1 (1 + δ ). In the subgame perfect Nash equilibrium for the infinitely repeated game, the split is
( s*, 1 − s *) = ⎛⎝
δ ⎞ 1 , . 1+ δ 1+ δ ⎠
(4.9)
This equilibrium result is related to the firms’ “patience” via the discount factor δ . The bargaining leader is better off receiving a higher share than its rival.21 A case in point is negotiating a short-sale agreement over a real-estate property. Suppose that newcomers have decided to acquire a cozy apartment in the city center but stay in a hotel until they find the appropriate opportunity. Staying in a hotel is costly and increases their opportunity cost of waiting, resulting in a lower δ . They naturally prefer to find their ideal apartment early on and avoid paying out rents for a prolonged time. In bargaining for the apartment, they will likely accept to pay a premium due to their higher opportunity cost and impatience. The owner of the apartment may take advantage of the situation and sell the property at a higher price. 4.2.2
Cooperation between Cournot Duopolists in Repeated Games
We analyzed in section 3.2.2 the classic case where Cournot duopolists choose their quantity simultaneously in a noncooperative manner. The simultaneous Cournot competition model rests on the premise that firms maximize their short-term profit. This leads to a situation where even 21. If the follower suffers from delay, it is more likely to accept the deal offered by the leader earlier as it is costly to wait longer for a more lucrative deal. The leader can take advantage of this, proposing a less attractive deal. This first-mover advantage increases with higher risk (higher discount rate or lower discount factor). Moreover the values obtained in equilibrium by the parties decrease with the degree of impatience δ .
Market Structure Games: Dynamic
139
though the monopoly outcome would have been preferable for both firms considered individually, it is never reached as a stable industry equilibrium (prisoner’s dilemma). This result is based on the debatable assumption that firms formulate their strategies at the same decision time regardless of past history and ignoring the long-term impact of today’s decisions. In real life, firms frequently compete with one another over an extended period and are faced with recurring competitive situations over multiple stages. This kind of strategy setting may be captured by repeated games or supergames.22 Box 4.4 provides a real-world example of collusion in the German retailing market. Here we sketch a refinement of the Cournot model to examine how repeated strategic interactions may alter the equilibrium play.23 We again consider duopolist firms facing linear demand as in equation (3.1) and symmetric production cost, c. The Nash equilibrium for a duopolist in the standard symmetric Cournot setup, obtained in equation (3.14), is qC = ( a − c ) 3b, with total industry output being QC = 2 (a − c ) 3b. This industry output in Cournot duopoly is higher than in monopoly (QC ≥ QM). The price, however, is lower. Clearly, the two firms would be better off setting jointly their aggregate production equal to the monopoly quantity (QM). However, in the standard Cournot model, each player has an incentive to deviate from the collusive quantities (QM 2 , QM 2). Eventually Nash equilibrium quantities (qC , qC ) that are not jointly optimal are chosen. In infinitely repeated games, however, the desirable cooperative equilibrium (QM 2 , QM 2) may be sustainable under certain conditions. Friedman (1971) considers such a duopoly game where the market is assumed in a steady state.24 In each period, each duopolist makes a tactical decision on the quantity to supply to the market. In this repeated game, duopolists end up being better off if they behave as follows: 22. In simultaneous games, firm actions maximize short-term profits. This mechanism explains why the collectively optimal outcome is not necessarily reached as a (stable) Nash equilibrium. In multistage games, a firm may have an incentive to cooperate if a (tacit) agreement may create a favorable platform for future higher profits. Even though a firm would earn a higher short-term profit by deviating from the collusive agreement, it will not be enticed to do so if it values future collaborative profits more. The long-term benefits gained from a tacit agreement may offset the short-term gains from behaving selfishly. Infinitely repeated games can result in collaborative behaviors being sustainable in situations where sufficiently patient firms act in their own interest. 23. We do not intend to give an advanced account of repeated games here. For a comprehensive treatment of repeated games, reputations, and long-run relationships, see Maileth and Samuelson (2006). A good treatment of repeated games is also given in Fudenberg and Tirole (1991, ch. 5). 24. Growth is here assumed zero, so there is no need to account for the interplay between growth and discounting.
140
Chapter 4
Box 4.4 Suspected collusion in the German retailing market
German Antitrust Authorities Investigate Mass Retailers S. Amann and F. Ott, Spiegel Online German antitrust officials are currently probing some of the country’s largest supermarkets and retailers over suspected cases of price fixing on chocolate—both at the production and resale levels. Investigators believe as many as 24 companies set illegal minimum prices on products. On Thursday morning, German antitrust investigators launched a surprise search of the offices of some of the biggest names in the country’s retail sector. A total of 56 German Cartel Office employees and 62 police officers visited the offices of retail giant Metro, Germany’s largest supermarket chains, including Edeka, Rewe, and Lidl, as well as the drug store chain Rossmann and pet supply store Fressnapf. Authorities also visited the offices of chocolate bar-maker Mars. Investigators have evidence that a total of 24 companies may have illegally agreed to price-fixing deals on coffee, sweets, and pet food. They believe millions of consumers may have paid more for these goods than they should have. For industry observers, however, the raids were less surprising. Late last year, the Federal Cartel Office imposed )160 million ($233 million) in fines against coffee producers Melitta, Dallmayr, and Tchibo for entering into a secret agreement to coordinate price increases. American food conglomerate Kraft was also involved but avoided penalty because it turned itself in and cooperated with the competition authority during the investigation. Both Tchibo and Melitta have contested the fines, and the case is expected to go before the higher regional court in Düsseldorf. . . . But it is also clear that the agency has been investigating some of the larger players in the field over other products for some time now. Industry expert Roeb says it’s not surprising that investigations are now focused on makers of sweets following the coffee investigations. “Certain product groups are particularly prone to price fixing,” he says. There are high fluctuations in commodity prices, there’s a relatively small number of countries that can produce the commodities and the number of producers is limited. “That makes the market clear and manageable,” he says. Attractive for All Involved What’s new in the current investigation, however, is the suspicion that both producers and retailers may have agreed to price fixing. “The vertical price fixing is unique in this case,” Cartel Office spokesman Kay Weidner said. Companies are allowed to set recommended prices, but it is illegal to agree
Market Structure Games: Dynamic
141
Box 4.4 (continued)
to concrete prices. Antitrust investigators believe the 24 companies came to a deal on a minimum price for products. If the allegations are true, it would mean that both traders and companies adhered to that agreement, thus violating German competition law. Such agreements are, of course, attractive for all involved as they guarantee both producers and retailers reliable prices and higher profits. Such arrangements are additionally attractive for retailers in that they can boost the sales of their own brands. “Merchants can price their own brands below the agreed-upon prices for name brands without the fear that the name brand prices will follow,” said one branch insider . . .. Those familiar with the market are convinced that the Cartel Office wanted to set an example. “With today’s investigation, we wanted to make it clear that vertical price fixings are also in violation of antitrust law,” said Cartel Office spokesman Weidner. A 2000 law allowing for those involved in price fixing to turn state’s evidence and thus avoid penalty—a regulation recently taken advantage of by Kraft Foods—is giving antitrust regulators a boost. One measure of the Cartel Office’s recent success is the value of fines it has levied from year to year. In 2006, the antitrust authorities collected just )2.5 million in fines. In 2007, however, that number exploded to )114 million before almost tripling in 2008 to )317 million. In 2009, following the penalties handed down to the coffee producers, the Cartel Office brought in over )400 million. Such statistics are good news for those companies not involved in price fixing. And for consumers. According to German consumer protection groups, coffee drinkers in Germany paid a total of )4.8 billion too much for their morning jolt of caffeine from 2000, when the coffee producers began colluding, until the three companies were first searched in July 2008. Price Fixing Probe: German Antitrust Authorities Investigate Mass Retailers by Susanne Amann and Friederike Ott reprinted with permission from SPIEGEL Online. Publication date: January 15, 2010.
1. Agree to produce half the monopoly quantity if the other player also produces half.25 2. Deviate from the (tacit) agreement and produce the Cournot–Nash quantity forever if the other player deviates. This aggressive stance is the (harsh) punishment from having deviated in the first place. 25. This assumes that (QM 2 , QM 2 ) is already the industry state at the outset.
142
Chapter 4
Such behavior relates to tit-for-tat or trigger strategies. Such strategies are also observed in nature, as discussed in box 4.5. This strategic stance is a translation of the biblical saying “an eye for an eye, a tooth for a tooth.” It supposes that fair behavior by one player induces fairness by the other, and vice versa. Under monopoly, the equilibrium quantity 2 is QM = ( a − c ) 2b and profit equals π M = (a − c ) 4b. In the standard 2 Cournot duopoly game, firms earn a profit π C = ( a − c ) 9 b in equilibrium. If firms behave cooperatively, such as by following a tit-for-tat 2 strategy, they each produce QM 2 = (a − c ) 4b, earning π M 2 = (a − c ) 8 b at each stage. If firm i sticks to the tacit agreement and produces QM 2 while firm j deviates, the optimal quantity for firm j obtains by solving QM ⎡ ⎛ QM ⎞ ⎤ ⎛ ⎞ max ⎢ p ⎜ + q j ⎟ − c ⎥ q j = max ⎜ a − bq j − b − c⎟ q j . q q j ≥0 ⎣ ⎝ 2 ≥ 0 ⎠ ⎝ ⎠ j 2 ⎦ When deviating, firm j would optimally produce q D = q j* = 3 (a − c ) 8b, 2 earning profit π D = 9 (a − c ) 64b. In the aftermath, however, firm j would compete forever à la Cournot, receiving Cournot duopoly profit π C each period. Since π D > π M 2 > π C , firm j has an incentive to deviate in the short run. However, it must also assess the long-term negative effect of this deviation. We next analyze this trade-off. The value of cooperating forever is ∞ ⎛ πM ⎞ πM C ≡ ∑δ t ⎜ = ⎝ 2 ⎟⎠ 2 t =0
∞
∑ ⎛⎝ 1 + k ⎞⎠ 1
t =0
t
=
1 ⎛ πM ⎞ . 1 − δ ⎜⎝ 2 ⎟⎠
Alternatively, if the firm deviates this period and operates in Cournot duopoly forever thereafter, it receives the present value: ∞ ∞ δ ⎞ C 1 ⎞ D ≡ π D + ∑ δ tπ C = π D + π C ∑ ⎛ = πD + ⎛ π . ⎝ ⎠ ⎝ + k − δ⎠ 1 1 t =1 t =1 t
For tacit cooperation to sustain itself in each period, the following condition must hold: C > D, or M ⎛ 1 ⎞ π > π D + ⎛ δ ⎞ πC. ⎝ 1−δ ⎠ 2 ⎝ 1−δ ⎠
Considering the given profit values π C , π M, and π D, the condition above holds if δ > 9 17 or k < 8 9. So once again we confirm that the degree of impatience or the opportunity cost of waiting (which is exogenous to the firms’ decisions) affects critically the sustainability of cooperative behavior. In industries characterized by high riskiness (high k
Market Structure Games: Dynamic
143
Box 4.5 Repeated prisoner’s dilemma and tit for tat in nature
Tit for Tat Chris Meredith, Australian Broadcasting Co. Long before humans started playing games, natural selection discovered the fundamentals of game theory and shaped animal societies according to its rules. Within species, individuals adopt alternative competing strategies with frequencies that reflect the success of each strategy . . .. However, cooperation within and between species has generated only one strategy, tit for tat . . . You Scratch My Back . . . Evolutionary biologists have had considerable trouble explaining the evolution of cooperative behavior. The problem is that cooperation can always be exploited by selfish individuals who cheat. It seems that natural selection should always favor the cheats over the cooperators. Co-operation involves doing and receiving favors, and this means that the opportunity to cheat and not return a favor is a very real possibility. Trivers (1971) tackled this problem and developed the theory of reciprocal altruism based on the idea that cooperation could evolve in species clever enough to discriminate between cooperators and cheats. The concept is summarized in the saying “you scratch my back and I’ll scratch yours.” Trivers’s theory of reciprocal altruism is particularly successful in explaining human behavior because reciprocal altruism is a major part of all human activities . . .. [it] was an important advance in our understanding of the evolution of cooperation, but it was a “special theory” rather than a “general theory.” The discovery of how cooperative behavior could evolve in species far less intelligent than humans came in a surprising way—from a detailed study of the well-known paradox “the prisoner’s dilemma.” The Prisoner’s Dilemma The prisoner’s dilemma refers to an imaginary situation in which two individuals are imprisoned and are accused of having cooperated to perform some crime. The two prisoners are held separately, and attempts are made to induce each one to implicate the other. If neither one does, both are set free. This is the cooperative strategy available to both prisoners. In order to tempt one or both to defect, each is told that a confession implicating the other will lead to his or her release and, as an added incentive, to a small reward. If both confess, each one is imprisoned. But if one individual implicated the other, and not vice versa, then the implicated partner receives a harsher sentence than if each had implicated the other. The prisoner’s dilemma is that if they both think rationally, then each one will decide that the best course of action is to implicate the other although they would both be better off trusting each other. Consider how
144
Chapter 4
Box 4.5 (continued)
one prisoner thinks. If his partner fails to implicate him, then he should implicate his partner and get the best possible payoff. If his partner has implicated him, he should still “cheat”—since he suffers less than if he trusts his partner. However, the situation is more complicated than this analysis suggests. It is fairly obvious that the players’ strategic decisions will also depend on their likelihood of future encounters. If they know that they are destined never to meet again, defection is the only rational choice. Both individuals will cheat and both will end up relatively badly off. But if the prisoner’s dilemma is repeated a number of times, then it may be advantageous to cooperate on the early moves and cheat only toward the end of the game. When people know the total number of games of prisoner’s dilemma, they do indeed cheat more often in the final games. Robert Axelrod was interested in finding a winning strategy for repeated prisoner’s dilemma games. He conducted a computer tournament. The result of the tournament was that the simplest of all strategies submitted attained the highest average score. This strategy, called tit for tat, had only two rules. On the first move cooperate. On each succeeding move do what your opponent did the previous move. Thus tit for tat was a strategy of cooperation based on reciprocity . . .. Tit for Tat These results provide a model for the evolution of cooperative behavior. At first sight it might seem that the model is relevant only to higher animals that can distinguish between their various opponents. If so, tit for tat would simply be Trivers’s theory of reciprocal altruism restated. But tit for tat is more than this and can be applied to animals that cannot recognize each other—as long as each individual starts cooperative encounters with very minor, low-cost moves and gradually escalates as reciprocation occurs . . .. Four features of tit for tat emerged: 1. Never be the first to defect. 2. Retaliate only after your partner has defected. 3. Be prepared to forgive after carrying out just one act of retaliation. 4. Adopt this strategy only if the probability of meeting the same player again exceeds 2/3. According to Axelrod, tit for tat is successful because it is “nice,” “provokable,” and “forgiving.” A nice strategy is one that is never first to defect. In a match between two nice strategies, both do well. A provokable strategy responds by defecting at once in response to defection. A forgiving strategy is one which readily returns to cooperation if its opponent does so; unforgiving strategies are likely to produce isolation and end cooperative encounters . . . Source: Excerpts from Tit for Tat by Chris Meredith, [The Slab] Australian Broadcasting Co., 1998.
Market Structure Games: Dynamic
145
or low δ ), tacit collusion between duopolists may not be individually preferable and sustainable as an industry equilibrium. In such situations firms may prefer higher short-run profit π D (π D > π M / 2) even at the cost of sacrificing cooperative profits later on. A small value of δ (or equivalently a higher value of k ) makes a punishment meant to begin next period and apply thereafter (where punishment is tantamount to going back to Cournot behavior) less effective in deterring a profitable deviation this period (π D > π M / 2). If the market is more stable or less volatile (high δ or low k ), tacit collusion may become self-enforceable as firms have no incentive to cheat or deviate from the agreed-upon behavior. Friedman’s (1971) model of tacit collusion among Cournot duopolists is a special case of what is referred to as the folk theorem (e.g., see Friedman 1977; Fudenberg and Maskin 1986). This theorem basically asserts that for infinitely repeated games, many strategy profiles, including the tacit collusion profile, that are not optimal from a short-run, static perspective can sustain as a perfect industry equilibrium provided that players are sufficiently patient or discount factors are large (discount rates are low).26 For more on the economic intuition behind repeated games, see our interview with Robert Aumann in box 4.6 where he also discusses the underlying notion of rationality in game theory. Chamberlin (1933) recognizes other factors that influence the sustainability of collusive behaviors, such as detection lags and firm heterogeneity. Tacit collusion is enforced by the threat of retaliation, for example, as part of a trigger strategy. If firms cannot immediately react when rivals deviate due to detection lags, retaliation is delayed. This makes deviation 26. The folk theorem formalized by Fudenberg and Maskin (1986) is more general than suggested here. It asserts that if the players are sufficiently patient then any “feasible,” “individually rational” payoffs can be enforced by a perfect equilibrium in infinitely repeated games under complete information. In itself, the folk theorem has little to do with collaborative behavior. Many strategy profiles are perfect equilibria for sufficiently patient players in such infinitely repeated games. To improve the models’ prediction power, economists often look for an argument that allows selecting one equilibrium among many as being more likely to arise. A selection process often used rests on the assumptions that (1) symmetric players are likely to coordinate on an equilibrium that allows for symmetric payoffs, and (2) the “focal” equilibrium should be Pareto optimal from the players’ perspective. This suggests that duopolists would coordinate on half the monopoly output. The “correctness” of this selection is more a belief than a result relying on solid game-theoretic foundations. One should ideally resort to more appropriate selection techniques, such as risk-dominance, to select among equilibria. Harsanyi and Selten (1988) examine such approaches. Fudenberg and Tirole (1986) suggest that infinitely repeated games are too “successful” to provide a solid structure for analyzing oligopoly dynamics; they instead propose several alternative approaches.
146
Chapter 4
Box 4.6 Interview with Robert J. Aumann, Nobel Laureate in Economics (2005)
1. Economic sciences have been criticized for the presumed rationality of economic agents. Do you envision a role for a Center for the Study of Irrationality? I belong to the Center for Rationality at Hebrew University. We study both, rational as well as psychological or behavioral approaches. Recent experiments, such as the ultimatum game, probability matching, or Tversky and Kahneman’s behavioral work, confirm that our acts are not always rational, i.e., they do not follow self-interested optimizing behavior in each situation. Rather, we often follow certain rules or norms of behavior that usually, or on average, lead to broad desirable outcomes for survival or success over many similar decision situations over time. Thus optimization is over rules that provide repeated guidance over time rather than over individual situation actions (I refer to this as rule- vs. act-rationality). Rules may lead to optimal behavior in general, but not necessarily in every case. Such rules may be evolutionary or unconsciously adopted. For example, we eat when we feel hungry. 2. Your work on repeated games is particularly interesting. Do you believe that cooperation is more descriptive of real-world firm interactions than classic competition? If so, what is the intuitive logic for this?
Market Structure Games: Dynamic
147
Box 4.6 (continued)
In repeated games players encounter the same situation over and over again. In such games a player has to take into account the impact of his current action on the future actions of other players, i.e., reputation or relationship effects. In such situations cooperation is more likely to be sustainable under certain conditions. Intuitively, the presence of a cooperative equilibrium arises because the threat of retaliation is real, since one will play the game again with the same person. On many occasions the optimal way of playing a repeated game is not to repeat a Nash strategy of the constituent game (e.g., repeated prisoner’s dilemma), but to cooperate and play a socially optimum strategy or follow the “social norm.” In the repeated prisoner’s dilemma, cooperation can be sustained if the discount rate is not too high, i.e., if the players are interested enough in future outcomes of the game. Cooperation is more likely when interaction over time occurs among a few players. The time element/repetition is important. Cooperation may be harder to attain when there are many players.
less costly in present-value terms and tacit collusion harder to sustain.27 In case of asymmetry among firms (e.g., involving different fixed or variable production costs), it is difficult to determine a “focal” choice (e.g., production quantities) on which firms are likely to cooperate. This further hinders the sustainability of tacit collusion. 4.2.3
Co-opetition: Sometimes Compete and Sometimes Cooperate?
It is by now well accepted by corporate executives that partnerships with suppliers, customers, and sometimes even with competitors, may bring about significant competitive advantages. As noted, some game-theoretic models can provide economic rationale for this notion. However, until recently strategic management frameworks have not adequately addressed this issue. Porter’s five-forces framework, for instance, tends to view other parties (competitors, suppliers, or buyers) as threats to a firm’s profitability. The various relationships along the value chain, however, do not necessarily present a threat. Firms may create win-win relationships with 27. In the extreme case of infinite detection lags, firms cannot at all react to their rivals’ actions over the play of the game. This case collapses to a situation where firms formulate open-loop strategies that are adapted to calendar time only. This is equivalent to a setting where firms make their decisions simultaneously. In quantity competition, firms would produce Cournot–Nash equilibrium quantities forever.
148
Chapter 4
their suppliers and even their competitors. There are various situations where collaboration with external parties may create value: •
Joint R&D ventures with rivals.
Partnership with suppliers to enhance the benefit to end consumers or improve productive efficiency (e.g., via just-in-time production). •
Co-development with a customer’s R&D team to better tailor endproducts to customer requirements. •
Agreement among competitors to set industry standards (e.g., Blu-ray technology). •
•
Coordinated lobbying among competitors in the same industry.
As a result of opportunities created by these broader collaborations, the entire value chain, including activities performed by outside parties, should be re-considered. Porter’s (1980) value chain is based on the premise that everything is done in-house. Today it is possible to redesign the value chain in many industries to better cope with uncertainty and interactive relationships, including outsourcing. Strategists have called for a more collaborative model of the value chain based on partnerships. With an increasing number of business processes becoming commoditized within and across industries, executives need to rethink the very basis for competition in their businesses. “Cooperative” strategies nowadays appear on top of corporate agendas. To provide a better framework that takes account of collaborative relationships, Brandenburger and Nalebuff (1995) propose the concept of value net, founded in microeconomics and game theory. They term this kind of strategies co-opetition, as they involve a mix of cooperation and competition. Firms need to decide which of their business processes are core or crucial to make their strategies succeed, and which can be performed in a relatively generic and low-cost fashion, potentially outsourced to external parties. Interactions among firms are structured along the value net depicted in figure 4.9. The value net consists of four key players: suppliers, customers, substitutors, and complementors. Substitutors are external parties who act in a contrarian fashion, whereas complementors help create value since their actions benefit both firms. The value net includes relationships with external parties presenting threats or opportunities. A firm can increase economic profits and value either through value creation (increasing the size of the pie) or through value redistribution (sharing the pie in more
Market Structure Games: Dynamic
Reduce prices
Customers
Dividing up markets Substitutors
Increase prices
Making markets Company
Price competition
Complementors Creating new value
COMPETITION Reduce margin
149
COOPERATION Suppliers
Increase margin
Figure 4.9 Value net and co-opetition Adapted from Brandenburger and Nalebuff (1995)
favorable terms). Value redistribution can be accomplished, for instance, through more skillful bargaining with buyers and suppliers. Such a focus is risky as firms rarely outperform their rivals solely through value redistribution. Competition in redistribution is fiercer than competition to create new value. Yet firms can cooperate in different ways to increase the size of the pie. Once this is accomplished (in cooperation with others), value redistribution can be easier.28 The value net is helpful to better account for cooperation opportunities that might be beneficial to the firm. Such situations where firms can either compete or cooperate can be analyzed with tools offered by option games. Trigeorgis and Baldi (2010) assess the value of optimal patent leveraging strategies under both demand uncertainty and competitive rivalry using a methodology allowing for a mix between competition and cooperation. They 28. Brandenburger and Stuart (2007) subsequently develop a hybrid approach involving both noncooperative and cooperative game theory called biform games to better account for such complex strategic interactions. Their approach is characterized by two stages. In the first stage, players behave cooperatively to increase the value of the total market “pie.” Afterward they behave noncooperatively to share the market pie based on their market power. The bargaining power wielded in the second stage may stem from competitive advantages, such as technological leadership, created in the first stage. Biform games focus on shaping the competitive environment, namely first creating or reshaping a market and then building up competitive advantage to capture a larger slice of it. Such approaches may gain in acceptance over the coming decades. A practical approach providing management with state-of-the-art conceptual frameworks would be helpful.
150
Chapter 4
L
7
No (zero) (symmetric)
5
6
8
9
Small
Bracketing (asymmetric)
ate per
Coo
High
Medium
(monopoly/ abandon)
4
3
t
h Fig
Patent wall
Cross-licensing
M
2
Sleep/ abandon
1
H
Licensing
Bracketing (symmetric)
Demand
Low
Large (asymmetric)
Competitive advantage (patent innovation)
Figure 4.10 Compete versus cooperate as part of a patenting strategy Adapted from Trigeorgis and Baldi (2010)
illustrate how optimal patent strategy depends on the level and volatility of demand and on the size of competitive advantage arising from the patented innovation. The key question they consider is, when business conditions are uncertain, under what circumstances should rivals fight and when should they collaborate in using their intellectual property (IP) assets, namely when should two competitors follow a fighting or a cooperating patent strategy? They show that the circumstances under which firms should fight or cooperate are not trivial. Under demand uncertainty rivals may sometimes find it preferable to compete (e.g., defending themselves via raising a patent wall around their core patent or fighting fiercely by attacking each other via patent bracketing) and at other times to collaborate (e.g., via cross-licensing to each other or even licensing one’s patented innovation to its rival). The menu of different fight or cooperate strategies is summarized in figure 4.10. The option games approach enables to capture certain features of an adaptive business strategy. The increasing cone of market and strategic uncertainty makes the value of a dynamic strategy that enables switching among a broader menu of competing or cooperating alternatives key to survival and success in a changing marketplace.
Market Structure Games: Dynamic
151
Conclusion This chapter and the previous one discussed how industrial organization can be helpful in providing insights about certain competitive situations. Chapter 3 discussed some static benchmark models involving price and quantity competition. Chapter 4 considered the time dimension, discussing several dynamic settings. Dynamic models of complete or incomplete information are more challenging than their simultaneous-move counterparts and give richer insights on how firms should consider the long-term consequence of their current actions. In such multistage games, strategic decisions that appear suboptimal from a short-term, static perspective may indeed be optimal in the long term. Dynamic games are useful to understand that committing and killing one’s options may sometimes be advisable as a devise to create competitive advantage in subsequent stages. They also provide economic foundations for collaborative behavior in certain markets involving repeated relationships. The results discussed in chapters 3 and 4 serve as building blocks for the option games methodology we deploy later.29 Selected References Osborne (2004) offers an accessible account of game theory. Averted readers might prefer the more advanced treatment offered by Fudenberg and Tirole (1991). Besanko et al. (2004) provide a good overview of industrial organization focusing on the strategic insights of the models. Tirole (1988) is a key reference in this area. Fudenberg and Tirole (1984) discuss the taxonomy of commitment strategies. Rubinstein (1982) examines bargaining over an infinite horizon. Friedman (1971) elaborates on the sustainability of tacit collusion in infinitely repeated Cournot games. Besanko, David, David Dranove, Mark Shanley, and Scott Schaefer. 2004. Economics of Strategy, 3rd ed. New York: Wiley. Friedman, James W. 1971. A non-cooperative equilibrium for supergames. Review of Economic Studies 38 (1): 1–12. 29. Most dynamic models in industrial organization assume either steady state or a deterministic evolution of the underlying parameters. Mainstream industrial organization does not explicitly consider the impact of stochastic market uncertainty on the equilibrium results. Merging dynamic games with real options analysis helps bridge this gap, better explaining optimal decision-making in the face of uncertainty.
152
Chapter 4
Fudenberg, Drew, and Jean Tirole. 1984. The fat cat effect, the puppy dog ploy and the lean and hungry look. American Economic Review 74 (2): 361–66. Fudenberg, Drew, and Jean Tirole. 1991. Game Theory. Cambridge: MIT Press. Osborne, Martin J. 2004. An Introduction to Game Theory. New York: Oxford University Press. Rubinstein, Ariel. 1982. Perfect equilibrium in a bargaining model. Econometrica 50 (1): 97–109. Tirole, Jean. 1988. The Theory of Industrial Organization. Cambridge: MIT Press.
5
Uncertainty, Flexibility, and Real Options
Up to now we have mainly focused on industrial organization models in a certain or deterministic world. Before discussing further how to combine game theory with real options under uncertainty, we review in this chapter the basics and insights of real options analysis to improve our understanding of flexible real investment decisions.1 The real options approach to analyzing investment under uncertainty has by now gained standard corporate finance textbook status. Real options analysis involves the application of methods utilized to price financial options and other derivatives to real assets; that is, it is an extension of option-pricing theory or contingent-claim analysis to real investment situations. Financial options are financial assets (generally traded on the capital market) that give their holders the right—but not the obligation—to buy or sell an underlying asset at a specified price for a given time period. Option-pricing theory was developed to price this asset class. Real options draw on an analogy between financial options (calls or puts) and real-world contingent cash-flow streams. And yet, even when an analogy can be drawn, real options are quite different. For example, they may not be traded on the capital market and may simultaneously be held by more than one investors. Still, the analogy between real investment projects and certain traded derivative assets holds conceptual value. For instance, having the option to abandon a project for a salvage value should the market evolve worse than expected is similar to holding a put option giving the right—but not the obligation—to “sell” the underlying asset at a strike price equal to the salvage value. In such a case, the analogy applies well. Real options are now commonly 1. Readers familiar with real options analysis may skip this chapter and go directly to the description of option games provided in the subsequent chapter.
154
Chapter 5
accepted as a powerful real asset valuation and management approach. Several economics and finance books have been dedicated to this approach, more prominently Dixit and Pindyck (1994) and Trigeorgis (1996). To put our examination of real options in a concrete, applied context, we discuss in section 5.1 the investment challenges faced by European electricity suppliers. Section 5.2 discusses how managers of an electric utility can address such challenges utilizing real options analysis. Section 5.3 describes option-pricing theory and illustrates its application in situations involving concrete investment problems from the energy sector. 5.1
Strategic Investment under Uncertainty—The Electricity Sector
Over the past few decades many firms have experienced new developments in their competitive landscape, including regulatory, technological breakthrough and demand pattern changes. Few of these developments could have been predicted. Increasing uncertainty casts doubt on current predictions about market developments, technological trends or rivals’ behavior. In the midst of such uncertainty, adaptability to market developments can be of significant strategic impact. The European energy sector exemplifies this challenge quite well. National markets have opened up to new entrants and energy prices have become increasingly volatile. Even though the need to add generation capacities is well recognized in the electric utility sector (see International Energy Agency 2007), tackling complex issues such as when or where to invest in generation units is all the more difficult in this highly unpredictable environment. From this industry perspective we examine next the major sources of uncertainty and the business risk exposures implied by the new generation technology choices. 5.1.1
Need for New Investment in Europe
A key factor monitored by bodies regulating electric utilities is reserve margins. This indicator measures the power adequacy in terms of installed power generation capacity over peak demand in a given geography. Energy suppliers have to build up sufficient generation capacity to cover the base load as well as excess capacity to ensure that even in peak demand periods electricity output is sufficient. In
Uncertainty, Flexibility, and Real Options
155
Europe (EU12)
France
Italy
CAGR%
CAGR%
CAGR%
4.5
4.5
4.5
4.0
4.0
4.0
3.5
3.5
3.5
3.0
3.0
3.0
2.5
2.5
2.5
2.0
2.0
2.0
1.5
1.5
1.5
1.0
1.0
1.0
0.5
0.5
0.5
0.0
0.0 86–91 91–96 96–01 01–06
0.0 86–91 91–96 96–01 01–06
Electricity consumption
86–91 91–96 96–01 01–06
Generation capacity
Figure 5.1 Growth trends in the European electricity markets From Energy Information Administration Database. CAGR stands for “compound annual growth rate.”
other words, reserve margins must remain positive. If they fall to low levels, consumers face generation inadequacy potentially leading to blackouts. In the last decades most European countries have experienced substantial energy demand increases. As shown in figure 5.1, these increases were hardly met by capacity additions, resulting in shrinking reserve margins. In addition, most power plants built in the 1970s in the aftermath of the oil crisis are expected to be decommissioned or refurbished in the next decade across Europe as they become obsolete or no longer abide by new environmental standards. Reserve margins in some European regions (e.g., Brittany in France) are already approaching critical levels, indicating dire investment need in the coming years. Another means to improve reserve margins is to curb electricity demand, especially in peak load, by implementing energy-efficiency
156
Chapter 5
measures or other market mechanisms (e.g., customer participation) to induce consumers shift demand from peak load to lower load periods. Such initiatives are, however, not always as effective, so the need for additional generation capacity remains. Electric utilities across Europe are expected to channel huge financial resources into new power generation capacity to ensure system adequacy and reliability going forward. These investments will take place under growing uncertainty and increased environmental constraints with the aim to promote green technologies. 5.1.2
Sources of Uncertainty
As illustrated in table 5.1, utilities face a number of uncertainties, be they idiosyncratic (e.g., changing demand patterns, electricity demand growth), technological, or firm specific. Rapid changes occurring in recent years challenge would-be investors in determining when to invest (optimal investment timing), where to add new generation facilities (network Table 5.1 Uncertainty factors for electric utilities Idiosyncratic risks
Technology-specific risks
Firm-specific risks
Demand uncertainty • Demand growth • Changing demand patterns • Country-specific prices • Price developments • Effectiveness of energy-efficiency measures Regulatory risks • Plant licensing and approval • Regulation of transmission lines Competitive risks • Market power of incumbents • Market entrance
Construction risks • Investment cost overruns • Unforeseeable lead time Fuel-related uncertainty • Unsecured supply (e.g., wind, gas)a • Input price volatility (e.g., gas, coal, uranium) Environmental uncertainties • Prices on CO2 and greenhouse gas emissions • Support on green technologies • Waste management and phaseouts (nuclear power) • New environmental standards
Capital structure • Bankruptcy risks • Interest payments Cost structure • Economies of scale and scope • Learning-curve effects Company’s portfolio of corporate activities • Internal hedging
a. The 2008 dispute on gas between Russia and Ukraine led to serious supply disruptions in eastern and central Europe (e.g., Ukraine, Poland, Germany). Source: Adapted from International Energy Agency (2007).
Uncertainty, Flexibility, and Real Options
157
Electricity price (monthly averages in €/MWh) 100
80
60
40
20
0 2002
2003
2004
2005
2006
2007
2008
Figure 5.2 Electricity price fluctuations in Europe from 2002 to 2008 From Powernext
design), or what mix of technologies to invest in (technology choice). We next look at the business risks each company in the sector faces and the risks involved in the generation technology choice.2 Idiosyncratic Business Risks Since electricity cannot be effectively stored, electricity prices are very sensitive to shocks (e.g., demand pattern fluctuations, plant disruption) and are therefore extremely volatile. Figure 5.2 shows electricity price fluctuations during the period 2002 to 2008. Wholesale electricity prices in many European countries started to skyrocket in 2004 and have remained at a substantial high average level since. This overall price increase can be attributed to three underlying factors. First, most fuel prices (e.g., gas, oil, coal) have trended upward. Second, utilities now have to pay for CO2 emissions. Finally, the tightening of reserve margins has resulted in utilizing more expensive generation technologies, leading to higher average generation costs. Energy suppliers for the most part managed to pass this cost through to their customers (given the low price elasticity of demand). 2. We do not intend to elaborate on firm-specific risk factors but instead adopt the viewpoint of an “average firm” in the electricity sector.
158
Chapter 5
Besides, demand patterns can vary markedly across regions, some being more often subject to huge demand peaks (e.g., due to intense use of air-conditioning in southern European geographies). Other country-specific factors might also play a role. For instance, temperatures are different across northern and southern Europe and have differential effects. Some countries have a high share of industrial consumption (e.g., Germany), while others have more tertiary activities (e.g., the United Kingdom). The national production mix may also spill over into the electricity prices. When demand increases, utilities need to operate more generation units, including costly ones, to ensure power adequacy. The national average market price is likely to be higher owing to the costly national production mix if transmission lines are ineffective. Local resistance in the form of “not-in-my-backyard” attitudes may also act as a hindrance to ensuring adequate capacity and investment. Various European governments contemplate initiating energy-efficiency measures to curb future electricity demand, besides achieving environmental objectives. Smart meters have been introduced in some European countries (e.g., in Italy) both for industrial customers and households, enabling customers to be better informed of current electricity prices and alter their consumption patterns accordingly. Although governments and regulatory bodies have shown interest at pushing energy-efficiency measures, it is not clear whether such initiatives will be enforced and will achieve their goals. Governmental intervention may take many forms: subsidies or fiscal incentives toward new technological options, lengthy plant licensing processes for nuclear power plants, antitrust regulation or administrative market-entry barriers to protect incumbents. Technology-Related Business Risks Capital expenditures may greatly vary from technology to technology and might follow different development paths. The steel price is an important variable in any generation plant investment. Other construction-related costs as well might fluctuate depending on general realestate market conditions. New technologies may be characterized by decreasing investment costs over time due to economies of learning. Through plant design standardization, R&D costs can be spread out to a larger number of projects. This is critical for nuclear plants, especially when lack of process optimization due to limited experience results in substantial cost overruns.
Uncertainty, Flexibility, and Real Options
159
Operating and fuel costs are a major source of uncertainty. Coal-fired plants are more sensitive to the underlying fuel price volatility than nuclear power, but much less than combined-cycle gas turbines (CCGTs). Operating and maintenance costs may differ depending on the technology considered and may undergo distinct development. At the end of the day, the relative competitiveness of generation technologies varies over time. Investment decision-making must be dynamic, with the up and down potential of each underlying factor being seriously considered in adjusting the generation mix. Policy makers’ reluctance toward a steady, long-term environmental policy is another source of uncertainty. From an individual value-maximizing viewpoint, utilities tend to select the “cheapest” technology regardless of total societal costs. A practical means to avoid this problem is to internalize the indirect costs (e.g., damage on the environment) resulting from power generation. This is what the European Union intended when introducing the EU Emission Trading Scheme (EU ETS) in 2005. 5.1.3
Generation Technologies and Business Risk Exposure
A key question is not simply whether to invest but also which available generation technologies to choose. The technology choice ultimately determines the project’s sensitivity to certain underlying risk factors and its overall business risk exposure. When selecting among available technological options, one considers the variable and fixed costs involved in each case. The fixed cost components are the upfront investment cost, the decommissioning cost, and the fixed operating and maintenance costs. The up-front investment cost is very high for a nuclear or hydro plant and less so for CCGTs. The major variable cost component is the input fuel cost. Completion delays, cost overruns, and the plant’s lifetime are also important factors. Supply security may also come into play. Certain technologies may possibly put the system at risk as they might not be always available or reliable (e.g., wind). Cost factors may vary, which drives cost uncertainty for utilities. There is no superior power generation technology among the group of mature technological options. Each has certain features that make it better suited in certain situations. No technology turns out to be cheaper, cleaner, and more reliable than the others. Depending on whether a firm is willing to pay large fixed costs (e.g., nuclear power) or large variable costs (e.g., coal fired), one might prefer one technology over another.
160
Chapter 5
Among the alternative technological options some are considered more conventional, such as coal fired, combined-cycle gas turbines (CCGT), and nuclear power. The coal-fired technology involves the lowest (variable) costs under most circumstances. This technology, however, has a high carbon footprint and is significantly more expensive if environmental costs are factored in. The CCGT technology has several advantages, including lower capital investment costs and short construction times. It is also one of the technologies offering the greatest operational flexibility. This is offset by current high fuel costs. This technology is highly sensitive to gas prices since fuel costs represent a significant share of total costs. CCGT technology, however, has a poor environmental footprint in terms of CO2 emissions. Hydro power generation also involves very large (sunk) investment costs. Reservoirs are very flexible, however, since they can be closed and opened at very little cost.3 Available sites though are limited and plant standardization is hardly possible, which may lead to substantial delays and investment cost overruns. Recent high natural gas prices and CO2 emission costs have lead certain countries (mainly France) to boost investment in nuclear power plants, whose efficiency has been significantly improved relative to other technological options. However, civil nuclear power has a bad track record of delays, cost overruns, and catastrophic disruptions (e.g., Fukushima). Many countries (e.g., Italy, Germany) are reluctant to embrace civil nuclear power, while a few still invest in this technology with France taking the lead. Certain alternative technological options are gradually emerging as mainstream technologies. Onshore wind power has nearly reached a 10 percent capacity share in Europe (EU12). Other renewable technologies such as biomass, small hydro, and solar, have not yet gained enough acceptance but pave the way for more environmental-friendly power generation. Over the past two decades investments in various new generation units have significantly altered the generation mix in many European countries. A noticeable trend is the increasing share of natural gas-fired capacity (especially CCGTs) and of renewables technologies (especially onshore wind-power turbines). The offshore wind power technology has also gained in acceptance, with Germany commissioning a 400-MW wind farm (BARD offshore 1) in 2011 and the United Kingdom building up a 500-MW offshore wind farm on the eastern coast (Greater Gabbard). EU member countries generally give subsidies to 3. Other technologies such as nuclear, coal or fuel, and gas (with the exception of CCGT) power typically require a significant time lag between the decision to fire up the plant or turbine and the production of electricity itself.
Uncertainty, Flexibility, and Real Options
161
increase investment in renewables, primarily wind power and hydro. Despite being environmentally friendly, the wind power technology is often challenging for utilities as it can only operate with sufficient wind. Another alternative for electric utilities is to invest in transmission lines to enable improved integration of electricity systems with neighboring European countries. Transmission lines enable an electric utility to compensate for low reserve margins in one region through imports from another neighboring country. The presence of interconnection lines between regions is beneficial not only to utilities, which have the option to supply the market under better economic conditions, but also to the general public. Transmission lines pave the way for “shared” options or resources, enabling better power supply management when reserve margins get tighter at the national level with higher regional demand compensated by higher generation in areas that were not connected before. Business risk exposure depending on generation technology is summarized in table 5.2. Current market trends are not solely due to the emergence of superior technologies but also to the prevailing market and regulatory conditions favoring these technologies. Figure 5.3 shows the development in terms of generation capacity of various technological options over the recent two decades in Europe. Changes in fuel costs, construction costs and CO2 emission prices significantly affect the relative attractiveness of each technology. Since Table 5.2 Business risk exposure of conventional generation technologies Technology
Investment cost
Time-tobuild
Operating cost
Fuel cost
Security of supply
CO2 emissions
Coal-fired CCGT Hydro Nuclear Wind Low exposure Medium exposure High exposure Note: The table excludes idiosyncratic uncertainty (which is the same whatever the technology) as well as firm-specific risk.
162
Chapter 5
CAGR% (1987–2007)
Generation capacity by technology type in EU12 (in million kW) 600
Total
1.5
Renewables 17.7
500 Nuclear
1.2
Hydro
0.2
Thermal
1.2
400
300
200
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
0
1987
100
Figure 5.3 Generation capacity by technology type in Europe From Energy Information Administration Database
investment in generation capacity is largely sunk, firms face high business risks when deciding at the outset which technology to select. Unexpected events may make other technological alternatives more suitable under specific future market conditions. A key parameter an electric utility should take into consideration when committing to a given power plant is exposure to fuel price (variable cost) volatility. Wind power needs no fuel as such. For nuclear plants, fuel costs (mainly uranium) represent a small share of total operating and investment costs (most being dedicated to enrichment, conversion, and fabrication, being therefore quasifixed). In contrast, CCGTs are very sensitive to fuel costs. Because natural gas prices are very volatile, this brings substantial fuel-sensitivity for CCGTs. 5.2
Common Real Options
Electric utilities must take into account the aforementioned risk factors and market dynamics when they work out their investment strategies. They can benefit from an improved understanding and guidance concerning the risk factors, particularly when formulating investment decisions to enhance their generation capacity and future economic profits.
Uncertainty, Flexibility, and Real Options
163
Table 5.3 Common real options Real option type
Description
Relevant industries
Deferral or waiting option
Management can wait before making the investment to see how the market unfolds.
Resource extraction industries, real-estate development, capitalintensive industries.
Staging or time-to-build option
When a managerial decision takes time or is done in stages, management can default if market prospects prove worse than expected.
Technology-based firms (R&D), longdevelopment capitalintensive industries (e.g., electric utilities), startup ventures.
Expand or extend option
If the project turns out better than expected, management can spend more to expand the project scale or it can extend the project’s useful life.
Natural-resource industries (e.g., mining), real-estate development.
Contract or abandon option
If the market prospects are worse than expected, managers can contract or abandon it for salvage.
Capital-intensive industries (e.g., airplane manufacturers), new product introductions.
Switching option
Management can select among the best of several alternatives, e.g., inputs, outputs or locations, under the prevalent market conditions.
Multinational firms with production facilities in different currencies, platform strategy in the automotive sector.
Compound option
If investment takes place in stages, the first project can be valued in view of the future growth options it creates.
High-tech, R&D, industries with multiple product generations, strategic acquisitions.
As summarized in table 5.3, management can benefit from different types of real options. We here discuss common types of real options in the context of an electric utility. The necessary tools to quantify the values of such real options are discussed in the subsequent section. Deferral or timing option Management is not always confronted with a now-or-never investment decision. Often it might have the flexibility to time its investment decision after observing how events unfold. Suppose that French utility EDF has identified that in the Brittany region reserve margins are falling to such low levels that they may jeopardize power supply security. EDF, being authorized to open up nuclear power plants in France, resolves to operate such a plant in Brittany if it is deemed worthwhile. Since the involved capital investment cost I is large and cannot be recouped, management wishes to decide on solid ground when more sure that the need for new generation capacity in this
164
Chapter 5
region is here to stay. EDF in effect holds an investment timing or “waitand-see” option to benefit from the resolution of uncertainty about electricity prices (reflective of the regional imbalance between demand and supply). Suppose that EDF may exercise its option to invest only once, at maturity (year T ). Let VT indicate the time- T value of the investment’s expected operating cash flows. Just before expiration the option will pay off the greater of the net value created, VT − I , or 0, meaning at maturity the option is worth max {VT − I ; 0}. The option to invest or defer is thus analogous to a call option on the gross project value VT with exercise price equal to the required capital investment outlay I . Waiting, though it may come at the cost of forgoing early cash flows, may pay off under certain conditions and help avoid costly premature investment. Option to stage or default during construction (time-to-build option) Cash flows are not generated overnight once managers make an investment decision. Typically large construction projects are staged. During power plant construction, if market conditions deteriorate, management can choose to forego any future planned capital outlays. The actual investment staging consists of a series of capital outlays, offering at any given stage the opportunity to revise the initial go-decision and stop incurring further costs should future prospects turn out worse than expected. In such a case each stage t ( ≤ T ) can be viewed as an option written on the value of subsequent stages by incurring the (time-t) investment cost outlay I t required to proceed to the next stage. The investment opportunity can be valued similarly to compound options (options on options). Option to expand or extend Given the raised public awareness of environmental challenges ahead and the enforcement of more stringent environmental legislation, electric utilities are increasingly investing in renewables technologies, such as wind power. A possible plan design for the utility is to start up small, scalable wind farms with a limited number of turbines, with the possibility to expand. The value of the initial wind farm is Vt at time t ( ≤ T ). If future electricity prices or governmental subsidies are higher than expected, management can expand the number of turbines or the scale of production (by e percent) by making an additional cash outlay I e. At time t ( ≤ T ), the entire project can be viewed as the base-scale wind farm, Vt, plus a call option on future (expanded) investment, namely Vt + max {eVt − I e ; 0} = max {(1 + e ) Vt − I e ; Vt }. The initial wind farm thus enables the firm to capitalize on future expansion opportunities. This
Uncertainty, Flexibility, and Real Options
165
expansion option, which will be exercised only if future electricity prices or subsidies turn out more favorable, can make the basic small, scalable wind farm project worth undertaking. Option to scale down or contract If market conditions turn out weaker than originally expected, management can operate below total power generation capacity or even reduce the scale of operations (by c percent), thereby saving part of the planned cash outflows or fixed costs (I c). This flexibility to mitigate loss is analogous to a European put option on part (c percent) of the base-scale project, with exercise price equal to the potential cost savings (I c), paying off max {I c − cVT ; 0} at maturity. It may sometimes be preferable to build a plant with lower initial construction costs and higher maintenance expenditures in order to acquire the flexibility to contract operations by cutting down on maintenance if market conditions turn out unfavorable. Option to shut down (and re-start) operations A power plant does not necessarily have to operate in each and every period. It may be profitable to operate flexible (e.g., CCGT peak-load power) plants with higher marginal costs if they can be shut down when electricity prices are low and not sufficient to cover variable operating costs. In this case the utility might be better off not operating temporarily, especially if the costs of switching between the operating and idle modes are relatively small.4 In peak-demand periods, as market electricity prices rise to peak levels, operation can start up again and be quite profitable. Enron allegedly made huge profits in California operating such peak power plants only a few days or weeks in the year when prices peaked, exploiting the tremendous volatility in local electricity prices. Operating such a peak-load plant is analogous to a call option enabling management to receive in year t revenues Pt by incurring variable costs Ct as exercise price. The contingent payoff at time t (≤ T ) is π t = max {Pt − Ct ; 0}, with present (option) value π 0(t ) ≡ e − rt Eˆ 0[π t ]. Because the plant embeds such shutdown and restart options at each (discrete) time period t until maturity T T , the total plant value is V0 = ∑ t =0 π 0( t ) provided switching costs are small or negligible.5 Option to switch use (e.g., inputs or outputs) Instead of committing to a certain input an electric utility may select the best of several fuel alternatives should future conditions vary. We discuss below two types 4. For simplicity, we assume henceforth that switching costs are negligible, allowing decision-making to be path independent. 5. This case with no switching cost has been analyzed by McDonald and Siegel (1985) along the Black–Scholes lines.
166
Chapter 5
of switching options, relating to inputs or outputs. Over the past years natural gas has been under increasing competitive pressure owing to the introduction of substitute products, especially liquefied natural gas (LNG). The prices for natural gas and LNG are positively correlated, but they undergo different market development trends that can make one input more affordable than the other (for an equivalent output efficiency) in a given period. An effective strategy is to invest in flexible gas-fired generation technologies (especially CCGT) that can use either of these fuels. The utility would be willing to pay a certain premium to acquire such a flexible technology, compared to the (best of the) rigid alternatives that confer no or less choice (either natural gas or LNG).6 Naturally the correlation between natural gas and LNG is fairly high since the products are close substitutes. If the correlation between the two fuels is lower, the switching option will be even more valuable. Generally, process flexibility can be achieved not only through an adequate technology choice (e.g., building a flexible generation facility that can switch among alternative fuel inputs) but also by maintaining relationships with a variety of suppliers, changing the mix as their relative prices change. Another form of switching option relates to the optionality to design operations such as to produce alternative outputs, selecting the most profitable output once price uncertainty gets resolved. Recently there has been a consolidation trend in the energy industry toward the merging of electric and gas utilities. A case in point is the merger of the French gas utility GDF with Suez. This move partly resulted from the synergies arising from the increasingly growing share of gas-fired power generation (CCGTs) in Europe. From this viewpoint the gas utility (GDF) may either sell the natural gas to the end consumers or supply natural gas to gas-fired power generation units in view of the actual energy prices (gas vs. electricity). Another example of the option to switch outputs relates to the integration of European electricity markets due to the introduction of merchant transmission lines. Such interconnection lines enable the Italian electric utility Enel buy cheap nuclear power from France, or to 6. Let At be the value (as of time t) of utilizing natural gas and Bt of using LNG as input. The cost of switching from one input to the other may differ depending on which fuel was previously in use, exhibiting some form of path dependency. Denote by I ( At −1 → Bt ) the switching cost when swapping from natural gas to LNG and by I ( Bt −1 → At ) the cost of switching from LNG to natural gas. Should market conditions prove currently better for LNG over natural gas, the firm may switch from natural gas to LNG by incurring the switching cost I ( At −1 → Bt ) . The utility can select the best of the two operating modes, max { At ; Bt − I ( At −1 → Bt )} . Inversely, if the LNG fuel was initially used, the payoff at the following node will be max {Bt ; At − I ( At −1 → Bt )} .
Uncertainty, Flexibility, and Real Options
167
sell electricity in France should the price there be higher than the Italian market price. Option to abandon for salvage value If electricity prices suffer a longstanding decline, management does not have to sustain operations forever. It may find it better to shut down operations, decommissioning the less performing generation units (e.g., plants with higher variable costs). Management has a valuable option to abandon a project permanently and stop paying the production costs. This option is analogous to an American put option on current project value, Vt, with exercise price the “salvage value,” St, entitling management to receive Vt + max {St − Vt ; 0} or max {Vt ; St } before option expiration in year T . The option to close down the plant provides downside risk protection if the firm is not committed to go on generating electricity when market prospects worsen. Since most assets in the electricity sector are dedicated to generate power with no possibility to produce other goods, the resale price of production facilities is limited. The prospect to forgo negative cash flows when shutting down a plant can provide a sufficient incentive and make the abandonment option valuable. The salvage value for which the plant can be sold or exchanged, St, may fluctuate over time as does the project’s value Vt.7 Corporate (compound) growth options An early investment may set the path for future opportunities to follow. Such growth options are particularly valuable when learning-curve effects are involved. Because of more stringent environmental constraints and demand for higher energy efficiency, several new generation technologies are being developed (while older ones are being substantially researched on and improved). A case in point is the evolutionary pressurized reactor (EPR) technology developed by Areva, EDF, and Siemens as the new generation of pressurized water nuclear reactors. Installing a single nuclear plant with the EPR reactor may appear unattractive to developers owing to high R&D costs and lack of scale economies. It could be of interest, however, to build one as an operating prototype. Future nuclear power plants could leverage on the experience gained from developing, designing, and building the first EPR plant. The investment in the first EPR plant is a prerequisite in a chain of interrelated projects. The prototype derives its value not so much from its expected project-specific cash flows but rather from unlocking future growth opportunities in the form 7. In this case the abandonment option can be viewed and valued as a switching option to select between two stochastic assets (with no switching cost). Myers and Majd (1990) examine a similar problem.
168
Chapter 5
of a chain of new, better performing nuclear power plants. From an options perspective the opportunity to invest in an innovative generation technology is analogous to an option written on options (construction of other new-generation plants); that is, it is an interproject compound option. Even if the initial stand-alone project does not generate positive net value on its own, the experience generated during the development of the first-generation EPR plant may serve as a springboard for developing future enhanced-efficiency nuclear power generation units. Unless the firm decides to commit and initiate the first EPR investment, subsequent generations would not even be feasible. Such growth options are found in many other industries especially in industries which are infrastructure-based, R&D-intensive, or involving multiple product generations or applications (e.g., in semiconductors, computers, pharmaceuticals) as well as in industries where having a global footprint is key. Portfolios of real options A well-diversified power generation portfolio includes several affordable technologies that hedge exposure to various technology-specific business risks while achieving power adequacy. Fluctuations in the key cost factors (e.g., investment costs, fuel costs, CO2 emissions prices) can alter the relative attractiveness of alternative generation technologies. A well-diversified portfolio of generation capacities allows utilizing technologies better suited to changing market conditions. Portfolios of options may also involve negative interactions or positive synergies.8 Even though the installed generation capacity is well-diversified on the overall European level, it is not necessarily the case at the national level. There are noticeable “unbalanced” mixes in France (large share of nuclear power) or the Netherlands (almost 70 percent gas fired). The technology portfolios in the European Union compared to individual member countries are shown in figure 5.4. Diversification in terms of technologies is a sensible strategy for an electric utility to help manage risks. As part of their risk management strategies, utilities can consider investing in other technology types or setting up transmission lines. Transmission lines make it possible to leverage on the Europe-wide welldiversified generation mix and reduce exposures in a given geography to certain technology-specific business risks. Plants involving high fixed costs (e.g., nuclear plants) should be committed to base-load demand in 8. For general option interactions, see Trigeorgis (1996, ch. 7). In the electricity market, coupling wind farm and hydro with pump storage creates a portfolio of power generation technologies whose value is higher than the sum of the parts. In such coupled systems, overproduction from wind farm can be used to pump water back in the hydro system using this energy source (in the hydro system) at a later point in time.
Uncertainty, Flexibility, and Real Options
169
Total capacity 100% Renewables Nuclear
80%
Hydro
60%
40% Thermal
20%
0%
BE
DK
FR
DE
GR
IE
IT
LU
NL
PT
ES
UK EU12
15
13
112
127
13
6
82
1
23
14
77
80
562
Total capacity (in million kW)
Figure 5.4 European generation capacity in 2007 by technology type—Europe (EU12) and member countries From Energy Information Administration Database
order to spread these costs over as many hours as possible. Flexible power plants (e.g., CCGTs) characterized by large variable costs should operate during peak hours when load is higher and electricity prices sufficiently high to cover these costs. A precise rigid recommendation for the generation mix is unwarranted since the optimal mix changes continuously over time. Figure 5.5 shows a static version of the recommended generation mix as a function of electricity demand and marginal costs. The marginal costs are hardly stable over time, so the graph changes dynamically. Box 5.1 discusses how to think about managing portfolios of options via a gardening metaphor. Marco A. G. Días from Petrobras discusses some real options applications in Brazil in box 5.2. 5.3
Basic Option Valuation
Should electricity prices or other market factors evolve differently than initially expected, the utility’s management has several options to adapt to enhance the future cash flow stream or limit losses. The aforementioned real options, however, cannot be properly valued using the classical discounted cash-flow (DCF) approach. Real options analysis is a more useful tool to analyze managerial flexibility since it
170
Chapter 5
Marginal costs (in €/MWh)
Demand-off peak
Demand peak
Extreme demand
Old plants
Gas-fired
Coal-fired
Nuclear, hydro Must run (e.g., wind)
Electricity demand (in MW)
Figure 5.5 Technology use as a function of demand level Adapted from International Energy Agency (2007, p. 127)
Box 5.1 Managing portfolios of options: A gardening metaphor
Strategy as a Portfolio of Real Options T. Luehrman, Harvard Business Review Managing a portfolio of strategic options is like growing a garden of tomatoes in an unpredictable climate. Walk into the garden on a given day in August, and you will find that some tomatoes are ripe and perfect. Any gardener would know to pick and eat those immediately. Other tomatoes are rotten; no gardener would ever bother to pick them. These cases at the extremes—now or never—are easy decisions for the gardener to make. In between are tomatoes with varying prospects. Some are edible and could be picked now but would benefit from more time on the vine. The experienced gardener picks them early only if squirrels or other competitors are likely to get them. Other tomatoes are not yet edible, and there’s no point in picking them now, even if squirrels do get them. However, they are sufficiently far along, and there is enough time left in the season, that
Uncertainty, Flexibility, and Real Options
171
Box 5.1 (continued)
many will ripen unharmed and eventually be picked. Still others look less promising and may not ripen before the season ends. But with more sun or water, fewer weeds, or just good luck, even some of these tomatoes may make it. Finally, there are small green tomatoes and late blossoms that have little likelihood of growing and ripening before the season ends. There is no value in picking them, and they might just as well be left on the vine. Most experienced gardeners are able to classify the tomatoes in their garden at any given time. Beyond that, however, good gardeners also understand how the garden changes over time. Early in the season, none of the fruit falls into the “now” or “never” categories. By the last day, all of it falls into one or the other because time has run out. The interesting question is: What can the gardener do during the season, while things are changing week to week? A purely passive gardener visits the garden the last day of the season, picks the ripe tomatoes, and goes home. The weekend gardener visits frequently and picks ripe fruit before it rots or the squirrels get it. Active gardeners do much more. Not only do they watch the garden, but based on what they see, they also cultivate it: watering, fertilizing, and weeding, trying to get more of those in-between tomatoes to grow and ripen before time runs out. Of course, the weather is always a question, and not all the tomatoes will make it. Still, we would expect the active gardener to enjoy a higher yield in most years than the passive gardener. In option terminology, active gardeners are doing more than merely making exercise decisions (pick or not to pick). They are monitoring the options and looking for ways to influence the underlying variables that determine option value and, ultimately, outcomes. Option pricing can help us become more effective, active gardeners in several ways. It allows us to estimate the value of the entire year’s crop (or even the value of a single tomato) before the season actually ends. It also helps us assess each tomato’s prospects as the season progresses and tells us along the way which to pick and which to leave on the vine. Finally, it can suggest what to do to help those in-between tomatoes ripen before the season ends. Source: Reprinted with permission of Harvard Business Review from “Strategy as a Portfolio of Real Options,” by T. Luehrmann, September– October 1998, pp. 89–99. Copyright © 1998 by the Harvard Business Review School Publishing Corporation; all rights reserved.
172
Chapter 5
Box 5.2 Interview with Marco A. G. Días, Petrobras
1. Besides the United States, Brazil is likely the most popular user of real options analysis in the world. Why you think is that? What is the role of instability and uncertainty historically in Brazil? Can you comment on the adaptability of the Brazilian people and businesses? Real options (RO) is more popular in Brazil than in most developed countries. The history of instability and uncertainty obligates both people and businesses to be more flexible to adapt to the frequently changing environment. We say that in Brazil even the past is uncertain! So flexibility is more valuable here than elsewhere. One example is the flex-fuel car. Here RO started as the villain and ended up as a hero! Due to the oil price shocks in the 1970s, Brazil initiated the ethanol-fuel automobile production in the 1980s. But with low petroleum prices the owners of sugar mills preferred to make sugar instead of ethanol (switch output option), leaving the service stations without ethanol for customers. Ethanol car production practically disappeared with the fall of consumer confidence in the ethanol automobile. But in the 2000s a new technology appeared in Brazil: the flex-fuel car using either gasoline or ethanol. The flex-fuel car provided switch-input options for the consumer, offsetting the fear of the producer switch-output (sugar-ethanol) option. The flex-car was an immediate success. In the last years almost all automobiles sold in the Brazilian market are flex-fuel. The best antidote to the producers’ switch output option was the consumers’ switch input option! The flex-fuel technology increased consumer confidence and boosted the automobile market demand, leaving everybody better off: ethanol producers, automobile producers, and consumers. A real options success story! 2. How, and to what extent, is real options thinking used at Petrobras? Can you give specific examples of its use and its importance in influencing key decisions? There are many examples of application of real options at Petrobras. Some of these applications are listed below, including several public cases where
Uncertainty, Flexibility, and Real Options
173
Box 5.2 (continued)
the decision of the petroleum regulatory agency (ANP) was often favorable to Petrobras. i. The petroleum sector was opened up in Brazil in the late 1990s. In 1998, ANP presented for public debate a proposal for the duration of the exploratory phase, suggesting only 5 years for deepwater blocks exploration. We conducted analysis using real options, suggesting between 8 and 10 years. Subsequently ANP, once it became aware of the results, enlarged the duration to 9 years. Petrobras thus had more time to discover and appraise new oilfields; the recent large pre–salt discoveries needed more than 6 years to be discovered after the auction. RO thus contributed in the public debate with a lot of success! ii. In 2000 to 2001, the Brazil–Bolivia gas pipeline became a subject of litigation between TBG (a pipeline company controlled by Petrobras) and British Gas (BG) and Enersil for the pipeline free access. BG and Enersil wanted free access to the pipeline with flexibility to use it or not, while paying the same tariff as other companies without this flexibility (“takeor-pay” contracts). We demonstrated to ANP that this flexibility has value so that the tariff must be higher for BG compared with “take-or-pay” tariffs. The decision of ANP was to permit free access to the pipeline but require paying a higher price for the tariff. iii. In 2005, a biodiesel project was analyzed with real options because of the “flex” technology for the inputs, namely flexibility to use vegetable oils from soybean, cotton, castorbean, etc. The RO value was decisive for the project to get approved by the board of directors. iv. In 2003, Petrobras International solicited another real options project named “Strategic Valuation of E&P International at West Africa Offshore.” Using RO, we showed the importance to stay in Africa offshore. Petrobras kept its business there, and nowadays the African production is very significant for Petrobras’s international operations. v. We studied GTL (gas-to-liquid) technology using RO (switch-input and switch-output options) in 2006 to 2008. The study recommended the project (though the 2008 crisis and other priorities, such as large discoveries in pre-salt, put the project in wait mode). 3. Do you see a role for using game theory in conjunction with real options analysis? Yes, definitely. At Petrobras game theory is being taught since 2007, but separate from courses on real options. This course, although recent, motivated three real-life applications already. In the future, I think option games courses will be offered at Petrobras also and related applications will follow.
174
Chapter 5
can allow future decisions to be adapted to future market conditions. Static NPV represents an extreme case where the management commits at the outset (at t = 0) to a stringent plan of action, as if the utility could not alter its operational or investment decisions over time. Here we review basic option valuation principles to help equip those readers in need of a basic tool kit for valuing the real options an electric utility or any other firm faces. The two most known option-pricing models are attributed to Black and Scholes (1973) and Cox, Ross, and Rubinstein (1979).9 The Black–Scholes (BS) or Black–Scholes–Merton model involves advanced mathematics and notions of financial theory in continuous time, while the discrete-time multiplicative binomial model of Cox–Ross–Rubinstein (CRR) offers a more intuitive introduction to option pricing.10 Originally these models were designed to price financial options but have since been extended to valuing real options. Robert C. Merton discusses the development and impact of continuous-time finance, option-pricing theory, and the relevance of real options in box 5.3. The valuation approaches underlying the net-present-value (NPV) paradigm and real options analysis involve similar assumptions but alternative versions of risk adjustment. The traditional approach based on net present value essentially involves discounting expected cash flows at a discount rate k that reflects the nondiversifiable risk of the project. An alternative approach, that is core to option pricing, is to make the adjustment for risk to the expected cash flow rather than to the discount rate: the resulting certainty-equivalent cash flow can thus be discounted at the risk-free rate of interest r (instead of k ). Discrete-time and continuoustime models offer alternative ways to characterize these certainty equivalents. Discrete-time models are generally better suited when one needs to handle practical or complex valuation problems (e.g., portfolios of real options). The continuous-time approach assumes instantaneous decisionmaking. Discrete-time models are easier to implement, though continuous-time models have an appeal as they help better identify the theoretical value drivers and examine the underlying trade-offs. We first present the basic valuation idea in discrete time and later extend it briefly to the continuous-time context. 9. The Black–Scholes model is also often referred to as the Black–Scholes–Merton model to pay tribute to Robert C. Merton for developing much of the foundation work in Merton (1973). 10. The two setups are closely related. The discrete-time CRR model converges to the continuous-time Black–Scholes model for small time increments or large number of inbetween steps. In both cases the basic underlying idea is that in a complete capital market one can replicate over the next time period an asset’s price dynamics by creating a portfolio that provides the same payoffs in each state of the world.
Uncertainty, Flexibility, and Real Options
175
Box 5.3 Interview with Robert C. Merton, Nobel Laureate in Economics (1997)
1. Did you envision the widespread use or application of options thinking and tools when you first worked on options and stochastic-calculus applications? How did you come up with the idea? I recognized early on that option pricing had a much wider application than to stock options narrowly, such as using it to develop a unified theory for pricing the capital structure of the firm. I traded warrants, convertibles, and OTC options before I ever studied economics. At MIT I worked with Paul Samuelson in 1968 on warrant pricing, and separately attacked the intertemporal optimal lifetime portfolio problem with continuous trading using the Itô calculus as a tool to describe the dynamics of actual sample paths. When I discussed with Myron Scholes what he and Fischer Black were doing in discrete-time intervals between trades to find a dynamic strategy for hedging out the beta risk of an options/stock portfolio, it was natural to apply this same technique and show in the limit of continuous trading that one could hedge all (not just beta) risk and thus could replicate the payoffs to any derivative via dynamic portfolio trading in the underlying asset. 2. Paul A. Samuelson recently passed away. His seminal work spans many economic fields, including finance. Can you comment on his early contribution to continuous-time finance? In his 1965 rational theory of warrant pricing, Paul Samuelson introduced geometric Brownian motion for underlying stock prices; he generated the Kolmogorov equations for warrant pricing and with H. P. McKean derived
176
Chapter 5
Box 5.3 (continued)
pricing for the early exercise provision of American-style warrants. In an attached appendix to Samuelson’s published 12th von Neumann Lecture, I provided the connection between his warrant pricing model and the Black–Scholes model.a This was the first time that the Black–Scholes model appeared in published print. 3. To what extent has continuous-time finance reshaped the theory of pricing and valuation? The replication idea has been employed for decades in just about every venue of financial security pricing; my Nobel Lecture (Merton 1998) includes a list of various applications of the model methodology, including real options. 4. What are your views on the usefulness of real options analysis? Is real options analysis handicapped if the underlying asset (project) is not traded or portfolio replication of the embedded option is not readily available? I believe real options analysis is extremely useful. Real options valuation is no more handicapped than any of the other tools of valuation, such as NPV, where you need data on an equally risky asset to estimate beta, etc. Conceptually the model can be adapted to nontrading of the underlying asset and even to nonobservable interim prices (see Merton 1998, pp. 326–36). Since in all equilibrium asset-pricing models (e.g., the CAPM or arbitrage pricing theory) assets that have only nonsystematic or diversifiable risk are priced to yield an expected return equal to the riskless interest rate, and given that the portfolio tracking error (following a portfolio strategy that minimizes that error) is uncorrelated with all traded asset returns, the option pricing formula would apply even in those applications in which the underlying asset is not traded. a. Paul Samuelson was John von Neumann Lecturer at the SIAM Annual Meeting in 1971. This lecture resulted in the article by Samuelson (1973).
5.3.1
Discrete-Time Option Valuation
Assume that a new power plant would generate a stream of cash flows having present value V today (t = 0). In one period, the plant value can take one of two possible values: it will move up to V + or down to V − with real probabilities q and 1 − q, respectively. Figure 5.6 depicts the underlying asset’s value dynamics in a one-period binomial lattice. Assume further that this asset is traded in capital markets or that there
Uncertainty, Flexibility, and Real Options
177
V+ V V− t=0
1
Figure 5.6 Binomial lattice for the underlying asset (project) value
is a twin security traded in the market that has the same risk profile as the asset under consideration. Under traditional NPV analysis, the future values of the power plant (V + and V − ) are related to its present value (V ) as a discounted expectation: V=
E [V1 ] qV + + (1 − q) V − = . 1+ k 1+ k
(5.1)
Suppose that investing in the plant involves capital cost I . Investing immediately would result in project NPV = V − I . The standard (NPV) approach, however, is unable to properly value projects involving operational flexibility, such as the option to delay the investment for a year.11 Real options involve cash flows that are asymmetric on the downside versus the upside and are contingent on future uncertain events. Risk, and therefore discount rates, may vary in a complex way over time and across various future states. Optionality can be properly valued using option-pricing theory. The basic idea behind option valuation is that one can replicate an option by constructing a portfolio consisting of a (long or short) position in the underlying asset and a (short or long) position in a risk-free bond. This portfolio can be constructed so as to exactly replicate the future cash flows or returns of the option in each state of the world.12 Since the option and its equivalent portfolio would provide the same future returns in all states, they must sell for the same current value to avoid risk-free arbitrage profit opportunities. Equivalently, we could create a riskless replicating portfolio and discount the payoffs from this portfolio at the 11. When we consider a project with differing starting dates as mutually exclusive alternatives, one can capture a form of timing flexibility and act optimally by choosing the alternative with the highest NPV. This approach based on mutually exclusive alternatives extends the standard “NPV rule” asserting to invest in positive NPV projects. 12. We assume that the market is complete so that the replication argument holds.
178
Chapter 5
risk-free rate, r.13 To value the project as if in a risk-neutral world, one needs to utilize the so-called risk-neutral probabilities.14 Alternatively, the present value of any contingent claim can be obtained from its expected certainty-equivalent value discounted at the risk-free rate r. Through the ability to construct a riskless portfolio, investors’ risk attitudes do not matter in valuing the option and need not be explicitly considered. Therefore, we can equivalently—and more conveniently— obtain the option value as if we were in a risk-neutral world. In such a world all assets would earn the risk-free return (r), and so risk-neutral expected cash flows can be appropriately discounted at the risk-free rate. Let p denote the risk-neutral probability of an upward move (and 1 − p the probability of a downward move). The present value of the underlying asset, such as the power plant, in a risk-neutral world is V=
Eˆ [V1 ] pV + + (1 − p) V − = , 1+ r 1+ r
(5.2)
where Eˆ [⋅] denotes the risk-neutral expectation. The risk-neutral probability of an up move is then p≡
(1 + r ) V − V − V+ −V−
.
(5.3)
13. Consider a portfolio made of N shares of the underlying asset Vt and B risk-free bond(s) that pay €1 next period. Since the bond is risk-free, it yields in each state of the world a return equal to 1 plus the risk-free return r. Holding B bonds at time t is worth B (1 + r ) in one period. Consider a portfolio that replicates the payoffs of the option in each state. To avoid arbitrage opportunities in the capital market, this portfolio must sell for the same price as the option it replicates, that is, C + = N × V + − (1 + r ) B and C − = N × V − − (1 + r ) B. This system of two equations with two unknowns gives the following values for N and B N=
C+ − C− V+ −V−
and
B=
C (1 − H ) , 1+ r
with ⎛ C+ −C− ⎞⎛ V ⎞ H =⎜ + ⎟ − ⎟⎜ ⎝ V − V ⎠⎝ C ⎠ being a discrete measure of the elasticity of the option with respect to the underlying asset value. The position, N , invested in the asset to replicate the option payoff is the option’s hedge ratio (or option’s delta). In discrete time, it is obtained as the difference (spread) of the option prices divided by the spread of asset prices. 14. The NPV approach factors investors’ risk-aversion in the risk-adjusted discount rate k . The ability to construct a replicating portfolio enables the current value of the option claim to be independent of the actual probabilities or investors’ risk preferences. Option-pricing theory bypasses risk-aversion by valuing options as if investors were in a risk-neutral world.
Uncertainty, Flexibility, and Real Options
179
If the underlying asset evolves according to the multiplicative binomial process with up factor u (where V + = uV ) and down factor d (where V − = dV), the risk-neutral probability above is given by15 p≡
(1 + r ) − d u−d
.
(5.4)
Consider now a deferral option on the underlying power plant’s value. Suppose that this real option has value C + or C −, as a function of V + or V − , respectively, in one period. In a risk-neutral world, the expected return of this option must also equal the risk-free rate r. This results in the following fundamental option-pricing formula:16 C=
Eˆ [C1 ] pC + + (1 − p)C − = . 1+ r 1+ r
(5.5)
Example 5.1 Option to Invest (or Defer) Suppose that EDF has the option to build a power plant in Brittany this year or wait one year until regional elections are settled. EDF has no fear of preemption and, depending on the party chosen, may gain political support through subsidies. By waiting, EDF will forgo one period of profit but can benefit from the resolution of political uncertainty. If the plant is built immediately, EDF will receive gross project value V = C100 million (m) ; net of the capital investment cost I = C80 m, this results in an NPV of C20 m. Suppose that the plant’s value in one period will move up by 80 percent (or u = 1.8) or down by 40 percent (d = 0.6) depending on the outcome of next year’s elections, with each outcome equally likely (q = 0.5). A year later, the plant will have an expected value (from subsequent cash flows) of V + = C180 m if the 15. Note that d < 1 < 1 + r < u for the no-arbitrage argument to hold. Alternatively, formula (5.4) can be obtained by considering returns. In the up case, the return is R + ≡ V + V − 1 = u − 1. In the down case, it is R − ≡ V − V − 1 = d − 1. The risk-neutral probability, p, is obtained from the equilibrium condition that the expected return on the asset in a risk-neutral world must equal the risk-free rate r: pR + + (1 − p) R − = r, or
p≡
(1 + r ) − d u−d
.
Probability p is lower than the real probability of an upward move, q, since p accounts for investors’ risk-aversion, giving lower weight to upside events. p is the value probability q would have in equilibrium if investors were risk neutral. 16. Equation (5.5) provides a formula for the value of the option in terms of V , r and the asset volatility (u and d ). Effectively, u is the discrete-time equivalent of the continuoustime volatility parameter eσ h (which is a function of the volatility of the asset σ and the time step h). In the electricity case we can derive the risk-neutral probability p from the price dynamics of electricity prices using forward prices for electricity.
180
Chapter 5
outcome is favorable or V − = C60 m in the adverse case. Suppose that the expected rate of return or discount rate is k = 20 percent and the risk-free interest rate is r = 8 percent. The risk-neutral probability, obtained from equation (5.4), is p=
(1 + r ) − d u−d
=
1.08 − 0.6 = 0.4 ( < 0.5) . 1.8 − 0.6
If there are no options creating asymmetry in the payoff profile, the riskneutral valuation formula of equation (5.2) would yield the same value for the plant as traditional DCF valuation based on (5.1): 0.4 × 180 + (1 − 0.4 ) 60 1.08 0.5 × 180 + (1 − 0.5) 60 = 1.20 = C100 m.
V=
The option to defer the investment can be quite valuable, however, since the firm would invest only if prices and project value rise sufficiently, while it has no obligation to invest under unfavorable developments. The value of the plant launched one year from now is C + = max {180 − 80; 0} = 100 in the event of a positive election outcome, or C − = max {60 − 80; 0} = 0 in the event of a negative outcome. The value of the option to invest next year, based on equation (5.5), is C=
0.4 × 100 + 0.6 × 0 ≈ C 37 m. 1.08
EDF thus has a very valuable option to defer the investment for a year (37 > 20), waiting until further information about the outcome of political elections and the electricity prices in Brittany is revealed. Example 5.2 Option to Expand Alternatively, EDF may install new turbines in one of its wind farms in Brittany, expanding production scale by making a complementary investment if the newly elected regional government gives support to renewable energies. In year 1, EDF can choose to maintain base-scale operation (receiving project value V − or V + at no extra cost) or expand operations by 50 percent (e = 0.50) by adding capacity at extra cost I e = 40. The original investment opportunity can be seen as the base-scale project plus a call option on future growth, providing C + = V + + max {eV + − I e ; 0} = max {(1 + e ) V + − I e ; V + } after an up move,
Uncertainty, Flexibility, and Real Options
181
or C − = max {(1 + e ) V − − I e ; V − } in the adverse case. In the case at hand, EDF will choose to expand in the up case, obtaining C + = max {1.5 × 180 − 40; 180} = 230, but it will maintain the base scale in the adverse case earning C − = max {1.5 × 60 − 40; 60} = 60. The expanded NPV (including the value of the option to expand if the market grows) based on equation (5.5) is C=
0.4 × 230 + 0.6 × 60 ≈ C118.5 m . 1.08
Example 5.3 Interconnection Line The Italian electric utility Enel is considering installing an interconnection line with France that would enable it to benefit from electricity price differentials between the two countries. Suppose that the electricity price in France is constant at PF = 1 due to reliable nuclear power technology. The Italian electricity price, being PI = 1 today, will move up by 50 percent to PI+ = 1.5 (u = 1.5) or down by 33 percent to PI− = 0.67 (d = 2 3) with equal probability (q = 0.5) each year. If the Italian electricity price rises next year, Enel can take advantage of the transmission line importing cheaper electricity from France by buying at the fixed French price PF = 1 and receiving the higher Italian selling price PI+ = 1.5. This is analogous to the previous option to expand with payoff max {PI+ − PF ; 0} = 0.5. In the adverse case, if Italian prices drop to PI− = 0.67 next year, Enel can export electricity to France receiving the higher French price PF = 1; the option payoff is then max {PF − PI− ; 0} = 0.33. This option is analogous to a put that allows to receive the French price (strike price) of C1 by paying the lower Italian electricity price (underlying asset) of PI− = 0.67. The interconnection line thus provides Enel with two valuable options: one creating an upside potential to sell more electricity in Italy by importing cheaper nuclear power from France (a call option), and another limiting the downside risk to Enel by selling in France rather than in Italy if local prices drop (a put option). The price received by Enel will be P + = max {PI+ ; PF } or
P − = max {PI− ; PF }.
If local prices move up next year, Enel will charge P + = max {1.5; 1} = 1.5. If they move down, it will obtain the guaranteed (French nuclear) price P − = max {0.67; 1} = 1. Without the transmission line, Enel could only sell at local prices, being exposed to the full price fluctuation risk, receiving PI+ = 1.5 or PI− ≈ 0.67. The average (next-year) price in Italy would have been E [ PI ] = qPI+ + (1 − q) PI− = 0.5 (1.5 + 0.67 ) ≈ 1.1. With the transmission
182
Chapter 5
line, however, the average price is E [ PI ] = 0.5 (1.5 + 1) = 1.25 ( > 1.1). Thus the transmission line allows to sell at higher prices on average. The transmission line would be mispriced if managers ignore the embedded switching flexibility value and base their investment decision on the future average price, max {E [ PI ]; PF } = 1.1. Real options analysis, by considering the optimal switching decision at each period in each state, makes it possible to circumvent this “flaw of averages.”17 What is the correct “average” price discounting for the value of the transmission line? From equation (5.4), the risk-neutral probability of an up move (with risk-free rate r = 0.05) is p ≡ (1.05 − 0.67) (1.5 − 0.67) = 0.46. From equation (5.5) the value of the merchant interconnection line per unit of output is 0.46 × 1.5 + 0.54 × 1 ≈ 1.17 . 1.05 Outside Europe, Hydro-Québec, a state-owned corporation in Canada with large production capacity in hydro (95 percent), is profitably exploiting such transmission lines. Hydro reservoirs are very flexible resources, so that Hydro-Québec can increase or decrease output at very low cost almost overnight. In contrast, Ontario and the northeastern states of the United States rely mainly on nonflexible thermal power plants that virtually have a constant output, explaining why prices there are very sensitive to changes in demand patterns. At night, Hydro-Québec buys electricity from Ontario and the NE-US at very low prices (due to low local demand), downscaling its own production. During the day, it raises own production and sells them back electricity at high prices (high local demand).18 One can extend the above one-period binomial analysis to a larger number of steps though a repetitive process. This is discussed in appendix 5A and illustrated briefly in example 5.4 below for two steps. Example 5.4 Option to Invest or Defer (Two Steps) Consider a situation analogous to example 5.1, where Enel of Italy has the option to enter the Russian electricity market in two years’ time. Suppose again that the market value, currently C150 m (V = 150), follows a binomial process with an upward multiplicative factor u = 1.5 and 17. We can characterize this value difference by applying Jensen’s inequality to convex or concave functions. The payoff function f (⋅) of the call option is convex in the underlying factor X , such that E [ f ( X )] ≥ f ( E [ X ]). On the converse, a put has a concave payoff function, so that the opposite inequality holds. Savage (2009) applies Jensen’s inequality to challenge certain managerial practices based on the “flaw of averages.” 18. We thank Marcel Boyer for suggesting this example.
Uncertainty, Flexibility, and Real Options
183
downward factor d = 1 u ≈ 0.67 in each period. Enel must incur an infrastructure investment cost of I = C80 m to enter this geography at T = 2 years. The risk-free interest rate is r = 0.04. In the scenario following two consecutive up moves, the gross market value, V ++ = uuV = 1.5 × 1.5 × 150 ≈ C 338 m, exceeds the investment cost, I = C80 m. Enel will then enter the market, receiving a net (forward) investment opportunity value of C + + = max {338 − 80; 0} = C 258 m. In the intermediary state (that occurs after a downward move following an up move or inversely), the gross market value is V +− = udV = 1.5 × 0.67 × 150 = C150 m. If Enel invests, it receives V +− − I = 150 − 80 = C 70 m. It will thus again exercise its investment option at maturity, receiving C +− = C70 m. In the down state, after two consecutive down moves, the gross market value is V − − = ddV = 0.67 × 0.67 × 150 ≈ C 67 m. Enel will not invest I = C80 m for a negative NPV (67 − 80 = −13). It will instead abandon the investment option, receiving C − − = 0. Figure 5.7 shows the market value evolution and the investment option’s payoffs at maturity. The current investment option value is assessed by a backward process using risk-neutral valuation along the two-step binomial tree. The riskneutral probability of an up move, determined from equation (5.4), is p = 0.45. Going backward to t = 1, in the up state the investment option value is given by equation (5.5) as Binomial tree representing market value evolution
Option payoff
Option tree
338 C ++ = 338 − 80 = 258
225
150
p
p 150
C +– = 70
C + = 148 1−p
C = 80
C +– = 70 p
1−p
100
C ++ = 258
C – = 30 1−p
67
t=0
1
2
C
––
C –– = 0
=0
t=0
Figure 5.7 Binomial tree evolution and payoff for the option to defer (2 steps)
1
2
184
Chapter 5
C+ =
pC ++ + (1 − p)C +− 0.45 × 258 + 0.55 × 70 = ≈ C148 m. 1+ r 1.04
In the down state, the option has (time-1) value C− =
0.45 × 70 + 0.55 × 0 = C 30 m. 1.04
Finally, one step earlier, the present value (t = 0) of the investment option for Enel is pC + + (1 − p)C − 0.45 × 148 + 0.55 × 30 = ≈ C 80 m. 1+ r 1.04
C=
Alternatively, using the t = 2 expectation, based on applying the equation from appendix 5A for the binomial distribution with n = 2 steps: p2C + + + 2 p (1 − p) C + − + (1 − p) C −− 2
C=
(1 + r )2
0.45 × 258 + 2 × 0.45 × 0.55 × 70 + 0.552 × 0 1.04 2 ≈ C 80 m. =
2
That is, the current value of the investment opportunity for Enel to enter the Russian market in two years is &80 m, which is more that the value to enter it today. The net present value of entering the market immediately (at t = 0) is NPV = V − I = 150 − 80 = C 70 m. 5.3.2
Continuous-Time Options Analysis
Real options analysis can be either dealt with in discrete or in continuous time. Each approach has its own merits. The continuous-time approach is more helpful to derive basic investment principles.19 The CRR discrete-time analysis rested on the assumption that the underlying asset, Vt, follows a multiplicative binomial process. In continuous time this corresponds to assuming that the underlying asset follows the geometric Brownian motion (GBM) dV = ( gV ) dt + σ V dz,
(5.6)
where g denotes the actual growth trend of the process, σ 2 its variance and z is a standard Brownian motion.20 19. Continuous-time models are useful when model assumptions enable the derivation of analytical solutions. 20. See the appendix of the book for detail on the GBM.
Uncertainty, Flexibility, and Real Options
185
Black and Scholes (1973) use this process to derive their famous formula for pricing European call options. At maturity T , a European call option pays off the greater of the net value VT − I or zero, meaning CT = max {VT − I ; 0}. Under risk-neutral valuation, the call option at time t = 0 is worth C = e − rT Eˆ [CT ], where r is the continuously compounded risk-free interest rate.21 The Black–Scholes (BS) formula for the value of a European call option (on a nondividend-paying asset) is C = V N( d1 ) − Ie − rT N(d2 ),
(5.7)
where N (⋅) is the cumulative standard normal distribution.22 Parameters d1 and d2 are given by d1 =
ln (V I ) + [ r + (σ 2 2)]T
σ T d2 = d1 − σ T .
,
(5.8)
This formula is a cornerstone in option-pricing theory. One can obtain it based on the replicating portfolio argument as in Black and Scholes (1973) and Merton (1973).23 The discrete-time and continuous-time approaches are not really competing paradigms; they view the same problem from different mathematical angles. The multistep Cox–Ross–Rubinstein (CRR) option-pricing formula is derived in appendix 5A. For a given maturity, T , as the time 21. Under the risk-neutral probability measure, the asset price does not exactly follow the GBM of equation (5.6), but an adjusted GBM involving a “risk-neutral drift,” gˆ , equal to r in the Black and Scholes model. 22. Let p (·) denote the probability density under the risk-neutral measure. By decomposing C , we obtain ∞
C = e − rT ∫ max {VT − I ; 0} p(VT ) dVT 0
∞
= e − rT ∫ (VT − I )p(VT ) dVT I
= e − rT × ξ − e − rT I × θ , where θ ≡ Pr (VT ≥ I ) and ξ ≡ Eˆ [VT | VT ≥ I ] are, respectively, the probability that the option ends up “in the money” and gets exercised at maturity, and the expected value of the asset when it does. From equations (A.16) and (A.19) in the appendix of the book, θ = N ( d2 ) and ξ = Ve rT N ( d1 ) . We employ the risk-neutral drift term r, here, instead of g. 23. Our derivation of BS in note 21 rests on probabilistic properties of the European call option and of geometric Brownian motion. The replicating-portfolio approach generalizes to a larger family of processes (Itô processes) and can accommodate other payoff functions. As noted, under mild conditions, it is possible to create a portfolio replicating the payoff to a call option. This portfolio consists of N shares of the underlying asset and a short position, B, in a risk-free bond. In continuous time, N = CV (V ) and B = e − rtC (1 − ε ) , with ε ≡ CV (V ) × V C . In the BS case involving geometric Brownian motion, the hedge ratio (position in the underlying asset) used in the replicating portfolio is N = CV (Vt ) = N( d1 ) .
186
Chapter 5
step, h ≡ T n, becomes increasingly smaller (as h approaches 0 or the partition of the time interval becomes finer with n going to infinity), continuous replication is approximated and the multiplicative binomial process converges to the geometric Brownian motion. In the binomial model the parameters u, d , and p are consistent with their continuoustime counterparts if 24 u = eσ
h
1 and d = . u
(5.9)
Under these conditions the multistep CRR binomial option-pricing formula, discussed in appendix 5A, converges to the BS formula in (5.7).25 Example 5.5 Option to Invest (Black–Scholes) Let us revisit example 5.4 above. Enel may delay investment in the Russian electricity market for two years until the true market development is revealed. Underlying project value is V = 150. Suppose that this value fluctuates continuously over time (driven by global energy supply and demand factors) with volatility σ = 40%.26 The risk-free interest rate is r = 4%. The investment outlay for the power plant is I = 80. From equation (5.8), d1 =
ln (150 80 ) + [ 0.04 + ( 0.4 2 2)] 2 0.4 2
≈ 1.54,
and d2 ≈ 1.54 − 0.4 2 ≈ 0.97. From the cumulative standard normal distribution, N (d1 ) ≈ 0.94 and N (d2 ) ≈ 0.84. From the Black–Scholes formula of equation (5.7), the investment option value is C = 150 × 0.94 − 80 × e −0.04 × 2 × 0.84 ≈ C 79 m. This is close to the value obtained in example 5.4 above using the CRR binomial model (C80 m) with only two steps (n = 2). 24. The probability of an up move is given by p=
1 2
+
1 αˆ ′ 2 σ
h,
where αˆ ′ ≡ ln r − (σ 2 2) . Cox, Ross, and Rubinstein (1979) show that, in the limit, the complementary binomial distribution function B used in appendix 5A converges to the cumulative standard normal distribution function N(⋅). 25. The CRR formula converges to the BS formula if h ≤ σ 2 αˆ 2 , with αˆ ≡ r − (σ 2 2). 26. This volatility value, σ = 40 percent, is close to u = 1.5 in example 5.4, as given by u = eσ h .
Uncertainty, Flexibility, and Real Options
187
The Black–Scholes formula of equation (5.7) deals with a relatively simple situation where a single risk factor evolves stochastically. In reality, several risk factors may affect firm value. Margrabe (1978) examines a more general situation where a firm can exchange one (nondividend-paying) stochastic asset (I) for another (V). For example, the capital investment cost as well as the project value may evolve stochastically. Suppose that both project value, Vt, and investment cost, I t, follow correlated geometric Brownian motions dV = ( gV V ) dt + σ V Vdz, dI = ( g I I ) dt + σ I I dz′.
(5.6′)
These factors are assumed correlated with correlation coefficient ρ. We want to value a European call option giving the right to receive at maturity uncertain project value VT by paying uncertain investment cost IT , i.e., C (V , I ) = e − rT Eˆ [max {VT − IT ; 0}]. One way to simplify the problem is to define project value, V , in units of investment outlay, I , thereby reducing the problem dimensionality by one dimension (from two to one). Let X ≡ V I be this composite (relative) stochastic factor, with relative (instantaneous) variance given by
σ X 2 = σ V 2 + σ I 2 − 2 ρσ V σ I .
(5.10)
The value of the investment outlay I in terms of itself is 1 and the interest rate on a riskless loan (paying no dividend) in units of I becomes 0. The Black–Scholes formula still applies, with two needed adjustments: (1) r = 0 and (2) σ 2 becomes σ X 2 as given by equation (5.10).27 This results in Margrabe’s (1978) extension for the European option to exchange stochastic cost I for V at maturity T : C(V , I ) = V N(d1 ′ ) − I N(d2 ′ ),
(5.11)
where 1 ln (V I ) + σ X 2T 2 d1 ′ = , σX T d2 ′ = d1 ′ − σ X T .
(5.12)
27. Given these adjustments and the homogeneity of the option value function, we obtain from Black–Scholes formula (5.7) that C (V , I ) = X N ( d1′ ) − 1e −0 T N ( d2 ′ ) . I
188
Chapter 5
Example 5.6 Option to Temporarily Shut Down Operations28 The Italian electric utility is equipped with CCGT technology. The generation cost, Ct , is driven by two factors: the input gas price, PtG, which evolves stochastically according to dPtG = (rPtG ) dt + σ G PtG dzt, and technological efficiency, measured by a constant heat rate H.29 The output electricity price, Pt E, follows the geometric Brownian motion, dPt E = (rPt E ) dt + σ E Pt E dzt. Electricity and gas prices are correlated with coefficient ρ . The electric utility is not compelled to operate the CCGT plant at any time t if variable costs are not covered. The contingent profit stream at time t is thus π t ≡ max {Pt E − Ct ; 0}, where the generation cost, Ct = H × PtG, where H is the efficiency coefficient, is the exercise price of this European call option. The present value of the time-t contingent profit π 0(t ) can be valued (as of time 0) using Margrabe’s formula from (5.11) with maturity t. From equation (5.11) the expected present value of π 0( t ) = C( P0E , P0G ) is C( P0E , P0G ) = P0E N( d1′ ) − H × P0G N( d2 ′ ),
(5.11′)
where H × P0G is the present value of the (time-t) exercise price. The parameters d1’ and d2’, obtained from equation (5.12), are given by 1
d1′ =
ln ( P0E ( H × P0G )) + σ X t 2
σX t
(5.12′)
and d2 ′ = d1′ − σ X t with σ X2 = σ E2 + H 2 × σ G2 − 2ρHσ E σ G following (5.10).30 Suppose that the current prices of electricity and gas are P0E = C12 and P0G = C10, with efficiency coefficient H = 1. Electricity and gas prices have volatility σ E = 30 percent and σ G = 20 percent, with correlation coefficient ρ = 0.40. From equation (5.10), σ X2 = 0.32 + 12 × 0.2 2 − 2 × 0.4 × 1 × 0.3 × 0.2 ≈ 0.08. For a two-year horizon (t = 2) we have 28. The present example is adapted from McDonald (2006, ch. 17). 29. The heat rate H corresponds to the number of British thermal units necessary for the generation of one MWh of electricity. 30. McDonald and Siegel (1985) derive the closed-form solution for this problem. Assuming that the two assets pay no dividends, the general solution in McDonald and Siegel (1985) obtains as Margrabe’s (1978) formula for the option to trade one risky asset for another.
Uncertainty, Flexibility, and Real Options
d1′ =
ln (12 (1 × 10)) + (0.08 2 2) × 2 0.08 2
189
≈ 1.67 ,
d2 ′ = 1.67 − 0.08 2 ≈ 1.55, so N (d1′ ) ≈ 0.95 and N (d2 ′ ) ≈ 0.94. Having flexible operations with the possibility to shut down operations in two years results in a value, based on equation (5.11), of π 0 ( 2 ) = C(12, 10 ) = 12 × 0.95 − 1 × 10 × 0.94 ≈ 2.0. Assuming the CCGT plant will be decommissioned in T years, the power plant that embeds such operational flexibility in each year t has total T value ∑ t = 0 π 0( t ). Conclusion We discussed multiple sources of risk affecting companies in the energy sector and the breakthrough innovation of real options analysis. Optionbased valuation is a useful tool to corporate managers and strategists, providing a consistent and unified approach toward incorporating the value of real options associated with the investment decisions of the firm. We discussed how to quantify in principle the value of various types of operating options embedded in capital investments with applications in the energy sector. Some of these options enhance the upside potential (e.g., options to defer or expand), while others reduce downside risk (e.g., options to contract, switch use, interconnect or default on staged planned outlays). This valuation approach serves as foundation for the option games approach developed later in the book. Selected References The International Energy Agency (2007) identifies various challenges ahead for companies in the energy sector and suggests possible ways to tackle the business risks involved. Trigeorgis (1996) offers a broad overview on real options. Dixit and Pindyck (1994) discuss various real options in continuous time. Cox, Ross, and Rubinstein’s (1979) binomial model is widely used for pricing options in discrete time. Black and Scholes (1973) and Merton (1973) derive the key properties and formula for valuing European call options. Black, Fischer, and Myron S. Scholes. 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81 (3): 637–54.
190
Chapter 5
Cox, John C., Stephen A. Ross, and Mark E. Rubinstein. 1979. Option pricing: A simplified approach. Journal of Financial Economics 7 (3): 229–63. Dixit, Avinash K., and Robert S. Pindyck. 1994. Investment under Uncertainty. Princeton: Princeton University Press. International Energy Agency. 2007. Tackling Investment Challenges in Power Generation. Paris: IEA Publications. Merton, Robert C. 1973. Theory of rational option pricing. Bell Journal of Economics and Management Science 4 (1): 141–83. Trigeorgis, Lenos. 1996. Real Options: Managerial Flexibility and Strategy in Resource Allocation. Cambridge: MIT Press.
Appendix 5A: Multistep Cox–Ross–Rubinstein (CRR) Option Pricing Consider a European call option that gives the right—but not the obligation—to receive at maturity the underlying asset value VT by paying the exercise price or investment cost I . This call option pays off at maturity (T ) the greatest of VT − I and 0, or CT = max {VT − I ; 0}. Suppose that the time to maturity T is divided into n time steps, each of equal length h ≡ T / n, and let j be the number of up moves in n time steps. At maturity in the last period n, after j up moves, the call option pays off C n = max { u j d n− jV − I ; 0}. The risk-neutral probability of an up move, p, over an interval is given in equation (5.4).31 We can generalize equation (5.5) to obtain a binomial option pricing formula for n periods C=
Eˆ [CT ]
(1 + r )T
=
⎡ n ⎛ n⎞ j ⎤ n− j p (1 − p) max {u j d n − j V − I ; 0}⎥, T ⎢∑ ⎜ ⎟ (1 + r ) ⎣ j = 0 ⎝ j ⎠ ⎦ 1
(5A.1)
where n! ⎛ n⎞ ⎛ n⎞ j n− j ⎜⎝ j ⎟⎠ ≡ (n − j )! j ! and ⎜⎝ j ⎟⎠ p (1 − p) denotes the binomial distribution giving the probability that the asset will take j upward jumps in n steps, each jump occurring with risk-neutral 31. As discussed elsewhere, in equation (5.9), for consistency the value of parameters u and d should be related to the time increment, h.
Uncertainty, Flexibility, and Real Options
191
probability p. The summation of all possible (from j = 0 to n) option values at expiration, multiplied by the state probability that each scenario will occur, gives the expected option value at maturity T ( n) . This expected option value, Eˆ [C ], is discounted at the risk-free rate r over the n time periods. If we let m be the minimum number of up moves (over n periods) “triggering” call option exercise (above which V > I ), the binomial option-pricing formula in (5A.1) becomes C = VB ( m, n, p′ ) −
I
(1 + r )n
B (m, n, p),
(5A.2)
where B( ) is the complementary binomial distribution function that gives the probability of at least m up moves in n periods n ⎛ n⎞ n− j B ( m, n, p) ≡ ∑ ⎜ ⎟ p j (1 − p) , ⎝ ⎠ j j=m
with p′ ≡
u p. 1+ r
II
OPTION GAMES: DISCRETE-TIME ANALYSIS
In the first part of the book, we introduced basic principles of strategic management and real options, and discussed how an industrial organization perspective may provide useful insights to managers about how to behave vis-à-vis rivals under certain business conditions. Our belief is that these separate approaches should be combined, leveraging the strengths of each discipline to provide enhanced managerial guidance, dealing concomitantly with both market and strategic uncertainties. In part II of the book, we put these perspectives together, discussing some useful models at the interface between game theory and real options as part of a unified, discrete-time analysis. Discrete-time option games are more suitable to help explain intuitively the basic concepts and logic behind the timing and interactions of real investment decisions and determining optimal investment strategies to guide the behavior of rational option holders. In what follows we introduce concepts and tools gradually in terms of increasing complexity, starting first with a simple “equilibrium selection procedure” and building up in terms of complexity over subsequent chapters. We illustrate the simple idea behind option games via illustrative examples in chapter 6. In subsequent chapters we analyze how strategic interactions among rivals may alter the firms’ behavior in cases where the investment opportunity is analogous to a shared European call option, circumventing the issue of optimal timing under rivalry.1 We base much of this analysis on Smit and Trigeorgis’s (2004) extension 1. Investment opportunities are often viewed as being analogous to American call options. To simplify, we start with the simpler case of European options that give the option holder only one investment exercise possibility, at maturity. Using European options has two main advantages. First, it allows circumventing the problem of optimal timing in multiplayer settings, thereby precluding preemption or war of attrition effects. Second, for discrete-time analysis with finite horizons, it enables us to have investment triggers that are independent of the time or stage considered. Here the investment trigger is fixed and prescribes the investment decision at the end period (maturity).
194
Part II
of Fudenberg and Tirole’s (1984) framework for analyzing business strategies under uncertainty in light of whether firms react in a reciprocating or contrarian manner. Exogenous demand uncertainty is modeled via discrete-time multiplicative binomial models, as in Cox, Ross, and Rubinstein (1979). Uncertainty arising from strategic interactions at each end demand node is modeled via two-by-two matrices (in strategic form), whose equilibrium payoff replaces the node payoffs in the standard binomial tree. The cases of Cournot quantity and Bertrand price competition are analyzed in discrete time, both in the context of a proprietary R&D investment and when there are spillover effects (shared benefits). An extension and application in case of two-stage R&D investment games is also provided. In chapter 7 we discuss how the above principles can be applied in the context of Cournot quantity and Bertrand price competition. In chapter 8 we describe how commitment and early investment in two-stage games (e.g., in R&D or advertising campaigns) may alter the strategic value of an investment opportunity. Whether the firststage commitment investment increases or decreases the option value depends on the effect of the commitment (tough or soft) and on the reactions of competitors (strategic substitutes or complements). The analysis is extended to derive optimal investment strategies under uncertainty, providing new insights about R&D investment, spillover effects, goodwill building, and patent strategies.
6
An Integrative Approach to Strategy: Option Games
In part I we discussed basic approaches providing insights about how to behave in an uncertain competitive environment. We reviewed strategic management, industrial organization, and real options as separate, standalone disciplines. Each approach can separately bring about useful insights in analyzing business situations. Nonetheless, each discipline, taken separately, also has drawbacks. Standard game theory has not dealt so far with stochastic dynamics; static games by their very nature do not involve such a problem, while dynamic games are mostly cast in a steady or deterministically evolving environment. Real options analysis, while suitable to account for stochastic uncertainty, often makes the simplifying assumption that strategic interactions do not materially affect the investment decisions or project values of firms. Strategic management has a lot to benefit by more explicitly incorporating the trade-off between the value of flexibility and commitment. The best way to overcome these drawbacks is to follow an integrative approach using the combined tools and concomitant insights of game theory and real options. This is what “option games” is all about, standing at the intersection between the theory of investment under uncertainty (real option analysis) and the game-theoretic analysis of strategic investments. In section 6.1 we discuss how option games can provide useful insights to management faced with conflicting strategic choices. We discuss two prominent issues here: optimal investment timing, and the trade-off between flexibility and commitment.1 We elaborate on these issues further in upcoming chapters. Section 6.2 provides a simple illustration to help figure out the logic behind option games. Sections 6.3 and 6.4 go deeper and discuss applications to R&D and the mining/chemicals industry, respectively. 1. These two issues are not really that distinct. Optimal timing is concerned with the choice of the right moment at which to incur a sunk investment cost, which is a form of commitment. Thereby the firm kills the option to delay further, losing valuable flexibility.
196
Chapter 6
6.1 Key Managerial Issues: Optimal Timing and Flexibility versus Commitment 6.1.1
Optimal Investment Timing under Uncertainty
Consider the example of a multinational financial institution, such as Deutsche Bank, contemplating investing in China where profits have been growing and prices escalating. Deutsche Bank ponders whether to acquire a stake in a local bank at the earliest opportunity or wait to see if prices subside as the hype diminishes. Many international organizations face such a dilemma. The market in China is not fully liberalized and administrative barriers have long blockaded entry by foreign financial institutions. These foreign institutions are faced with a trade-off between investing now incurring a large investment outlay or waiting for the liberalization of the market in the wake of WTO negotiations.2 A good understanding of investment timing requires a simultaneous assessment of both market uncertainty and the anticipated reactions of competitors eager to seize their slice of the pie. Should the firm invest now? Invest later? Abandon the project altogether? If the market develops favorably, investing can prove quite valuable. But if the market flops, investing prematurely may prove a regrettable mistake, especially when investment costs are sunk. To protect itself from adverse market developments, a firm that has the flexibility to wait will require a delay investment premium until the market is sufficiently mature to compensate for the risk. Real options analysis can provide valuable insights concerning the optimal timing decisions of firms under uncertainty. Investing when the project NPV is positive is inferior to selecting optimally the time at which the project value is maximal, with due accounting for the time value of money. Optimal investment timing under uncertainty is a key challenge. In competitive settings, the optimal timing policy may differ substantially from that of a monopolist. Rivals may preempt, eroding the incentive to defer the decision. In other situations, rivals may prefer to wage a war of attrition in the hope that their rival will retreat sooner. In these settings the optimal timing decisions, as the result of a multiplayer problem, 2. Deutsche Bank actually decided not to wait, acquiring several local banks such as Harrest Fund Management and Huaxia Bank. In their decision-making, Deutsche Bank took into account the risk of international rival banks preempting it.
An Integrative Approach to Strategy
197
must form an industry equilibrium. In such investment problems the presence of competition generally leads firms to invest earlier than a monopolist and erodes the deferral option value of the firm. 6.1.2 The Trade-off between Flexibility and Commitment In an uncertain competitive environment, any company considering a capital-intensive decision, like whether to invest in a new technological process to develop a new product, faces a trade-off between investing early to build up competitive advantage over rivals versus delaying investment to acquire more information and mitigate the potentially unfavorable consequences of market uncertainty. At the heart of this trade-off between commitment and flexibility are two conflicting value drivers: (1) exogenous uncertainty in the form of fluctuating demand, prices, or input costs may restrain a firm from committing early, and (2) in the face of competitive threat or pressure, a firm might be better off to build first-mover competitive advantage. The value of commitment as discussed in industrial organization challenges the belief that flexibility is always valuable.3 One thus needs to weight the relative merits of commitment versus flexibility, providing a balancing act between the two. This trade-off can be addressed by combining real options analysis and game theory. In boxes 6.1 and 6.2 senior consultants from BCG and McKinsey & Company discuss the usefulness of real options analysis for management practice and the prospects offered by taking a game-theoretic perspective. 6.2 An Illustration of Option Games Viewed in discrete time, an option game is an overlay of a binomial tree onto a payoff matrix.4 A binomial tree, as the one shown in figure 6.1, is 3. The reader may recall that chapter 4 dealt with the value of early commitment (industrial organization), while chapter 5 focused on the flexibility value via real options analysis. 4. In real options analysis, two approaches are commonly used: (1) the discrete-time approach, using binomial trees depicting the evolution of the demand state, and (2) the continuous-time approach, using stochastic processes to model the underlying variables. In chapter 5 we described how project value dynamics can be modeled based on a binomial tree lattice, how risk-neutral probabilities are derived, and how the current value of an investment option can be determined using the backward risk-neutral valuation principle. Smit and Ankum (1993), Smit and Trigeorgis (2001, 2004), and Ferreira, Kar, and Trigeorgis (2009) discuss option games in discrete time. This approach enables deriving key insights by use of simple numerical examples.
198
Chapter 6
Box 6.1 Interview with Rainer Brosch and Peter Damisch, Boston Consulting Group
1. In what ways do you believe real options thinking can contribute to strategy development? How useful have you found real options thinking in your consulting practice? We believe that real options thinking can contribute to strategy development in a very powerful way: it helps to analytically support strategic decision-making, especially in environments that are complex and exposed to many sources of uncertainty. The approach provides structural elements and a “vocabulary” that can be very valuable in strategy discussions that, by definition, center around managerial flexibility, options, and contingent decisions. A question like “how would the exercise price of a strategic option be affected by a specific managerial action?” could very well uncover a key issue. In many contexts a detailed valuation of business cases or strategies is an important element of our work; this typically can be achieved with much precision by an in-depth DCF and scenario analysis. However, in settings where significant uncertainty and managerial flexibility is involved, such as flexibility to change trajectory, abandon, or accelerate, the value of such optionality must be considered explicitly: this flexibility possibly allows capitalizing on positive market developments or reducing the impact of negative market developments, and thus impacts strategic choices. In every practical setting it is important to rigorously assess possible sources of optionality and decide how to best capture them. 2. Would you envision extending BCG matrix thinking using options and games for competitive analysis? Portfolio thinking is inseparably connected to strategy and is among the most challenging—and rewarding—aspects of management. Looking at a company as a portfolio of businesses opens up an important perspective, enabling to actively realize value which is above and beyond the sheer
An Integrative Approach to Strategy
199
Box 6.1 (continued)
sum of the parts. At the same time, this lens requires to actively address trade-offs within the portfolio, namely to tackle portfolio effects and synergies that are the basis of the portfolio perspective. From its first days BCG has pioneered strategy through portfolio analysis. The BCG Portfolio Matrix is one well-known example, capable of providing awareness and tremendous insight. Over the years we have continued to develop strategy and portfolio analysis in many directions, such as by integrating additional parameters, including among these strategic fit, value creation potential, role-based views, dynamic paths and trajectories, options, and competitive interaction. Today’s portfolio manager can rely on very advanced approaches, consolidating various views which are inseparably connected to options thinking and competitive analysis. Admittedly, it is always a challenge to highlight competitive interaction and even more so when options are involved. This is exactly what option games is about. Option games thus make a very important and directional contribution to strategy, tying together game theory and options thinking into a joint, analytically rigorous framework.
Box 6.2 Interview with Eric Lamarre, McKinsey & Company
1. In your corporate finance and risk management practice with clients at McKinsey & Company, how, and to what extent do you believe real options analysis offers better guidance to your clients than traditional capital budgeting techniques?
200
Chapter 6
Box 6.2 (continued)
There is no doubt that real options analysis generates a more insightful dialogue among senior managers. It helps uncover additional value not fully recognized by traditional NPV techniques and, more important, creates a structured conversation around the sources of risk and how a company plans to respond to these risks. While a typical investment business case merely lists potential risks, RO techniques place much greater emphasis on these risks, as well as on the managerial flexibility to react. 2. How did you first come up with or run into the option games concept? We first came across this concept in the mining industry. Option games are particularly helpful for a special class of strategy problems where uncertainty is high and a company’s actions or those of competitors can shape industry dynamics. This is sometimes the case in mining when major capacity expansions can materially impact the supply/demand balance. The first mover in adding capacity will hold an advantage, but must also take on more risk because future demand is uncertain. Managers intuitively understand this dynamics, but they may find that quantifying the value is difficult with standard DCF methodologies. 3. How useful have you found real options analysis in your consulting practice? Have your clients shown interest in this approach? Despite its compelling benefits, clients have been slow to adopt the RO approach for three reasons. First, often too much focus is placed on analytics and not enough on the organizational changes required to generate broad adoption inside a corporation. Second, having received little training on RO techniques, senior managers often revert to familiar methods despite the shortcomings these methods present in certain situations. Finally, poor execution during first experimentations often leads to disappointing results. There is sometimes too much focus on computer simulations and not enough on structuring the risk problem properly. If properly used, this new methodology can be a real source of competitive advantage, even more so when integrated within the organizational and strategy processes.
An Integrative Approach to Strategy
State value
201
Cumulative probability
p p
pp
V+ 1− p
V 1− p
V ++
p
V +− = V −+ 2 p (1 − p )
V− 1− p
V −−
(1 − p )
2
Figure 6.1 Binomial tree representing evolution of market uncertainty and associated probabilities
used to model the stochastic evolution of project value V , while two-bytwo matrices are used to capture the competitive interactions among players. Suppose that p is the risk-neutral probability of an up move per period. To each scenario at the end node in the binomial tree of figure 6.1 corresponds the cumulative risk-neutral probability shown in the right column after two steps: pp for the high demand state, 2 p (1 − p) 2 for the intermediary demand state, and (1 − p) for the low demand state. Consider a duopoly consisting of firms i and j sharing a European option to invest in an emerging market within two years. The annual risk-free interest rate is 4 percent (r = 0.04). Firms i and j can both invest now, wait and invest later (at maturity in year 2), or let the option expire. If none invests now, at the end node in year 2 the firms’ strategic choices (represented in two-by-two payoff matrices) are: invest or do not invest (abandon). At maturity both firms can invest, both can abandon, or only one invests (potentially involving a coordination problem). The basic structure of this option game in discrete-time is depicted in figure 6.2. Once the binomial tree charts the evolution of potential demand scenarios until maturity (year 2), in each end node a two-by-two payoff matrix depicts the resulting competitive interaction. The resulting equilibrium outcome (*) and corresponding player payoffs can be anticipated for each of the three payoff matrices. Once the equilibrium (*) strategic option values are obtained in each end state (C*++, C*+−, C*−−), working the tree backward enables the firm to assess the value each strategy creates under rivalry. The analysis reveals the benefits to each player from
202
Chapter 6
Binomial tree representing market uncertainty
Payoff matrix for Strategic option strategic uncertainty value Firm j
V
Invest
V+ V +−
V−
Invest
Invest Abandon
C*+ −
Abandon
V
C*++
Abandon
High demand ++
Firm i
Invest Abandon
t=0
1
2
Abandon
V −−
Low demand
Invest
Invest Abandon
C*−−
Figure 6.2 Structure of an option game involving both market (demand) and strategic (rival) uncertainty
pursuing a given strategy and enables management to determine how these benefits might change if certain key variables, such as growth or volatility, would change. Let us put this in a concrete context from the electricity sector (see example 5.4). Suppose that the Italian utility Enel and EDF of France both possess the option to enter the Russian electricity market in two years’ time.5 This investment option is analogous to a shared European call option with maturity two years, with the underlying market value following a multiplicative binomial tree process. Suppose that the market is currently worth C150 m (V = 150) and evolves with an upward multiplicative factor u = 1.5 and downward factor d = 1 u ≈ 0.67 in each period. If only one firm invests when the market is mature in year 2, that firm would seize the entire market pie (in effect will be a monopolist). If both utilities invest at t = 2, we assume that the market will be divided among the two firms relative to their market power. Suppose that the Italian 5. The intent here is to value, for each firm, the option to invest in this market as incorporated in the firm market value. A different issue might be of interest as well. Suppose the Russian government is selling two options to invest, with Enel and EDF as bidders. What will they bid? This analysis should include the possibility that one of the utilities may find it optimal to buy up both options and then exercise only one (if the rules and regulations made by the Russian government permit this). Such a problem might have a different answer.
An Integrative Approach to Strategy
203
utility (Enel) has a comparative advantage enabling it to acquire a higher slice of the market pie (s = 0.60), with its French rival obtaining the remainder (40 percent). Each firm must incur an infrastructure investment outlay of I = C80 m to enter the Russian market. At maturity in year 2, each firm will either invest (receiving the net project value at that time) or abandon the investment (receiving nothing). The values obtained by each firm in each competitive scenario are presented in two-by-two matrices; each of the tree end nodes of demand has a corresponding two-by-two matrix. Consider first the upper demand state in figure 6.3 that occurs after two consecutive demand up moves. In this case, the gross market value is V ++ = uuV = 1.5 × 1.5 × 150 ≈ C 338 m. In the event where only one firm (Enel or EDF) enters the market, it gets the full gross market value V ++ incurring the entry cost of I = C80 m, receiving a net (forward) value of V ++ − I = 338 − 80 = C 258 m. If the firm does not enter the market, letting its investment option expire, it receives nothing (0). If both firms invest at maturity (invest, invest), they split the market as follows: Enel obtains 60 percent of the gross market value (338) at the cost of I = C80 m, Binomial tree representing market uncertainty
Payoff matrix for Strategic option strategic uncertainty value Firm j Invest
338
Abandon
High demand
Firm i
Invest Abandon
225
C*++ = (123, 55) (0, 258)
(0, 0)
150
100
Invest
Invest Abandon (10, –20)
Abandon
150
(123, 55) (258, 0)
(0, 70)
(70, 0)
C*+− = (70, 0)
(0, 0)
Low demand
t=0
1
2
Abandon
67
Invest
Invest Abandon (–40, –53) (–13, 0)
C*−− = (0, 0) (0, –13)
(0, 0)
Figure 6.3 Binomial tree and equilibrium end-node payoff values in the Enel versus EDF rivalry over the Russian market The first element in (·, ·) represents firm i ’s (Enel’s) net value or payoff, while the second entry denotes the net value or payoff to firm j (EDF).
204
Chapter 6
Invest
(123, 55) (258, 0)
Abandon
Firm i (Enel)
Firm j (EDF) Invest Abandon
(0, 258)
(0, 0)
Figure 6.4 Two-by-two matrix in the upper demand node The first element in (·, ·) represents firm i’s (Enel’s) net value or payoff, while the second entry denotes the net value or payoff to firm j (EDF).
receiving net (forward) value: s × V ++ − I = 0.6 × 338 − 80 = C123 m; EDF gets 0.4 × 338 − 80 = C 55 m. These competitive situations are summarized in the two-by-two matrix of figure 6.4. The first number in each pair of payoff values (in parenthesis) represents the payoff to Enel (firm i), and the second to EDF (firm j). We next determine which competitive outcome is more likely to occur as a stable solution, applying the Nash equilibrium concept. Whatever EDF chooses, Enel earns a higher payoff by investing than by abandoning the project: if EDF invests, Enel receives C123 m when investing and 0 otherwise; if EDF abandons the option, Enel is better off investing obtaining net value C258 m rather than 0. Enel thus has a dominant strategy to invest. EDF also has a dominant strategy to invest, earning !55 m if Enel invests or C258 m if Enel lets its option expire. The resulting Nash equilibrium in the upper end node is for both firms to invest, with Enel receiving C123 m and EDF !55 m. The equilibrium payoffs, C*++ = (123, 55), are shaded or shown with *. The case arising in the medium demand state (occurring after a downward move following an up move or inversely) can be analyzed similarly. Here the gross market value is V − + = udV = 1.5 × 0.67 × 150 = C150 m. In the intermediate demand state there is room for only one firm to operate profitably in the market (150 < 2 × 80). If Enel or EDF ends up in a monopoly, it receives V − + − I = 150 − 80 = C 70 m. If the firm abandons, it receives nothing (0). If both firms invest, Enel receives s × V − + − I = 0.6 × 150 − 80 = C10 m, while EDF obtains 0.4 × 150 − 80 = − C 20 m. Again, Enel has a dominant strategy to invest, receiving a positive value in both situations. Given that Enel has a dominant strategy to invest, the best response of EDF is to abandon the market, receiving 0 rather than a negative payoff (−C20 m). Given that
An Integrative Approach to Strategy
205
each firm plays its best response to its rival’s actions, the Nash equilibrium payoff in the intermediate demand state is C*+− = ( 70, 0 ). In the down state (after two consecutive down moves), the gross market value is V − − = ddV = 0.67 × 0.67 × 150 ≈ C 67 m, which is lower than the needed investment outlay of I = C80 m. Neither firm therefore has an incentive to invest, since whatever the resulting competitive outcome, the firm would incur losses. Both firms thus have a dominant strategy to abandon the project, receiving 0. The resulting Nash equilibrium payoff is C*−− = ( 0, 0 ). The binomial tree and resulting Nash equilibria (highlighted) in each of the three demand states are shown in figure 6.3. The next step is to substitute these equilibrium payoff or strategic option values in the end nodes of the binomial tree, and determine for each firm the investment option value by backward valuation along the binomial tree. For this, we need to assess the risk-neutral probabilities of each end node that will allow determining the present value of the strategic option. Following the discussion in chapter 5, the risk-neutral probability of an up move is given by equation (5.4). In the present case with r = 0.04, u = 1.5, and d ≈ 0.67, the risk-neutral probability of an up move is p=
(1 + 0.04) − 0.67 1.5 − 0.67
= 0.45.
Going backward along the binomial tree at t = 1, in the up state the investment option for Enel is worth C+ =
pC ++ + (1 − p)C +− 0.45 × 123 + (1 − 0.45) × 70 = ≈ C 90 m. 1+ r 1.04
The (time-1) value for Enel in the down state is C− =
0.45 × 70 + 0.55 × 0 ≈ C 30 m. 1.04
Finally, one step earlier, the present value (t = 0) of the strategic investment option for Enel is C=
pC + + (1 − p)C − 0.45 × 90 + 0.55 × 30 = ≈ C 55 m. 1+ r 1.04
That is, the current value of the investment opportunity for Enel to enter the Russian market in two years, accounting for strategic interactions with European rival EDF in each possible state of market demand evolution, is C55 m.
206
Chapter 6
The value of the investment opportunity for EDF is similarly obtained to be 10 m.6 This basic valuation procedure is a cornerstone for the discrete-time analysis of option games. It will be used again in the examples in the rest of this chapter and in subsequent chapters. The next section provides an illustration of option games in the case of patentleveraging strategies. Section 6.4 provides a case application in the context of mine investments. 6.3
Patent-Fight Strategies
As another illustration of the usefulness of simple option games, Trigeorgis and Baldi (2010) consider different patent-leveraging strategies among two patent-holding firms in a duopoly. The setup of their problem together with the payoff matrices at maturity are depicted in figure 6.5. Binomial tree representing market uncertainty
Payoff matrix for Strategic option strategic uncertainty value Firm j Sleep
Firm i
324
(220, 8) (92, 31)
(9, 3) (–29, 33)
180
60
36
t= 0
1 Stage I
Patent acquisition for firm i (old technology for firm j )
Low demand
2
Sleep
Invest
108
Invest
100
Invest
(98, 33) (68, 152)
Invest
High demand
Sleep
Sleep
Sleeping
Wall
Wall
Bracketing
Sleep
Invest
Sleeping
Wall
C *++ = (92, 31)
C *+– = (34, 0)
(34, 0) (3, –17) Wall
Bracketing
Sleep
Invest
(9, 0) (–14, –1) Sleeping
Wall
C *–– = (9, 0)
(–5, 0) (–20, –7) Wall
Bracketing
Stage II Choice of patent fighting strategy
Figure 6.5 Binomial tree and equilibrium end-node payoffs for patent fighting strategies where firm i has a strong patent advantage 6. At time t = 1 in the up node, EDF will receive 55 m in the up state or 0 in down state, worth C + = (0.45 × 55 + 0.55 × 0 ) 1.04 = C 24 m. At t = 1 in the down state, EDF’s investment opportunity is worth zero. Going back one step earlier, the current ( t = 0 ) value of EDF is C = (0.45 × 24 + 0.55 × 0 ) 1.04 = C10 m.
An Integrative Approach to Strategy
207
At time t = 0 (or at the beginning of stage I), firm i innovates and acquires a new core patent that is superior to the old patented technology used by rival firm j. At time t = 2 (or at the beginning of stage II), each firm decides on its best patent-leveraging strategy, whether to fight, cooperate, or wait, depending on firm i’s cost advantage and the state of demand (high, intermediate, or low). The weaker rival, firm j, believing it has a fighting chance, may go on the offensive to identify and exploit gaps around firm i’s core patent. Firm i may pursue a similar offensive strategy, resulting in a patent-bracketing war. When both firms attack each other via patent bracketing, they share a reduced market value reflective of their respective market power. Alternatively, firm i can solidify its large advantage building a defensive patent wall around its core patent in the hope of driving the rival out. When one firm invests while the rival waits, it captures full monopoly NPV.7 Last, each firm can “wait and see,” virtually putting its patent in a “sleep mode.” When both firms sleep (wait) and postpone their fighting decision, firm i has an advantage (capturing more of the option value according to its higher market power). The type of competition depends in part on the size of the cost advantage resulting from the patented innovation. Absence of such advantage is likely to induce symmetric rivals to cooperate, while a large cost advantage by firm i will favor a fight mode instead. In case of a large cost advantage, different types of fight mode may result, depending on realized demand. Figure 6.5 focuses on the case where firm i has a strong advantage resulting from the innovation. This situation will result in patent fighting. In the two-by-two matrices under high, intermediate, or low demand, different types of fighting equilibria may result: Under high demand, each firm should invest regardless of the opponent’s decision (for firm i, 220 > 98 and 92 > 68; for firm j, 152 > 33 and 31 > 8). Invest is a dominant strategy for both. The resulting equilibrium strategies are for both firms to invest, ending up in a bracketing war with bottom-right payoffs C*++ = ( 92, 31). Under asymmetric reciprocating competition with high demand, both firms feel induced to fight via •
7. Firm i has an incentive to fortify and exploit its large cost advantage to drive the rival out of the market. The rival will be inclined to fight (even attack) if demand or volatility is high. Entering a reciprocating fight is costly and erodes profit margins for both firms, reducing total market pie (to 70 percent)—except when one firm ignores its fighting rival and lets its patent sleep.
208
Chapter 6
reciprocal patent bracketing—even though they would be better off to let their patents sleep, obtaining ( 98, 33).8 Under intermediate demand, firm i should invest, regardless of its rival’s decision (34 > 9 and 3 > −29), a dominant strategy. Knowing that firm i will invest and fight, firm j prefers to wait (sleep) rather than engage in a costly bracketing fight (0 > −17), resulting in patent walls with Nash equilibrium payoffs C*+− = ( 34, 0). Firm i will invest building a defensive patent wall around it, with firm j waiting (sleeping).
•
Under low demand, each firm has a strictly dominant strategy to let its patent sleep (for firm i, 9 > −5 and −14 > −20; for firm j, 0 > −1 and 0 > −7). Given the low level of demand, both firms would actually lose value by fighting each other. The equilibrium strategy is for both firms to “sleep.” Firm i lets its superior patent sleep, maintaining its option to become a monopolist should the market recover in the future (with continuation value 9). This amounts to the disadvantaged firm abandoning the market. The Nash equilibrium for the upper-left game payoff is C*−− = ( 9, 0 ). •
In the problem above the risk-free interest rate is r = 0.08 and the riskneutral probabilities for an up or down move are p = 0.4 and 1 − p = 0.6 . Given that the equilibrium investment option values at maturity (t = 2) for firm i are C*++ = 92, C*+− = 34, and C*−− = 9, in the high, medium, and low demand states, with associated probabilities pp = 0.16, 2 2 p (1 − p) = 0.48, and (1 − p) = 0.36, respectively, the current (t = 0) value of the strategic investment opportunity for firm i is p2C*++ + 2 p (1 − p)C*+− + (1 − p) C*−− ( 1 + r )2 0.16 × 92 + 0.48 × 34 + 0.36 × 9 = = 29. (1.08)2 2
C=
This yields an expanded net present value for the patent fight strategy of firm i of 29 m in case of a large cost advantage. Firm j’s value of the investment opportunity obtains similarly as C4 m.9 8. The fear of the rival investing in a patent wall and strengthening their position if they let their own patent sleep puts pressure on both firms to invest aggressively bracketing each other’s patent, a situation analogous to the prisoner’s dilemma. 9. Firm j obtains in each demand state C*++ = 31, C*+− = 0 , and C*−− = 0 , respectively. Firm j’s investment opportunity is worth C=
0.16 × 31 + 0.48 × 0 + 0.36 × 0 = C 4 m. (1.08)2
An Integrative Approach to Strategy
209
6.4 An Application in the Mining/Chemicals Industry Ferreira, Kar, and Trigeorgis (2009) present an actual application of option games in the mining/ chemicals industry.10 Deciding when to add capacity in the face of rivals is a challenging problem for any industry. This approach involves American-type real options and games and is solved backward by use of numerical analysis. Between 1995 and 2001 annual revenues for the US commodity chemicals industry fell from $20 bn to $12 bn, while companies’ operating profits fell on average by 26 percent a year. The collapse was in large measure caused by a tight economic environment and a rising dollar. But outside forces were only part of the story—industry players also made some very poor decisions. . . . It’s a story that regularly plays out in many industries. Indeed any company making big-budget investment decisions faces the same basic dilemma. On the one hand, it must make timely, strategic investments to prevent rivals from gaining ground. On the other, it must avoid tying up too much cash in risky projects, especially during times of market uncertainty. Using game theory models, managers can incorporate the collective effect on market-clearing prices of other companies that are expanding their capacity at the same time. Typically the way to do this is to create a payoff matrix, which compares your payoffs with those of your competitor under different scenarios. Unfortunately, the standard calculation of payoffs does not allow managers to factor in uncertainty for key market variables such as prices and demand, nor does it assign any value to flexible investment strategy. To get around this problem, we use a hybrid model that overlays real options binomial trees onto game theory payoff matrices. To Mine or Not to Mine? MineCo is planning to open a new mine to expand its capacity to produce minerals for its regional market. In this market, if demand exceeds local supply, customers will import from foreign sources, which effectively sets a cap on prices. From MineCo’s perspective there are two key sources of uncertainty: the growth rate of local demand, which has varied in recent years with shifts in the country’s political economy, and the risk that CompCo, its largest competitor, will invest in a similar project first. 10. This section is an excerpt from “Option games: The key to competing in capitalintensive industries” by Nelson Ferreira, Jayanti Kar, and Lenos Trigeorgis, Harvard Business Review, March 2009. It is reprinted by permission of Harvard Business School Publishing.
210
Chapter 6
The current demand is 2,200,000 tons and the current price (set by imports) is $1,000 per ton. The MineCo project involves adding 250,000 tons of capacity at a cash operating cost of $687 per ton (incurred each year the project is up and running) and a capital expenditure of $250 per ton, spread over three years. The Comp Co project faces cash operating costs of $740 per ton annually, projected capacity of 320,000 tons, and a capex of $150 per ton, also spread over three years. The investments take three years to complete, and both new mines have a lifespan of 17 years. For the purposes of simplicity, we assume that each firm can decide to invest in Y0 (with capex in Y0, Y1, and Y2 and production starting in Y3) or in Y3 (with capex to be invested in Y3, Y4, and Y5 and production starting in Y6). We begin by calculating the inputs that will serve as the basis for determining payoff values for each of the scenarios: demand evolution and the probabilities of upward and downward shifts in demand. We assume that demand will go up or down by a fixed multiple in each period (in this case the period is a year). Using historical data and surveys of the company’s managers, we predict demand will move up or down by about 5 percent in each period. We estimate the risk-adjusted probability of an upward shift in each period at 30 percent (therefore, a 70 percent probability of a downward shift in each period). Next we input these data into a binomial tree that tracks the evolution of demand over the next six years and overlay it with a tree that tracks the cumulative probabilities at each node in the demand tree (see figure 6.6). We will refer to this tree throughout the analysis in this section. Now let’s calculate the payoffs for MineCo and CompCo for each of the four scenarios arising from their decisions to invest now or wait until year three to decide. Scenario 1: Both Companies Invest Now If both firms decide to invest now, they will incur capital expenditures in Y0, Y1, and Y2, and both projects will start producing in Y3. Given this, we can model how evolution in demand and capacity will affect prices and thereby revenues and profits for each of the two companies. First, we create a binomial tree showing how market prices might evolve (see figure 6.7). The price at each node is determined by demand and supply, driven by the cash operating cost of the marginal producer (the producer just barely able to remain profitable at current levels of price and demand). If demand rises and MineCo or its competitor adds capacity at a higher marginal operating cost, local prices will rise.
An Integrative Approach to Strategy
Year 0
2200 100%
Year 1
2313 30% 2093 70%
Year 2
2431 9% 2200 42% 1991 49%
211
Year 3
2556 3% 2313 19% 2093 44% 1894 34%
Year 4
Year 5
Year 6
2687 1% 2431 8% 2200 26% 1991 41% 1801 24%
2825 0.2% 2556 2.8% 2313 13.2% 2093 30.9% 1894 36.0% 1713 16.8%
2970 0.1% 2687 1.0% 2431 6.0% 2200 18.5% 1991 32.4% 1801 30.3% 1630 11.8%
Figure 6.6 Demand evolution and probability tree
To calculate the annual operating profits at each node for each firm, we subtract that firm’s estimated annual cash operating costs per ton from the prices at each node for each operating year and multiply that number by the demand filled by the added capacity, estimated over the remaining life of the project. To illustrate, at the upper demand node in Y5, MineCo gets a margin of 313 (the 1,000 price less its cost of 687) per ton, which for 250, 000 tons of added capacity represents $78,250,000. In Y6 nodes, we have to add in the terminal value, which is an estimated present value of cash flows for the remaining 14 years of the mine’s useful life. To calculate this, we assume that price and demand remain constant subsequently and apply the standard discounting formula, which gives us a terminal value of $774,569,000. We add that to the Y6 annual operating profit (again, $78,250,000), and get a total value for the upper node in Y6 of $852,819,000. The resulting tree for MineCo (with the added capacity of 250,000 tons) is shown in the lower panel of figure 6.7. The tree for CompCo is similar (but not shown here)—the numbers are a little higher on the upside and more negative on the downside. Our final step is to weight the numbers at each node by the corresponding risk-adjusted probability (from the demand tree) and discount those expected payoff values by 5 percent per year (the risk-free interest rate) back from the position of the node to the present. We then sum up these numbers—the weighted, discounted annual operating profits at each node plus the terminal value—and subtract from that sum the
212
Market-clearing prices (in US$/ton)
Chapter 6
Year 0
1,000
Payoffs for MineCo (in US$ thousands)
Year 0
(20,833)
Year 1
1,000 1,000
Year 1
(20,833) (20,833)
Year 2
1,000 1,000 1,000
Year 2
(20,833) (20,833) (20,833)
Year 3
1,000 700 700 685
Year 3
78,250 3,250 3,250 (500)
Year 4
1,000 740 700 687 685
Year 4
78,250 13,250 3,250 0 (500)
Year 5
1,000 1000 700 700 685 685
Year 5
78,250 78,250 3,250 3,250 (500) (500)
Year 6
1,000 1,000 740 700 687 685 680
Year 6 852,819 852,819 144,407 35,421 0 (5,449) (19,073)
Figure 6.7 Scenario 1: Both companies invest now
present value of the annual capex investments made by each company. This gives us the net current payoff value, or final payoff value, for each company under scenario 1: For MineCo the expected payoff in Y0 is −$36 m; for CompCo, −$195 m. If both firms invest now, both lose money. Scenario 2: MineCo Invests Now, While CompCo Waits In this scenario MineCo invests first, giving it the advantage of being the sole producer from Y3 to Y6, while CompCo waits until Y3 to decide whether to invest. If demand evolves favorably, CompCo enters in Y3; if not, it abandons the project. We begin the valuation by calculating the market-clearing prices from Y0 through Y3, using the demand tree and given the fact that MineCo has invested in extra capacity and CompCo so far has not. Next, we calculate how prices will evolve from Y3 through Y6. There are four possible Y3 scenarios, each with an associated probability of occurrence (see demand tree in figure 6.8). At each of the nodes, we
