Charity with Choice, Volume 13 (Research in Experimental Economics)

CHARITY WITH CHOICE RESEARCH IN EXPERIMENTAL ECONOMICS Series Editors: R. Mark Isaac and Douglas A. Norton Recent Vol...

Author: R. Mark Issac

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CHARITY WITH CHOICE

RESEARCH IN EXPERIMENTAL ECONOMICS Series Editors: R. Mark Isaac and Douglas A. Norton Recent Volumes: Volume 7: Volume 8:

Emissions Permit Experiments, 1999 Research in Experimental Economics, 2001

Volume 9: Volume 10: Volume 11:

Experiments Investigating Market Power, 2002 Field Experiments in Economics, 2005 Experiments Investigating Fundraising and Charitable Contributors, 2006 Risk Aversion in Experiments, 2008

Volume 12:

RESEARCH IN EXPERIMENTAL ECONOMICS VOLUME 13

CHARITY WITH CHOICE EDITED BY

R. MARK ISAAC Florida State University, Tallahassee, Florida, USA

DOUGLAS A. NORTON Florida State University, Tallahassee, Florida, USA

United Kingdom – North America – Japan India – Malaysia – China

Emerald Group Publishing Limited Howard House, Wagon Lane, Bingley BD16 1WA, UK First edition 2010 Copyright r 2010 Emerald Group Publishing Limited Reprints and permission service Contact: [email protected] No part of this book may be reproduced, stored in a retrieval system, transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without either the prior written permission of the publisher or a licence permitting restricted copying issued in the UK by The Copyright Licensing Agency and in the USA by The Copyright Clearance Center. No responsibility is accepted for the accuracy of information contained in the text, illustrations or advertisements. The opinions expressed in these chapters are not necessarily those of the Editor or the publisher. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN: 978-1-84950-768-4 ISSN: 0193-2306 (Series)

Awarded in recognition of Emerald’s production department’s adherence to quality systems and processes when preparing scholarly journals for print

CONTENTS LIST OF CONTRIBUTORS

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EXPERIMENTS WITH PUBLIC GOODS: FROM COOPERATION TO FORMATION R. Mark Isaac and Douglas A. Norton

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TACIT COORDINATION IN CONTRIBUTION-BASED GROUPING WITH TWO ENDOWMENT LEVELS Anna Gunnthorsdottir, Roumen Vragov and Jianfei Shen

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THE EFFICIENCY-EQUALITY TRADEOFF IN PUBLIC SECTOR CHARITY PROVISION Daniel T. Hall

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RETAINED EARNINGS MAXIMIZING NONPROFIT ENTERPRISES Douglas A. Norton

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ENDOGENOUS PRODUCTION TECHNOLOGY IN A PUBLIC GOODS ENTERPRISE Douglas A. Norton and R. Mark Isaac

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WHAT CAN SOCIAL PREFERENCES TELL US ABOUT CHARITABLE GIVING? EVIDENCE ON RESPONSES TO PRICE OF GIVING, MATCHING, AND REBATES Linda Kamas and Anne Preston

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CHARITY AUCTIONS IN THE EXPERIMENTAL LAB Jeffrey Carpenter, Jessica Holmes and Peter Hans Matthews v

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LIST OF CONTRIBUTORS Jeffrey Carpenter

Middlebury College, USA

Anna Gunnthorsdottir

Australian School of Business, Australia

Daniel T. Hall

Georgia State University, USA

Jessica Holmes

Middlebury College, USA

R. Mark Isaac

Florida State University, USA

Linda Kamas

Santa Clara University, USA

Peter Hans Matthews

Middlebury College, USA

Douglas A. Norton

Florida State University, USA

Anne Preston

Haverford College, USA

Jianfei Shen

University of New South Wales, Australia

Roumen Vragov

The Right Incentive, USA

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EXPERIMENTS WITH PUBLIC GOODS: FROM COOPERATION TO FORMATION R. Mark Isaac and Douglas A. Norton ABSTRACT Purpose – The purpose of this chapter is to serve as an introduction and motivation for Volume 13 of Research in Experimental Economics. In many cases, these introductory chapters are prefaces, limited to giving a roadmap of the volume and brief discussions of the chapters and why they were included. However, in some cases a more extensive discussion of the state of the literature and discipline can be useful. We have the same goal for this chapter. Methodology – The methodology is that of a literature review combined with an analysis of the development of issues of endogeneity, selfselection, and formation in laboratory experimental research on public goods, charitable contributions, and nonproﬁt organizations. Findings – This chapter traces the path of experimental public goods research as viewed through several lenses. There is a correspondence between the period of carefully controlled conditions in laboratory research and the framework of neoclassical economic theory (Lindahl/Samuelson). Indeed this is one of the original purposes of the earliest experiments by economists. However, there has been a distinct shift away from Charity with Choice Research in Experimental Economics, Volume 13, 1–11 Copyright r 2010 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0193-2306/doi:10.1108/S0193-2306(2010)0000013003

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external control towards more endogenous evolution and selection over the past decade. Originality – There have been several surveys of public goods research (many are referenced in this chapter). To our knowledge, this is the ﬁrst to set out the history of, and the imperatives for, this new direction.

Often it is the case that introductions to edited volumes begin and end with the theme of the volume, a roadmap and discussion of the papers, and the logic for their selection. We do that also, but, we are reminded of McCloskey’s (2009) celebration of those times in which one has the opportunity to, ‘‘go back to the decision nodes and think again.’’ The themes that we intend for this volume, endogeneity and self-selection in charitable activity (‘‘Charity with Choice’’), are an invitation to engage in some of what McCloskey calls ‘‘Axelian rethinking’’1 of laboratory experiments on public goods and charitable activity. The experimental economics of public goods is ﬁrmly planted in the world of Lindahl, Musgrave, and Samuelson, with an appropriate travelogue being Samuelson’s (1954) ‘‘A Pure Theory of Public Expenditure.’’ This world speciﬁes a population of ‘‘n’’ individuals operating in a landscape of property rights and production conditions that create the classic economic environment for at least one public good. Samuelson derives the optimality conditions for a benevolent social planner, what he calls the ‘‘best state of the world.’’2 The central contribution of Samuelson was to throw a large dose of cold water upon a utopia in which the resulting ‘‘Lindahl taxes’’ could achieve this optimum: ‘‘But, and this is the point sensed by Wicksell but perhaps not fully appreciated by Lindahl, now it is in the selﬁsh interest of each person to give false signals, to pretend to have less interest in a given collective consumption activity than he really has, etc.’’ If that were not pessimistic enough, Samuelson also conjectured that no decentralized scheme could be devised that could optimally determine appropriate levels of the public good. Samuelson’s conjecture was rigorously proven to be correct (Hurwicz, 1975; Green & Laffont, 1977). Vickrey (1961), Groves (1973), and Clark (1971) each independently constructed versions of dominant strategy mechanisms that provide strong incentives for individuals to reveal their true valuations of a public good. However, these incentives are obtained only at the cost of a failure to balance the budget, leading to inefﬁciencies. Sameulson’s conjecture therefore is preserved.

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But where does Samuelson’s insight lead the experimental economist? Perhaps we should recall from Samuelson’s paper his closing comments: ‘‘To explore further the problem raised by public expenditure would take us into the mathematical domain of ‘sociology’ or ‘welfare politics’y.’’ After nearly four decades of experimental research the most powerful legacies of the Lindahl/Samuelson world are the questions that were never asked. How does this society of these particular ‘‘n’’ individuals come into existence so that interaction is possible? Do they combine with randomly selected preferences, or is their some self-selection or other ordering property at work? Why does this good have the characteristics of a public good in the ﬁrst place? Can these characteristics be altered? And, ﬁnally, consider the nature of Samuelson’s conjecture. It suggests the impossibility of achieving what might be viewed as a utopian result (perfect incentives for the revelation of preferences). But, even in the absence of a perfect incentive structure, there are many interesting questions about how different institutions for providing for public goods may be compared with one another. If we want to follow this latter path, examining and evaluating how public goods are provided, we will ﬁnd two important books. One is Mancur Olson’s The Logic of Collective Action (1965). The other is Richard Cornuelle’s Reclaiming the American Dream (1965). Olson took as a given that there is both success and failure in the voluntary provision of public goods, and asked ‘‘Why?’’ For Olson, the world is divided into two types of groups. In ‘‘large’’ groups, the type of free riding of standard economic analysis is the rule. There may be exceptions for other groups (Olson referred to them as ‘‘small groups’’). In small groups face-to-face interaction is possible (p. 62). However, below the surface in the Logic is a tension between two types of ‘‘public’’ goods: the public good that a speciﬁc group is trying to provide (this maps more or less into the Lindahl/Samuelson environment) and the public good of organizing what Olson referred to as the ‘‘latent group.’’3 Cornuelle (1965, new edition in 1993) cited examples from de Tocqueville and various other sources about America’s vibrant heritage of independent action. He called this forgotten middle ground, between the market and the government action, the ‘‘independent sector,’’ which represents voluntary associations that operate orphanages, soup kitchens, health care clinics, and other publicly beneﬁcial services. Cornuelle believed that resignation on both ends of the political spectrum was rooted in a less ambitious and less aggressive independent sector to which public conﬁdence in voluntary action was the remedy. But, even though he spoke passionately about the

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possibility and supports his vision with 19th and early 20th century thought he assumed the future was bright because, ‘‘the service motive is at least as strong as the proﬁt motive.’’ But, researchers in many social science traditions have documented the deterioration of civic engagement.4 Indeed, the landscape of public goods is wrought with tension. Humans do have the desire to beneﬁt others, but, we will often observe limited (or even no) contributions to that end. Although the standard (and dismal) economic prediction is free-riding, in reality, Americans in particular have a long tradition of voluntary collective action. Olson wrote as an economic theorist. Cornuelle observed and analyzed the naturally occurring world. But this volume is about experimental economics. However, to bring this discussion into laboratory experimental economics, it is necessary to step outside the discipline. With an older and deeper tradition of experimentation than exists in economics, it is not surprising that it was sociologists and psychologists who were eager to subject the free-riding conjecture to empirical scrutiny (Chamberlin, 1978; Marwell & Ames, 1979; Dawes, McTavish, & Shaklee, 1977).5 To the surprise of many economists, they often found the free-riding conjecture severely lacking in predicting human interaction. Johansen (1977) was prescient in asking why it was that economic theory seemed so out of sync with so much data. In pondering these ‘‘surprising’’ results, two research teams of economists independently reacted with a mixture of respect for the importance of the questions being asked and skepticism of the research methods (Isaac, McCue, & Plott, 1985; Kim & Walker, 1984). This skepticism was driven by both questions about the experimental methods and also, quite plausibly, because the researchers, being economists, viewed the world around them and saw the evidence of both Samuelson and Olson. People do litter. There are unmet needs of charity and compassion. Regulatory agencies do pursue the interests of organized as opposed to disorganized latent groups. The results of the Isaac, McCue, and Plott and the Kim and M. Walker experiments (designed to correct the perceived ﬂaws of the previous research) were striking. Within the structure of their carefully constructed incentives, designed to give free-riding a ‘‘best shot,’’ one could observe that public goods provision that was, in a Lindahl–Samuelson sense, suboptimal. But, nevertheless, there remained a signiﬁcant departure in much of the observed behavior from the pure free-riding prediction. The paper ‘‘Divergent Evidence on Free-Riding: An Experimental Examination of Possible Explanations’’ (Isaac, Walker, & Thomas, 1984)

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launched a long collaborative program between Isaac and J. Walker in an attempt to draw together a uniﬁed research framework about the seemingly divergent evidence on free-riding. In brief, Isaac and J. Walker asked ‘‘What matters?’’ Can we identify replicable situations in which the optimistic or the pessimistic outcome is more likely to occur? Using Smith’s (1982) two-part classiﬁcation of economic systems as a reference, we can see that experimental economists began to use laboratory economics experiments to analyze the effects of altering both the economic environment and economic institutions on the efﬁcacy of the voluntary provision of public goods. These variations typically were introduced as experimenter-controlled treatment conditions.6 In this early period of laboratory experiments, the inﬂuence of Lindahl, Samuelson, and Olson on the experimental public goods research agenda is obvious. In a typical experiment of this time, there was a ﬁxed group of n individuals where the number ‘‘n’’ was chosen as a parameter or a treatment by the experimenters. Almost universally, the experimental slots for these n participants were ﬁlled by whatever ‘‘random’’ arrival process is inherent in the laboratory subject recruiting mechanism of those researchers. Likewise, the institutions were ﬁxed or controlled as treatments by the experimenters. In this regard, the assumptions of the Lindahl, Samuelson, and Olson models line up well with the inherent strength of laboratory experimentation which controls the institutional and economic environment. But, perhaps loosening the tightness of control can improve this condition of ‘‘magical realism’’ in experimental economics (in which there are real contributions decisions being made by individuals in groups, but, in which the groups magically form). Since the publication in 2006 of Volume 11 of Research in Experimental Economics (titled ‘‘Experiments Investigating Fundraising and Charitable Contributors’’), there have been revolutionary transformations in experimental public goods research toward questions of institutional evolution, self-selection, and intentionality. These designs allow experimentalists to question what inﬂuences group formation before the point that public goods provision is attempted. In essence, experimental economists are investigating the backstory to group formation prior to the point that Samuelson’s ﬁrst words come into play. Certainly, this trend was not a creation simply of the experimental lab. As argued earlier, the tension had been present in The Logic of Collective Action. Davis and North (1971) had almost simultaneously proposed an economic model of institutional change. The anthropologically oriented (and now Nobel prize-winning) research by Elinor Ostrom was seeding ﬁeld

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observations into a successful laboratory experimental research program at Indiana University (see Ostrom, Walker, & Gardner, 1992). In the laboratory, one of the earliest examples of this new emphasis was work which became the Gunnthorsdottir, Houser, and McCabe (2007) paper. Their research reconstitutes experimental groups for a second round of public goods provision based on the subjects early round behavior. Numerous other studies of endogenous group composition have appeared over the past few years (Ehrhart & Keser, 1999; Cinyabaguma, Page, & Putterman, 2005; Page, Putterman, & Unel, 2005; Ahn, Isaac, & Salmon, 2008, 2009). These studies generally conclude that group composition can affect the level of public goods provision. The Ahn, Isaac, and Salmon papers, which allowed for not only endogenous group composition but also for group size to be determined endogenously, were able to explore the differential effects of rules about entry and exit into groups. Along another dimension, Norton and Isaac (2009) placed subjects in a group of ﬁxed size, but allowed them to choose their own level of taxation for providing public goods.7 We are convinced that research into such issues as endogenous group composition, group formation, movement into and between groups, and subject-selected institutions will yield important results in the next arc of experimental research. But this is not merely a ‘‘new direction’’ undertaken in academic isolation. The importance of charity and the independent sector place purpose behind these experimental academic pursuits. Research into the provision of public goods and charitable behavior is important to us because it has implications for the improvement of human life. We are proud that this volume expands the experimental literature on endogeneity. But we also hope that it acts as a catalyst to spur more research into voluntary charitable activity. The current volume presents six additional research papers pursuing these themes. First we present a chapter by Gunnthorsdottir, Vragov, and Shen. It is both a theoretical and experimental paper that advances the Gunnthorsdottir, Houser, and McCabe paper as well as Gunnthorsdottir, Vragov, Seifert, and McCabe (2009). The previous research reassigned subjects based on prior contributions history, but individuals were homogenous. In this chapter, the authors examine the more demanding environment in which individuals have heterogenous endowments. The authors observe something akin to a reverse market for lemons in which contributors, whether they have high or low endowments, seek to increase their contributions when they are competitively grouped based on their contributions. The results seem to parallel theoretical and empirical ﬁeld

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studies that suggests dimensions of homogeneity matter in groups with public goods provision (see Alesina, Baqir, & Easterly, 1999; Hungerman, 2009). The chapter by Daniel Hall investigates the properties of government redistribution as an organizational form for charitable activity. In his experiment, individuals can choose how much they want to work, so that the level of governmental charitable activity is endogenous. Both efﬁciency and equality effects of this endogeneity are tracked across his sessions. Lower work incentives via higher taxes reduce inequality between players but cost large losses in efﬁciency from lower labor supply. The implications for charity are mixed. Individuals may have less income to support monetary donations to charitable activity, but may have more leisure, which could support a greater supply of volunteer labor. Next, we turn our attention to the sphere of nonproﬁt (technically notfor-proﬁt) organizations. This part of the volume is introduced by Norton’s agenda for experimentation. Motivated by the desire to provide a stable source of capital to philanthropy, this chapter offers several research questions involving nonproﬁts as businesses. The growing popularity of the L3C legal arrangement conﬁrms the importance and need of more research in this area. The following chapter, by Norton and Isaac, is a direct demonstration of one of those possibilities. In this chapter, we look at a world of designing institutions of transparency for the managers of nonproﬁts. With donors or customers as the control on a nonproﬁt organization, we seek to uncover the impacts of displaying historical effort choice (which is a choice made by the manager) as well as managers signaling high credentials. The results are analyzed on an aggregate contributions level and they indicate that both sources of transparency have a positive impact on contributions; however, when both sources of transparency are paired together their impact on contributions is much more signiﬁcant. The experiments have direct implications for the types of information nonproﬁt organizations should be advised to incorporate in their business model. The last two chapters isolate some speciﬁc and practical questions regarding selection effects of donors and nonproﬁts. Kamas and Preston present theoretical models of three social preference types from previous research. They then conduct experiments to see how charitable giving with respect to price and type (productive v. distributive charities) of charitable gift are inﬂuenced by these preferences. They ﬁnd that all categories of social preference types give more under matching than rebates. Moreover, all subjects are responsive, to varying degrees, in the predictable ways to the price of the charitable good or service.

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Carpenter, Holmes, and Matthews (2008) report a laboratory experiment motivated directly by their previous ﬁeld work on the topic of charity auctions. Much of the existing theoretical and laboratory experimental work on alternative forms of charity auctions (including all-pay auctions and charity lotteries) have assumed a ﬁxed set of charitable bidders. But ﬁeld research has pointed in the direction that the preferences of the patrons of the nonproﬁts may play a signiﬁcant selection-censoring role in determining revenues to the charities. In this chapter, research returns to the laboratory to examine selection effects under controlled conditions. This chapter ﬁnds that people are more likely to participate in a ﬁrst price lottery auction or a basic silent auction. Greater participation is important because it increases the bidding competition and has positive revenue effects. We hope that this volume will inspire more research into endogenous formation, self-selection, movement, and more areas of public goods research. This means not only more laboratory experiments but also theoretical, empirical, and econometric advances that take account of these effects. In particular, the boundary between experiments in the lab and ﬁeld are likely to be blurred as evidenced by the recent special issue of Experimental Economics on ﬁeld experiments in charitable activity (2008). And, perhaps in revisiting the decision node of our experimental inquiry into public goods, we may also revisit historical decision nodes of charity provision. Care for the poor, sick, and hungry were not responsibilities of the state but of individuals in closer communities. If we pursue such a decision node, we can talk about transformed preferences in addition to alterations in incentives and institutional design.

NOTES 1. In honor of Axel Leijonhufvud. 2. Samuelson readily assents to the prior derivation of these conditions by several other authors, including Lindahl, Wicksell, Musgrave, and Bowen. 3. See footnote 49 in the 1975 edition. 4. Cornuelle cites two of his contemporaries (Myrdal and D.W. Brogan) as reaching such a pessimistic conclusion. Robert Putnam in Bowling Alone (2000) is a more current example. 5. There was also nascent experimental work on public at about the same time, but, perhaps because economists were more likely to accept the importance of free riding, these studies from the start investigated the engineering of new mechanisms to align individual and group interests. See Ferejohn, Forsythe, Noll, and Palfrey (1980) and Smith (1979).

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6. For a more extended survey of these environmental and institutional treatments and their effects, see Andreoni and Croson (2008), Chan, Mestelman, and Muller (2008), Davis and Holt (1993), Isaac (2002), Isaac and Walker (1986), Laury and Holt (2008), Ledyard (1995), and Schram, Offerman, and Sonnemans (2008). A separate stream of research (which goes beyond what we can discuss here) uses public goods experiments as a vehicle for examining whether or not individuals have the kind of selﬁsh preferences as typically considered in the Lindahl and Samuelson models. Early papers in this area included Andreoni (1993) and Brandts and Schram (2001). This brief preface regarding laboratory experiments can not do justice to the path breaking ﬁeld experimental work of Peter Bohm (see Dufwenberg & Harrison, 2008 for a tribute). 7. These experiments retain some tightness of control compared to the free form and discovery oriented boundary ﬁrst set out by Crockett, Wilson, and Smith (2009). In this regard, their research forms a boundary of allowable endogeneity.

ACKNOWLEDGMENTS We are grateful to our colleague John Hamman for thorough and insightful comments on an earlier draft of this chapter and to Kurt Schnier of Georgia State University who served as the editor on the two chapters of our own research. We also thank the anonymous referees (some unknown to us) without whose efforts this volume could not exist.

REFERENCES Ahn, T. K., Isaac, R. M., & Salmon, T. C. (2008). Endogenous group formation. Journal of Public Economic Theory, 10, 171–194. Ahn, T. K., Isaac, R. M., & Salmon, T. C. (2009). Coming and going: Experiments on endogenous group sizes for excludable public goods. Journal of Public Economics, 93, 336–351. Alesina, A., Baqir, R., & Easterly, W. (1999). Public goods and ethnic divisions. Quarterly Journal of Economics, 114, 1243–1284. Andreoni, J. (1993). An experimental test of the public goods crowding out hypothesis. American Economic Review, 83, 1317–1327. Andreoni, J., & Croson, R. (2008). Partners versus strangers: Random rematching in public goods experiments. In: C. R. Plott & V. L. Smith (Eds), Handbook of experimental economics results (Vol. 1). Amsterdam: North Holland. Brandts, J., & Schram, A. (2001). Cooperation and noise in public goods experiments: Applying the contribution function approach. Journal of Public Economics, 79, 399–427. Carpenter, J., Holmes, J., & Matthews, P. (2008). Charity auctions: A ﬁeld experiment. The Economic Journal, 118, 92–113. Chamberlin, J. R. (1978). The logic of collective action: Some experimental results. Behavioral Science, 23, 441–445.

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Chan, K. S., Mestelman, S., & Muller, R. A. (2008). Voluntary provision of public goods. In: C. R. Plott & V. L. Smith (Eds), Handbook of experimental economics results (Vol. 1). Amsterdam: North Holland. Cinyabaguma, M. T., Page, T., & Putterman, L. (2005). Cooperation under the threat of expulsion in a public goods experiment. Journal of Public Economics, 89, 1421–1435. Clarke, E. H. (1971). Multipart pricing of public goods. Public Choice, 8, 19–33. Cornuelle, R. (1993). Reclaiming the American dream: The role of private individuals and voluntary associations (new edition). New Brunswick, NJ: Transaction Publishers. (Original edition published in 1965 by Random House, New York City). Crockett, S., Wilson, B., & Smith, V. L. (2009). Exchange and specialization as a discovery process. Economic Journal, 119, 1162–1188. Davis, D. D., & Holt, C. A. (1993). Experimental economics. Princeton, NJ: Princeton University Press. Davis, L., & North, D. (1971). Institutional change and American economic growth. Cambridge: Cambridge University Press. Dawes, R. J., McTavish, J., & Shaklee, H. (1977). Behavior, communication, and assumptions about other people’s behavior in a commons dilemma situation. Journal of Personality and Social Psychology, 35, 1–11. Dufwenberg, M., & Harrison, G. W. (2008). Peter Bohn: Father of ﬁeld experiments. Experimental Economics, 11, 213–220. Ehrhart, K.-M., & Keser, C. (1999). Mobility and cooperation: On the run. Working Paper. Ferejohn, J. A., Forsythe, R., Noll, R. G., & Palfrey, T. R. (1980). An experimental examination of auction mechanisms for discrete public goods. In: V. L. Smith (Ed.), Research in experimental economics (Vol. 1). Greenwich, CT: JAI Press, Inc. Green, J., & Laffont, J.-J. (1977). Characterization of satisfactory mechanisms for the revelation of preferences for public goods. Econometrica, 45, 427–438. Groves, T. (1973). Incentives in teams. Econometrica, 41, 617–631. Gunnthorsdottir, A., Houser, D., & McCabe, K. (2007). Disposition, history, and contributions in public goods experiments. Journal of Economic Behavior and Organization, 62, 304–315. Gunnthorsdottir, A., Vragov, R., Seifert, S., & McCabe, K. (2009). Near efﬁcient equilibria in collaborative meritocracies. Working paper. Hungerman, D. (2009). Crowd out and diversity. Journal of Public Economics, 93, 729–740. Hurwicz, L. (1975). On the existence of allocation systems whose manipulative nash equilibria are pareto-optimal. Paper given at the 3rd World Congress of the Econometric Society, Toronto. Isaac, R. M. (2002). Games: Voluntary contributions. In: L. Nadel (Ed.), The encyclopedia of cognitive science. London: Nature Publishing Group. Isaac, R. M., McCue, K., & Plott, C. R. (1985). Public goods in an experimental environment. Journal of Public Economics, 26, 51–74. Isaac, R. M., & Walker, J. M. (1986). Group size hypotheses of public goods provision: An experimental examination. Quarterly Journal of Economics, 103, 179–199. Isaac, R. M., Walker, J. M., & Thomas, S. (1984). Divergent evidence on free riding: An experimental examination of possible explanations. Public Choice, 43, 113–149. Johansen, L. (1977). The theory of public goods: Misplaced emphasis? Journal of Public Economics, 7, 147–152.

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Kim, O., & Walker, M. (1984). The free rider problem: Experimental evidence. Public Choice, 43, 3–24. Laury, S. K., & Holt, C. A. (2008). Voluntary provision of public goods: Experimental results with interior nash equilibria. In: C. R. Plott & V. L. Smith (Eds), Handbook of experimental economics results (Vol. 1). Amsterdam: North Holland. Ledyard, J. O. (1995). Public goods: A survey of experimental research. In: J. H. Kagel & A. E. Roth (Eds), The handbook of experimental economics. Princeton, NJ: Princeton University Press. Marwell, G., & Ames, R. (1979). Experiments on the provision of public goods: I. Resources, interest, group size, and the free rider problem. American Journal of Sociology, 85, 926–937. McCloskey, D. (2009). Adam smith proposed an ethically serious and humanistic science of the wealth of nations. Presented at the 2009 Allied Social Sciences Conference in San Francisco. Norton, D. A., & Isaac, R. M. (2009). The role of trust, endogenous institutions, and the possibility of grace in public goods provision. Working paper. Olson, M. (1965). The logic of collective action. Cambridge, MA: Harvard University Press. Ostrom, E., Walker, J. M., & Gardner, R. (1992). Covenants with and without a sword: Selfgovernance is possible. American Political Science Review, 86, 404–417. Page, T., Putterman, L., & Unel, B. (2005). Voluntary association in public goods experiments: Reciprocity, mimicry, and efﬁciency. Economic Journal, 115, 1032–1053. Putnam, R. D. (2000). Bowling alone: The collapse and revival of American community. New York: Simon & Schuster. Samuelson, P. A. (1954). The pure theory of public expenditure. The Review of Economics and Statistics, 36, 387–389. Schram, A., Offerman, T., & Sonnemans, J. (2008). Explaining the comparative statics in steplevel public goods games. In: C. R. Plott & V. L. Smith (Eds), Handbook of experimental economics results (Vol. 1). Amsterdam: North Holland. Smith, V. L. (1979). Incentive compatible experimental processes for the provision of public goods. In: V. L. Smith (Ed.), Research in experimental economics (Vol. 1). Greenwich, CT: JAI Press, Inc. Smith, V. L. (1982). Microeconomic systems as an experimental science. American Economic Review, 72, 923–955. Vickrey, W. (1961). Counterspeculation, auctions, and competitive sealed tenders. Journal of Finance, 41, 8–37.

TACIT COORDINATION IN CONTRIBUTION-BASED GROUPING WITH TWO ENDOWMENT LEVELS Anna Gunnthorsdottir, Roumen Vragov and Jianfei Shen ABSTRACT Purpose and approach – We examine theoretically and experimentally how unequal abilities to contribute affect incentives and efﬁciency when players compete for membership in stratiﬁed groups based on the contributions they make. Players have either a low or a high endowment. Once assigned to a group based on their group contribution, players share equally in their group’s collective output. Depending on the parameters, the mechanism has several distinct equilibria that differ in efﬁciency. Findings – Somewhat counter to conventional expectation our theoretical analysis indicates that as long as certain assumptions are satisﬁed, efﬁciency increases rather than decreases the more abilities to contribute differ. The analysis also suggests various follow-up experiments about equilibrium selection, tacit coordination, and the effect of unequal abilities in systems with endogenous grouping. We conduct an experiment that shows that subjects tacitly coordinate the mechanism’s asymmetric Charity with Choice Research in Experimental Economics, Volume 13, 13–75 Copyright r 2010 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0193-2306/doi:10.1108/S0193-2306(2010)0000013004

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payoff-dominant equilibrium with precision; this precision is robust to a change in the structure and complexity of the game. Implications – The results suggest that people respond to merit-based grouping in a natural way and that competitive contribution-based grouping encourages public contributions even when abilities to contribute differ, which is the case in all communities and societies.

1. INTRODUCTION Can competitive grouping based on individuals’ group contributions increase cooperation and efﬁciency? Recent behavioral research has answered this question with a clear ‘‘yes’’:1 Experimental ﬁndings about the effects of endogenous group formation on provision levels indicate that the degree of excludability of public goods or team goods (Buchanan, 1965) is not the only factor that matters. The method by which players are assigned to their cooperative units is also very important. Worldwide, trends toward globalization and toward contribution-based rather than privilege-based grouping appear to go hand in hand, facilitated by equal-rights movements, scholarship programs, and increasingly global, and hence more intense, competition in business and education. The entry and promotion systems of business and nonproﬁt organizations are increasingly based on contribution rather than on superﬁcial criteria such as race, class, or gender.2 With the resulting increase in competitiveness, social units or systems that still group and stratify based on criteria unrelated to output are likely less competitive3 and might either change or disappear. However, before one can suggest that competitive grouping is indeed an effective tool to raise social contributions, the important issue of unequal ability to contribute must be addressed. Unequal abilities are a reality in all communities or societies, be it due to differences in health, education, cognitive abilities, and so on. In this chapter, we theoretically analyze and experimentally test a formal mechanism of competitive, contribution-based endogenous grouping, called ‘‘Group-based Meritocracy Mechanism’’ (GBM) (see Gunnthorsdottir, Vragov, Seifert & McCabe, 2009, henceforth GVSM, for an introductory analysis) and make the ability to contribute unequal between players, effectively creating two types of ‘‘citizens’’: those who are able to contribute more and those who can only contribute less. Applying the principle of payoff dominance (Harsanyi & Selten, 1988), one can make a precise prediction about the aggregate behavior of GBM

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participants even if their abilities to contribute are unequal: Inequality notwithstanding, the mechanism should lead to high social contributions and efﬁciency in most instances. GVSM analyzed and experimentally tested a basic version of the GBM with equal endowments, and found that the GBM’s payoff-dominant, asymmetric ‘‘near-efﬁcient equilibrium’’ (henceforth NEE) was reliably and precisely coordinated in the laboratory, even though it is unlikely that experimental subjects can consciously understand its structure. The current study builds on GVSM’s introductory work; the three main contributions here are as follows: (1) we show that GVSM’s ﬁndings of precise tacit coordination of the payoff dominant asymmetric equilibrium are robust to an increase in the complexity of the game, (2) we increase the realism of GVSM’s original model by introducing unequal abilities to contribute, and (3) we provide a general theoretical analysis which suggests an array of future experimental tests, as well as extensions of the current model. (1) GVSM’s subjects all had the same endowment and thus equal ability to make a contribution. We increase complexity by introducing two different endowment levels while keeping everything else (including the median/mean endowment) the same as in GVSM’s experiments. Under two endowment levels, the asymmetric NEE is more elaborate; it consists of three different strategies, whereas in GVSM’s setup it consisted of only two. We have discovered only one reliable method of ﬁnding the GBM’s equilibria involving positive contributions: the gradual elimination of possible strategy combinations by searching for incentives to deviate, a lengthy and somewhat involved process (see Section 3 and Appendix A). However, our experimental results show that GVSM’s initial ﬁndings about the ‘‘magical’’ (Kahneman, 1988, p. 12) coordination of the GBM’s asymmetric payoff-dominant equilibrium are robust to the increase in complexity implemented in the current study. (2) As mentioned earlier, unequal ability to contribute is a reality in communities and societies and should be incorporated in any design intended to increase cooperation. Our experimental results indicate that even when abilities to contribute are unequal, competitive, contribution-based team formation remains an effective and precise mechanism to raise social contributions, at least in the controlled environment of the laboratory. (3) The general theoretical analysis of a GBM mechanism with two endowment levels (henceforth 2-Type GBM) suggests that under contribution-based grouping, the effect of unequal ability to contribute is not straightforward: Group size, the overall proportions of players with high and low endowment, and the degree of inequality all impact efﬁciency.

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Interestingly, we ﬁnd that efﬁciency increases when the difference in ability to contribute increases. Our analysis suggests an array of further experimental tests of competitive endogenous grouping when abilities to contribute differ. By changing the game’s parameters experimenters can create many different cases, which allow the examination of (a) theories of equilibrium selection, in particular payoff dominance (Harsanyi & Selten, 1988); (b) tacit coordination of various types of asymmetric equilibria, which are nonobvious to subjects and which, depending on the parameters, have different properties; and (c) the effect of different degrees of inequality with regard to players’ ability to contribute on equilibrium structure and subject behavior.

1.1. Overview Section 2 describes the GBM mechanism and compares it to the Voluntary Contribution Mechanism (VCM) (Isaac, McCue, & Plott, 1985). We suggest that the VCM and the GBM can serve as rough models of privilege-based and merit-based social stratiﬁcation, respectively. Section 2 also contains a brief overview of the equilibrium structure of the basic GBM and its extension under study here, the 2-Type GBM. Section 3 provides a formal analysis of the 2-Type GBM. The examples in Section 3, with parameters commonly used in experiments, suggest an array of further experimental tests. Section 4 describes a GBM experiment where subjects have two different endowment levels. Section 5 contains the results and shows that the payoff dominant Nash equilibrium organizes aggregate behavior very well. In Section 6 we detail possible follow-up studies based on our theoretical analysis, discuss sociological and policy implications of our ﬁndings, and address shortcomings and potential criticisms.

2. THE GROUP-BASED MERITOCRACY MECHANISM WITH TWO DIFFERENT ENDOWMENT LEVELS A GBM is a society in which participants are assigned to groups based on their contributions to a group account. The game shares features with the VCM, the standard experimental model to examine free-riding, but with competitive contribution-based grouping added. We ﬁrst brieﬂy describe the VCM before addressing how the GBM differs.

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2.1. The VCM In a VCM, n participants are randomly assigned to G groups of ﬁxed size f. After grouping, players each decide simultaneously and anonymously how much of their individual endowment wi to keep for themselves, and how much to contribute to a group account. Contributions to the group account are multiplied by a factor g representing the gains from cooperation before being equally divided among all f group members. In the remainder of this chapter, we denote the rate g/f by m. m is the marginal per capita return (MPCR) to each group member from an investment in the group account. As long as 1/fomo1, this game is a social dilemma: efﬁciency is maximized if all participants contribute fully to their group, but each individual’s dominant strategy is to contribute nothing. In experimental tests of the VCM, mean group contributions start at about half of the sum of the endowments, and fall toward the dominant-strategy equilibrium of noncontribution by all within about ten repetitions (for overviews see, e.g., Ledyard, 1995; Davis & Holt, 1993).

2.2. The Basic GBM Mechanism with Homogeneous Endowments The GBM’s equilibrium structure differs from the VCM’s because in the GBM group membership is competitively based on individual contributions. As in the VCM, payoff functions, group size, and other parameters are ﬁxed. In contrast to the VCM, however, a GBM player has considerable control over her group placement through her public contribution decisions. Participants ﬁrst make their contribution decisions, then get ranked according to their contributions to the group account. On the basis of this ranking, participants are partitioned into equal-sized groups. Individual earnings are computed taking into account the group a player has been assigned to. For the game’s equilibrium analysis, it is important to note that any ties for group membership (which occur if some of the players equally contribute) are broken at random. All this is common knowledge.4 The GBM also differs from the VCM in how the entire society is modeled. In the VCM each arbitrarily composed group exists in isolation. Since team assignment is random, there is no social mobility either. The GBM, in contrast, is not just about a single isolated group, but about a society consisting of multiple groups, where socially mobile players are linked through a cooperative-competitive mechanism. Through their contribution decisions, they compete for membership in units with potentially different

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collective output and payoffs. The GBM’s equilibrium analysis must therefore extend over the multiple groups that make up an organizationally stratiﬁed society.

2.3. The VCM and the GBM as Models of Social Grouping In a VCM the choices a participant makes do not affect her placement in the experimental mini-society: each VCM player must accept what has been handed to her in the random grouping process. As Rawls (1971) points out, each individual must accept the ‘‘Lottery of Birth’’ with regard to factors that are ﬁxed at the beginning of life and over which the individual has no control, such as race or gender. In privilege-based societies however the Lottery of Birth remains disproportionally important throughout a person’s life, since these unalterable characteristics determine her organizational membership and place in society, and through it, her payoffs. This is why the VCM with its random grouping can be viewed as a model of an ascriptive (Linton, 1936), privilege-based society where the Lottery of Birth looms large. The GBM in contrast, with its competitive contribution-based grouping, can serve as a rough model of meritocratic social organization where people are grouped and stratiﬁed based on their choices; highcontributors join more productive cooperative units where payoffs are higher. The GBM’s incentive structure generates competition and increases efﬁciency. This is reﬂected in its equilibrium structure.

2.4. The Equilibria of the GBM with Homogeneous Endowments In contrast to the VCM with its dominant strategy equilibrium of noncontribution by all, GVSM show that in the relatively simple case when endowments are equal, the GBM has two pure-strategy equilibria5 which differ in efﬁciency. An equilibrium of non-contribution by all remains present, reﬂecting the fact that the GBM retains some social dilemma properties. However, with competitive grouping the social dilemma features are now much attenuated, and the equilibrium of non-contribution changes from a dominant-strategy equilibrium to a best-response equilibrium. The GBM with equal endowments always has a second, payoff-dominant and highly efﬁcient, asymmetric equilibrium. In this equilibrium, as long as the within-group interaction has social dilemma properties (i.e., 1/fomo1),

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all players contribute fully with the exception of cRof players6 who contribute nothing. GVSM call this payoff dominant equilibrium an NEE because it asymptotically approaches full efﬁciency as the number of players becomes large. However, the GBM’s payoff-dominant equilibrium becomes more complex when the endowments are not equal.

2.5. A GBM with Two Different Endowment Levels (2-Type GBM) We now change the basic GBM so that there are two different endowment levels.7 Some players have high endowments, others low endowments. This is common knowledge. We henceforth denote the high endowment wi as H and the low wi as L. 2.5.1. Incentives Under Two Different Endowment Levels Recall that as long as the within-group interaction has social dilemma properties, the mechanism retains a best-response equilibrium of noncontribution by all.8 With the unequal distribution of endowments common knowledge, players with a lower endowment wi ¼ L (henceforth ‘‘Lows’’) might not feel motivated to contribute. This in turn would affect the expected payoffs of players with a higher endowment wi ¼ H, (‘‘Highs’’), and could drive the system toward the inefﬁcient equilibrium rather than the NEE. However, this is not the case in our experiment: Even though Lows can never aspire to the level of earnings that Highs can achieve, the 2-Type GBM elicits high social contributions from Highs and Lows alike, and the NEE is reliably realized. 2.5.2. Increased NEE Complexity Under Two Different Endowment Levels One might expect that the 2-Type GBM’s NEE might be hard to coordinate because of its complexity. High demands are put on subjects’ ability to tacitly coordinate. In the game tested experimentally in Sections 4 and 5 the NEE consists of three corner strategies. Subjects thus must (1) somehow grasp that they should not play strategies drawn from the interior of their strategy spaces, {0, 1,y, 80} for Lows, and {0, 1,y, 120} for Highs, respectively, and (2) tacitly coordinate the three equilibrium strategies, 0, 80, and 120 in the correct proportions. This is complicated by the fact that (3) this NEE is not obvious, as reﬂected by the length of the analytical derivation of the conditions for its existence (Section 3). As mentioned, we ourselves have discovered only one reliable method of ﬁnding this NEE – the gradual elimination of strategy combinations by searching for incentives to

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deviate focusing ﬁrst on the necessary conditions for an equilibrium with positive contributions, then on the sufﬁcient conditions. (4) The 2-Type GBM’s NEE can be ephemeral in that its exact structure, even its existence, is often parameter dependent (see Examples 2 and 5 in Sections 3.4.3 and 3.5.3, respectively; see also Section 3.7). We show here below that different equilibrium predictions can be generated by slightly modifying the experimental parameters. Since both GVSM and the current authors ﬁnd that subjects coordinate the GBM equilibria quite precisely, such parameter changes should lead to discernibly different aggregate behavior.

3. THEORY Before formally describing the game’s equilibria and its properties, we provide an intuitive account of the equilibria of the 2-Type GBM (Section 3.1) and a brief overview of the formal steps by which the equilibria are derived, highlighting some of the theoretical ﬁndings and the examples that suggest future experimental tests (Section 3.2). Let us ﬁrst introduce three terms, formally deﬁned in Section 3.3. A group is the cooperative unit whose members equally share the earnings from their public account. Ranking all players by their contributions from highest to lowest with ties broken at random and the players grouping into G groups, one can deﬁne three general kinds of groups: the ﬁrst group, Group 1, contains the top f contributors; the last group, Group G, contains the bottom f contributors; any group in between is designated as an ‘‘intermediate group’’. A player’s type is deﬁned by her endowment, so that a player is either a ‘‘High’’ or a ‘‘Low’’. A class is a subset of players whose public contributions are identical. The ﬁrst class C1 is thus the subset whose members contribute the most, C2 the next class whose members contribute less, and so on; the last class CR is the subset who contribute least. 3.1. An Intuitive Account of the 2-Type GBM’s Equilibria We focus ﬁrst on the simpler (GVSM’s) version of the mechanism where all endowments wi are equal, then extend the same reasoning to the 2-type case.9 First, non-contribution by all is clearly an equilibrium – no single individual has an incentive to increase her contribution if everyone else contributes nothing. Are there equilibria with positive contributions? It can be veriﬁed that in an equilibrium with positive contributions, a group

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cannot contain players from three classes, since each player in the middle class could decrease her contribution by a small e and remain in the same group. Therefore, if an equilibrium with positive contributions exists, each group must contain either one or two classes of players. We next examine the three different kinds of groups separately: Group 1 can only contain one class, C1 – if it had two classes, any member of C1 would have an incentive to decrease her contribution by a small e and remain in Group 1 nonetheless, enjoying the top earnings associated with such a position. For the same reason the number of players in C1 must be greater than the group size f and not divisible by f. It is also easy to show that members of C1 must contribute their full endowments: If they do not contribute fully, each C1 member has an incentive to increase her contribution and thus her earnings, because her expected earnings are higher if she is with certainty in Group 1 than if she is grouped with some positive probability with lower classes in a lower group. Could the ﬁrst intermediate group, Group 2, possibly contain individuals from the next class, C2? We already know from the previous paragraph that Group 2 must already contain at least one full contributor. Since groups can contain either one or two classes, there are two cases to consider with regard to the composition of the other players in Group 2. (1) All other members of Group 2 also contribute fully, or (2) all its other members belong to the next class, C2, whose members contribute less. We will now examine case (2) and show that it is impossible if endowments are equal: Following similar logic as laid out with regard to Group 1 membership, if there were C2 players in Group 2, C2 must extend into the next intermediate group (Group 3) else there cannot be an equilibrium: if C2 did not extend into Group 3, any C2 player could decrease her contribution and stay in Group 2. Assume now that C2 does extend into Group 3: in such a case any C2 player will increase her contribution by e so that she can with certainly be in Group 2 and free ride off the full contributor(s) in it. Hence in an equilibrium with positive contributions members of any intermediate group must contribute fully. What about Group G? It is clear that Group G cannot contain one class only, because from above it follows that it already has at least one full contributor. If all members of Group G are full contributors, then everyone has an incentive to free ride and contribute nothing. Hence, Group G must contain two classes. Also, the individuals in its lower class CR contribute nothing, else any one of them has an incentive to lower her contribution, since she would remain in Group G nonetheless. To ﬁnd a stable point where the system is in equilibrium and no player has an incentive to unilaterally deviate, one needs to determine how many

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zero-contributors are needed in Group G. GVSM derived the conditions for the existence of such an equilibrium for the case with homogeneous endowments and called it an NEE. Does a similar equilibrium exist when there are two endowment levels? Following the same logic as earlier, one can verify that non-contribution by all is still an equilibrium; in an equilibrium with positive contributions each group still must have either one or two classes; Group 1 can still have only one class of full contributors; the number of C1 players must still be greater than the group size f and not divisible by f. However, differences arise in the ﬁrst intermediate group, Group 2, which might contain players which are in C2 by necessity, because of their lower endowment. Group 2 (or by extension some other intermediate group) can thus have either (1) one class or (2) two classes if some Group 2 members are Lows who would want to, but cannot, contribute as much as the Highs do. It follows that one intermediate group with two classes must exist in an equilibrium with positive contributions if there are more than f Lows and more than f Highs in the system. By the same logic as earlier it follows that in this case C2, consisting of fully contributing Lows, must extend to the intermediate groups below this mixed group, and that all intermediate groups below the mixed group can have only one class. What about Group G,the last group? Since we showed that a group can never contain more than two classes, we know that Group G has either (1) one or (2) two classes. We will show formally here below that both (1) and (2) can be equilibria depending on the parameters. We call (1), the conﬁguration where Group G consists of full contributors only, a ‘‘fully efﬁcient equilibrium’’ (FEE). Case (2) corresponds to the ‘‘near-efﬁcient equilbrium’’ (NEE) originally deﬁned by GVSM. We now provide a brief overview of our formal analysis and highlight its most important ﬁndings about the impact of unequal endowments. 3.2. A Description of the Formal Model 3.2.1. The Game Deﬁned In Assumption 1 (Section 3.3.2), we formally restrict the endowment wi to two levels, H or L. Without loss of generality we let L ¼ 1 and H ¼ (1 þ Dw) where DwW0. We will examine the effect of change in Dw in depth in Sections 3.5 to 3.7.10 In Assumption 2 (Section 3.3.2), we restrict the distribution of player types, Highs and Lows, in the following manner: type count is not fully divisible by group size, and for each type its count, nH or nL, must exceed the group size f.

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The reason for these restrictions is as follows: (1) The Sections 3.3 to 3.7 and Appendix A make it clear that even with these assumptions in place the process of ﬁnding the equilibria of the 2-Type GBM is lengthy and cumbersome. Relaxing Assumptions 1 and 2 would mean that there would be numerous additional cases to consider, each of which requires the same detailed examination of all possible strategy combinations as contained in Sections 3.5 to 3.7.11 (2) Cases that satisfy Assumption 2 are the most interesting since a distribution of types as stipulated by Assumption 2 encourages competition for group membership. Recall that in any GBM ties for group membership are broken at random, and that equilibrium payoffs are expected payoffs, computed before the random resolution of ties puts players in speciﬁc groups. For an equilibrium with positive contributions in all of the cases of the GBM studied so far (GVSM’s and ours) it is necessary that competition between players for group membership has this random component. 3.2.2. The Equilibrium of Non-Contribution by All In Section 3.4.1 we ﬁrst show the omnipresence of an equilibrium of noncontribution by all. This is the only equilibrium of the game where all players use the same strategy. This equilibrium is always present as long as the MPCR m is within the bounds that make the within-team interaction a social dilemma (Lemma 1). 3.2.3. Equilibria with Positive Contributions We focus ﬁrst on the necessary conditions for equilibria with positive contributions in Section 3.4. Theorem 1 states that there are only two equilibrium conﬁgurations with positive contributions possible; both are asymmetric and consist of corner strategies: (1) an FEE where both types contribute fully and (2) an NEE where all players contribute fully with the exception of cRof players12 who contribute zero. The two equilibria are depicted in Fig. 1. Appendix A contains the proof of Theorem 1. This proof involves the usual process of gradual elimination, including the step-by step elimination of initial ‘‘equilibrium candidate’’ E’ by searching for incentives by individual players to deviate. In Section 3.4.3 we also apply Theorem 1 to three examples relevant to experimental testing or to previous literature: In Example 1 we derive the equilibrium with positive contributions of the version of the 2-Type GBM experimentally tested in Sections 4 and 5 and show that it must be an NEE. Example 2 illustrates that not all 2-Type GBMs have an equilibrium with positive contributions; we slightly modify the type composition of the

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experimental game in Example 1 so that only the equilibrium of noncontribution by all remains. In Example 3 we connect our general analysis to GVSM’s original analysis of a GBM where all endowments are equal. We show that in such a case a FEE cannot exist, only a NEE is possible.

3.2.4. When is a Fully Efﬁcient Equilibrium (FEE) Possible? In Sections 3.5 and 3.6, we explore the conditions for the existence of FEE and NEE, respectively, by examining all players’ incentives to deviate. In this process we always start with the lowest class. Although lengthy and cumbersome, the process is relatively straightforward. We draw attention to Theorem 2 in Section 3.5, which states (subject to the constraints speciﬁed in Remarks 2 and 3 in Section 3.5.3) that the existence of a FEE depends on a combination of parameters including the group size f, the count of Highs and Lows in the system (nH and nL, respectively), and the MPCR m. An FEE ’s existence also depends on Dw, the difference between the high and the low endowment. Theorem 2 implies that if this difference increases, efﬁciency increases rather than decreases until an FEE, rather than an NEE, is possible. Theorem 2 has practical implications. It allows building a mechanism that is fully efﬁcient by intervening on the parameters. In the ﬁeld, Dw may be ﬁxed at least in the short run; same for nH and nL, the distribution of the two types in a community or society. However, the gains from cooperation m and with it, M, could for example be changed through technology that increases team productivity. It might however be easiest to intervene through the team size f, which in turn determines h ¼ nH mod f and ‘ ¼ nL mod f. Three remarks in Section 3.5.3 elaborate further on Theorem 2: if the MPCR m approaches 1 from below, full contribution by all becomes an equilibrium (Remark 1). (Of course, if mW1, it is a dominant strategy to contribute fully as it is in the VCM.) Remarks 2 and 3 focus on the impact of Dw, the difference in ability to contribute. If Dw is small, an FEE is impossible (Remark 2, compare to Example 3 in Section 3.4.3). However, although a large Dw is a necessary condition for a FEE, it is not sufﬁcient. Cases can be found where Dw is large yet no FEE exists (Remark 3). Example 4 (Section 3.5.3) illustrates how an FEE can be found combining Theorem 2 with a graphical approach. In Example 5 (Section 3.5.3) we apply Theorem 2 to our experimentally tested version of the mechanism, where L ¼ 80 and H ¼ 120, and ﬁnd that if H were raised to 200(2.5 L), an FEE would replace the current NEE.

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3.2.5. Existence of a Near-Efﬁcient Equilibrium (NEE) The exact type composition of an NEE is parameter dependent with regard to the last class of cRof non-contributors: In our experimental game with three groups of four players each, the last class CR consists of Lows. However, as the bottom right of Fig. 1 shows, if the group size or the number of groups increases CR might also contain Highs. However, cRof does not change with this, so that the NEE’s efﬁciency is not affected much. To the best of our knowledge, an NEE can be discovered only through a gradual elimination process of strategy conﬁgurations. The length and complexity of the analysis can be seen in Theorem 3, which summarizes Section 3.6.1. We also use speciﬁc examples to show that an NEE exists and to illustrate as best we can the conditions under which this happens (see Examples 1 and 2 in Section 3.4.3 and Example 5 in Section 3.5.3). 3.2.6. Can NEE and FEE Coexist? Section 3.7 demonstrates that it is possible to construct a case where FEE and NEE co-exist. Example 5 already illustrated that if HZ2.5, our experimental game would have an FEE rather than an NEE. Section 3.7 shows that at the exact point where H ¼ 2.5, a weak NEE and a weak FEE coexist: one L-player is indifferent between contributing and not contributing.

3.3. Model The set of players is N{1,y, n}. Each player iAN has an endowment wiW0. The distribution of endowments is common knowledge. Each player iAN makes a contribution siA[0, wi] to a public account and keeps the remainder (wisi) in her private account. The return from the private account is without loss of generality set to 1, the return from the public account is the Marginal per Capita Return (MPCR) mA(1/f, 1). 3.3.1. Players Compete for Group Membership After their investment decisions, all players are ranked according to their public contributions and divided into G groups of equal size f, so G ¼ n/f. Ties for group membership are broken at random. The f players with the highest contributions are put into Group 1; then f players with the next highest contributions are put into Group 2, and so on. Earnings are computed after players have been grouped. Each player’s earnings consists of the amount kept in her private account, plus the total public

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contribution of all players in the group she has been assigned to multiplied by the MPCR m. Given the other players’ contributions s1 ; . . . ; si1 ; siþ1 ; . . . ; sn si , let U i ðsi ; si Þ be player i’s expected payoff from contributing si. Let Prðkjsi ; si Þ be i’s probability of entering Group k when the contribution proﬁle is ðsi ; si Þ s, where k ¼ 1; . . . ; G; for simplicity we henceforth denote this probability by Prðkjsi Þ. Let S ki be the total contribution in group k except for player i. Therefore, player i’s expected payoff U i ðsi ; si Þ from a contribution combination s ¼ ðsi ; si Þ can be expressed as follows: U i ðsi ; si Þ ¼ ðwi si Þ þ

G X

Prðkjsi ; si Þ m Ski þ si .

(1)

k¼1

3.3.2. Formally Deﬁning the Game We can now transform this into a normal form game. The set of players is N; each player i’s strategy is her contribution si. The strategy space is the interval ½0; wi R; ﬁnally, player i’s payoff function is deﬁned by (1) for all iAN. The Nash equilibrium is deﬁned as follows: Deﬁnition 1 (Nash equilibrium). A contribution proﬁle s ¼ ðs1 ; . . . ; sn Þ is a Nash equilibrium if and only if U i ðsÞ U i s0i ; si for all s0i asi and all iAN. So far this game is a standard GBM as originally deﬁned by GVSM, where wi is the same for all players. We now increase the game’s complexity with the following two assumptions: Assumption 1 (Two different endowment levels). Each player’s endowment is either wi ¼ H or wi ¼ LoH. In what follows, we apply the following simpliﬁcation without loss of generality: we normalize L ¼ 1, and let Dw H 140 be the gap between the high endowment H and low endowment L ¼ 1. We call a player with endowment H a ‘‘High,’’ and a player with endowment 1 a ‘‘Low.’’ NH is the set of Highs. NL is the set of Lows. Their respective counts are nH jN H j and nL jN L j. It follows that N H [ N L ¼ N, or equivalently, nH þ nL ¼ n. Further, one can ﬁnd some non-negative integers A, B, hof, and ‘of, such that the counts of Highs and Lows can be expressed as: nH ¼ Af þ h and nL ¼ Bf þ ‘

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Assumption 2 (Distribution of player types whose endowments differ). The count of each type, High and Low, is more than, and not a multiple of, the group size f, that is, A 1, B 1, and A þ B ¼ G 1; h 1, ‘ 1, and h þ ‘ ¼ f. We need to deﬁne one more basic concept, which will be crucial when we identify all the game’s equilibria, namely a ‘‘class’’. 3.3.3. The Concept of ‘‘Class’’ Deﬁnition 2 (Class). Let CrDN. We call Cr a class if each player iACr contributes the same, that is, i, jACr if and only if si ¼ sj. We call a player iACr a Cr-player. Given a contribution proﬁle s, the players can be divided into RðsÞ n classes; we henceforth omit the argument s. Let C be the family of all classes, that is, C fC 1 ; . . . ; C R g. Both C and fN H ; N L g partition N, that is, [R r¼1 C r ¼ N H [ N L ¼ N. In a class C r 2 C, there are cr players; the contribution of each player in Cr is sr, that is, jC r j cr , and si ¼ sr for all i 2 C r . We index the classes such that srþ1 osr , where r þ 1 R; hence, C1 is the class consisting of the highest contributors, and CR is the class consisting of the lowest contributors. For each class Cr, we can ﬁnd non-negative integers Dr and c~r of such that the count of Cr-players can be expressed as cr jC r j ¼ Dr f þ c~r .

(2)

3.4. Formal Description of the 2-Type GBM’s Three Equilibria 3.4.1. The Equilibrium of Non-Cooperation by All is Always Present Lemma 1 (Equilibrium of non-contribution by all). si ¼ 0 for all players iAN is a Nash equilibrium. This is the only equilibrium satisfying jCj ¼ 1. Proof. Let sj ¼ 0 for all players jai. Player i obtains ðwi si Þ þ msi ¼ wi ð1 mÞsi if she contributes si. Her best response is therefore si ¼ 0. To verify that si ¼ 0 for all players i 2 N when jCj ¼ 1, let s1 40. Consider any player i 2 N. She gets ðwi s1 Þ þ mfs1 if she contributes s1, but if she deviates and contributes 0, she enters the last group G, and gets wi þ mðf 1Þs1 ¼ ðwi ms1 Þ þ mfs1 4ðwi s1 Þ þ mfs1 since mo1. Hence, si ¼ 0 for each player i 2 N in an equilibrium with only one class. &

28

ANNA GUNNTHORSDOTTIR ET AL.

The equilibrium with si ¼ 0 for all i 2 N always exists as long as the MPCR mo1. It is however not a dominant response equilibrium. Theorem 1 in Section 3.4.2 here below deﬁnes the necessary conditions for equilibria with positive contributions. Since si ¼ 0 for all i 2 N if jCj ¼ 1 by Lemma 1, in any equilibrium with positive contributions it must be that jCj 2. 3.4.2. The Two Equilibria Involving Positive Contributions This section shows that there are two equilibria involving positive contributions: (1) an FEE, and (2) an NEE: FEE: There are two classes; C1 is identical to NH, and C2 is identical to NL. All players contribute fully, that is: Classes: jCj ¼ 2, where C 1 ¼ N H and C 2 ¼ N L . ( H; if i 2 C 1 Strategies: si ¼ . 1; if i 2 C2 : NEE: There are three classes; C1 consists of Highs, C2 consists of Lows, and C3 consists of the players who are not in C1 or C2. Both C1 and C2 players contribute fully, but C3 players contribute nothing. The sum of C2 and C3 players together is greater than, and not a multiple of, group size; the count of C3 players is less than the group size, that is: 8 > < C 1 N H ; c1 4f and c~1 40 Classes: jCj ¼ 3, where C 2 N L ; c2 þ c3 4f and c~2 þ c~3 af > : C NnðC [ C Þ and c of 3 1 2 3 8 > < H; if i 2 C 1 Strategies: si ¼ 1; if i 2 C 2 > : 0; if i 2 C 3 In both equilibria with positive contributions strategies only take one of three forms: full contribution of the high endowment (H), full contribution of the low endowment (L ¼ 1), or zero contribution. Fig. 1 illustrates FEE and NEE. The dark gray sections in the horizontal bars represent Highs, the light grey sections represent Lows. The players’ strategies si are shown above the horizontal bars, the corresponding class is displayed below

29

Tacit Coordination in Contribution-based Grouping s1 = H

s2 = 1 Group (A+1)

FEE:

Group G C2

C1 s1 =

H

1

C1

s3 = 0 Group G

Group (D1+1)

NEE:

Fig. 1.

s2 =

C2

C3

The Two Equilibrium Conﬁgurations with Positive Contributions (Light Gray Sections Are Lows, Dark Gray Sections Are Highs).

the bars. The segments in the bars represent groups. For illustration purposes and without loss of generality, only four groups are shown. Theorem 1. If there is an equilibrium with positive contributions, then it is an FEE or NEE. Proof. Appendix A.

&

3.4.3. Applications of Theorem 1 In Example 1 we derive the equilibrium of the game tested experimentally in Sections 4 and 5. Example 2 shows that a speciﬁc version of the 2-Type GBM does not have an equilibrium with positive contributions. In Example 3 we apply Theorem 1 to a situation where all endowments are equal and show that the only equilibrium with positive contributions possible in such a situation is an NEE. Example 1. (Deriving the experimental NEE). Let n ¼ 12, nH ¼ nL ¼ 6, f ¼ 4, L ¼ 1 and H ¼ 1:5 (In our experimental test, L ¼ 80 tokens and H ¼ 1:5 L ¼ 120 tokens). According to Theorem 1 we only need to consider FEE and NEE. There is no FEE here since any player i 2 C 2 has an incentive to reduce her contribution. If i contributes 1, she enters the second group with probability 2/6, and the third group with probability 4/6, so the expected payoff is 0:5 ð2=6Þ 5 þ ð4=6Þ 4 ¼ 13=6, but if she contributes 0 she enters the third group with certainty and obtains 1 þ 0:5 3 ¼ 5=2413=6. Hence, if there exists an equilibrium with positive contributions, it must be an NEE. As the following table shows, the unique equilibrium with positive contributions is13 ðh1:5; 1:5; 1:5; 1:5i; h1:5; 1:5; 1; 1i; h1; 1; 0; 0iÞ

30

ANNA GUNNTHORSDOTTIR ET AL.

c1

c2

c3

NEE?

5 5 5 6 6 6

6 5 4 5 4 3

1 2 3 1 2 3

No No No No Yes No

Deviator i 2 C2 N L i 2 C3 \ N H i 2 C3 \ N H i 2 C2 N L + i 2 C3 \ N L

Deviation ðsi ! s0i Þ 1!0 0!1þ 0!1þ 1!0 0!1

Example 2 (No equilibrium with positive contributions exists). In a game with parameters as in Example 1, now let nH ¼ 7 instead of previously 6. It can be veriﬁed that there is no FEE. By Theorem 1 it sufﬁces to show that there is no NEE either. There are eight cases to consider: c1

c2

c3

NEE?

5 5 6 6 6 7 7 7

5 4 5 4 3 4 3 2

2 3 1 2 3 1 2 3

No No No No No No No No

Deviator i 2 C3 \ N H i 2 C3 \ N H i 2 C2 N L i 2 C3 \ N H i 2 C3 \ N H i 2 C2 N L i 2 C1 ¼ N H i 2 C1 ¼ N H

Deviation ðsi ! s0i Þ 0!1þ 0!1þ 1!0 0!1þ 0!1þ 1!0 H !1þ H !1þ

Example 3 (If endowments are all equal, the only equilibrium with positive contributions possible is an NEE). This example relies on some results in Appendix A. The general method developed so far can be used to reprove GVSM’s Observation 2. GVSM’s parameter z corresponds to cR ¼ jC R j, the number of players in the last class. If H ¼ L ¼ 1 and if there exists an equilibrium with positive contributions, it can be characterized as follows: jCj ¼ 2;

s1 ¼ 1;

s2 ¼ 0;

and

c2 of

Proof. By Lemma A1(a) (in Appendix A), in any equilibrium with positive contributions c1 40, c~1 4f; and s1 ¼ 1. Now consider the last class CR: 1. If cR 4f and c~R 40; in equilibrium, then sR ¼ 1 by Claim 1 (Appendix A). However, this means that jCj ¼ 1 and c~1 40; a contradiction to Lemma A1(a).

31

Tacit Coordination in Contribution-based Grouping

2. Assume c~R ¼ 0; in equilibrium. Then s2 ¼ 0 by Lemma A1(e). By the same logic as in Lemma A1(c), there cannot exist a class Cr satisfying 0osr o1; hence, jCj ¼ 2. According to Lemma A1(a) c~1 40. If c~2 were zero, it would contradict our initial assumption in Section 3.3.1 that the total number of players n ¼ G f. 3. Thus, it must be that cR of. It follows that sR ¼ 0 by Lemma A1(e). An argument analogous to Lemma A1(c) shows that jCj ¼ 2. & 3.5. Existence of a Fully Efﬁcient Equilibrium (FEE) An FEE exists if and only if Player i 2 C 2 has no incentive to reduce her contribution from 1 to 0 and Player i 2 C 1 has no incentive to reduce her contribution from H to 1 þ , 1, or 0, where e is a small positive real number. We ﬁrst consider C2, then C1. We use U wsi i ðC r Þ to denote player i’s expected payoff when her endowment is wi 2 fH; 1g, she contributes si 2 ½0; wi , and is in class Cr. We develop our analysis with the help of Fig. 2. 1m Theorem 2. Let M . An FEE exists if and only if m ½ðf 1ÞDw MH nH ð‘ M Þ nH M nL

h min ; (3) Dw ‘ Dw ‘ ‘

In the remainder of this section, we account for Theorem 2 by examining players’ incentives to deviate.

c1 = nH = A + h

c2 = nL = B + l h

l

Group G

Group (A+1)

s1 = H

Fig. 2.

s2 = 1

The Distribution of Players in an FEE.

32

ANNA GUNNTHORSDOTTIR ET AL.

3.5.1. Incentives to Deviate for C2 Players in an FEE Fix the contribution proﬁle si ðs1 ; . . . ; si1 ; siþ1 ; . . . ; sn Þ satisfying sj ¼ wj for all j 2 Nnfig. For any player i 2 C2 ¼ N L , if she contributes 1, she enters the following groups with positive probabilities: A þ 1; A þ 2; . . . ; G (see Fig. 2). The probabilities are: ( ‘=nL ; if k ¼ A þ 1 Prðkj1Þ ¼ f=nL ; if k ¼ A þ 2; . . . ; G PG PG Since k¼Aþ1 Prðkj1Þ ¼ 1, we have k¼Aþ2 Prðkj1Þ ¼ 1 PrðA þ 1j1Þ ¼ 1 ð‘=nL Þ. For ease of expression, let S Aþ1 hH þ ‘ that is, S Aþ1 is the sum of contributions in Group (A þ 1) from the full contribution proﬁle s ¼ ðsi ¼ 1; si Þ. By Eq. (1), player i’s expected payoff from contributing si ¼ 1 is ( ) G X L Aþ1 ½Prðkj1Þ f U 1 ðC 2 Þ ¼ ðwi si Þ þ PrðA þ 1j1Þ S þ k¼Aþ2

(

"

¼ ð1 1Þ þ m PrðA þ 1j1Þ S Aþ1 þ

‘ Aþ1 ‘ f S þ 1 nL nL h‘Dw h1i ¼m fþ nL

G X

#

)

Prðkj1Þ f

k¼Aþ2

¼m

where equality h1i holds since SAþ1 f ¼ ðhH þ ‘Þ ðh þ ‘Þ ¼ hðH 1Þ ¼ hDw. If player i 2 C 2 deviates and contributes si o1, she enters group G, and her payoff is ð1 si Þ þ m½ðf 1Þ þ si ¼ 1 þ mðf 1Þ ð1 mÞsi hence, her optimal deviation is si ¼ 0 since 1 m40 with payoff is U L0 ðC 2 Þ ¼ 1 þ mðf 1Þ. It follows that player i 2 C 2 has no incentive to reduce her contribution from 1 to 0 if and only if U L1 ðC2 Þ U L0 ðC 2 Þ, that is, h

ð1 mÞnL M nL m‘ Dw ‘ Dw

(4)

33

Tacit Coordination in Contribution-based Grouping

where M ð1 mÞ=m. M 2 ð0; f 1Þ.

Because

m 2 1=f; 1 ,

we

know

that

3.5.2. Incentives to Deviate for C1 Players in a FEE Since we now consider a player i 2 C1 ¼ N H , we rewrite the full contribution proﬁle as s ¼ ðsi ¼ H; si Þ, where sj ¼ wj for any j 2 Nnfig. If player i 2 C 1 contributes si ¼ H, she enters Group 1; 2; . . . ; A; A þ 1 with positive probabilities which are ( PrðkjH Þ ¼

f=nH ;

if k ¼ 1; . . . ; A

h=nH ;

if k ¼ A þ 1

Hence, i’s expected payoff from contributing si ¼ H is (" UH H ðC 1 Þ ¼ ðH H Þ þ m

A X

#

)

PrðkjH Þ fH þ PrðA þ 1jH Þ S Aþ1

k¼1

h h Aþ1 fH þ ¼m 1 S nH nH h‘Dw h2i ¼ m fH nH h1i

P where h1i holds because A k¼1 PrðkjH Þ ¼ 1 PrðA þ 1jH Þ ¼ 1 h=nH , and h2i holds because fH S Aþ1 ¼ fH ðhH þ ‘Þ ¼ ‘H ‘ ¼ ‘Dw. If player i 2 C1 contributes si 2 ð1; HÞ, she enters group (A þ 1) with certainty and obtains UH si ðC 1 Þ ¼ ðH si Þ þ m½ðh 1ÞH þ ‘ þ si ¼ H þ m½ðh 1ÞH þ ‘ ð1 mÞsi

(5)

From Eq. (5) we know that the optimal deviation is si ¼ ð1 þ Þ ! 1 if player i 2 C 1 wants to contribute si 2 ð1; H Þ. Thus,

lim U H 1þ ðC 1 Þ ¼ lim H þ m½ðh 1ÞH þ ‘ ð1 mÞð1 þ Þ !0 !0 ¼ H þ m S Aþ1 H ð1 mÞ ¼ mS Aþ1 þ ð1 mÞDw

34

ANNA GUNNTHORSDOTTIR ET AL.

Hence, player i 2 C1 has no incentive to reduce her contribution from H to H 1 þ if and only if U H H ðC 1 Þ lim#0 U 1þ ðC 1 Þ, that is M (6) h nH 1 ‘ Note that Eq. (6) is independent of H or Dw: it is fully determined by the distribution of player types and the MPCR m. Lemma 2 indicates that we do not need to consider whether i 2 C 1 has an incentive to contribute 1 if she has no incentive to contribute 1 þ . Lemma 2. If a player i 2 C 1 has no incentive to reduce her contribution from H to 1 þ , she also has no incentive to reduce her contribution from H to 1. Proof. If player i 2 C1 contributes 1, she enters Groups A þ 1; A þ 2; . . . ; G with positive probabilities. Therefore, her expected payoff from contributing 1 is ( ) G X H ½Prðkj1Þ f U 1 ðC1 Þ ¼ ðH 1Þ þ m PrðA þ 1j1Þ ½ðh 1ÞH þ ‘ þ 1 þ (

"

¼ Dw þ m PrðA þ 1j1Þ S Aþ1 Dw þ

k¼Aþ2 G X

#

)

Prðkj1Þ f

k¼Aþ2

Dw þ m PrðA þ 1j1Þ SAþ1 Dw þ½1 PrðA þ 1j1Þ S Aþ1 Dw

h1i

¼ mS Aþ1 þ ð1 mÞDw ¼ lim U H 1þ ðC 1 Þ !0

where /1S holds because SAþ1 Dw ¼ ðhH þ ‘Þ ðH 1Þ ¼ ½hHþ H ðf hÞ H þ 1 ðH þ f 1Þ H þ 1 ¼ f. Therefore U H H ðC 1 Þ U 1 ðC 1 Þ H H & when U H ðC 1 Þ lim!0 U 1þ ðC 1 Þ: Finally, if player i 2 C1 wants to contribute si o1, she should contribute si ¼ 0, so that her payoff is U H 0 ðC 1 Þ ¼ H þ mðf 1Þ. Hence, she has no H incentive to contribute 0 if and only if U H H ðC 1 Þ U 0 ðC 1 Þ, that is, h

½ðf 1ÞDw MH nH Dw ‘

Combining Eqs. (4), (6), and (7), one obtains Theorem 2.

(7)

Tacit Coordination in Contribution-based Grouping

35

3.5.3. Comparative Statics of the FEE and Two Examples Remark 1. It can be seen from Eq. (3) that when m is large enough, the FEE is an equilibrium for all possible parameters of the game. To illustrate, consider the extreme case. Let m ! 1, then limm!1 M ¼ limm!1 ð1 m=mÞ ¼ 0. Then the left-hand side (LHS) of Eq. (3) approaches 0, the right-hand side (RHS) of Eq. (3) becomes ðf 1ÞnH ; n H ¼ nH min ‘ and 0 h nH always holds. This result is intuitive: m ! 1 means that if a player puts one dollar into the public account, her strategic risk becomes increasingly negligible. Remark 2. In an FEE, the gap between Highs and Lows, Dw, cannot be very small. This result might strike the reader as counterintuitive since it implies that equality (in wi) prevents a fully efﬁcient solution. Consider once again the extreme case. Fix all other parameters and let Dw ! 0; then lim

Dw!0

M nL ¼ þ14h Dw ‘

so that Eq. (3) is violated. This result corresponds to GVSM (2009): when all players have the same endowment, it is not an equilibrium that all contribute fully. Remark 3. Although a large enough Dw is a necessary condition for the existence of an FEE, it is not sufﬁcient. To see this, let H ! þ1, so that Dw ! þ1, too; then Eq. (3) becomes ðf 1 M ÞnH ð‘ M ÞnH ð‘ M ÞnH ; ¼ (8) 0 h min ‘ ‘ ‘ We can see that there exist ‘ and M such that Eq. (8) fails. In particular, if M ! ðf 1Þ or equivalently, m ! 1=f, then there is clearly no FEE no matter how high H is and no matter what the distribution of types is, since ‘ ðf 1Þ. Example 4 (Numerical application of Theorem 2). Let m ¼ 0:5 ðso M ð1 mÞ=ðmÞ ¼ 1Þ, f ¼ 4, n ¼ 24, H ¼ 3. We refer to Fig. 3. Each point nH on the horizontal axis determines a particular ‘ according

36

ANNA GUNNTHORSDOTTIR ET AL. 12

2

10

(3)-RHS

8

6

4 h

2

2 (3)-LHS

6

8

10

12

Fig. 3.

14

16

18

20

nH

FEE.

to the equation nL ¼ n nH ¼ Bf þ ‘, and such an ‘ determines: (a) the h by the equation h ¼ f ‘ (the black dashed lines), (b) the Eq. (3)-LHS (the solid black curves), and (c) the (3)-RHS (the grey lines). Thus, if there is an h determined by a nH that lies between a solid black curve and a grey line, then there exists an FEE according to Theorem 2. Fig. 3 indicates that there is an FEE if and only if nH ¼ 18. Note that nH ¼ 4A þ h yields h ¼ ‘ ¼ 2 (the point in the ﬁgure where a black dashed line and a grey dashed line intersect). Furthermore, nL ¼ n nH ¼ 6, Eq. (3)LHS ¼ 1.5 and

ð3 2 3Þ 18 ð2 1Þ 18 Eq: ð3Þ RHS ¼ min ; ¼9 22 2 thus, 1:5oh ¼ 2o9, that is, Eq. (3) holds. We now show that this is indeed an equilibrium. In equilibrium i 2 C 2 gets 0:5ðð2=6Þ8þð4=6Þ4Þ ¼ 2:7. If she contributes 0, she gets 1 þ 0:53 ¼ 2:5o2:7. Hence, i 2 C 2 has no incentive to deviate. In equilibrium, i 2 C1 gets 0:5 ðð16=18Þ 12 þ ð2=18Þ 8Þ ¼ 5:8; If she contributes 1 þ , she gets no more than 0:5 8 þ ð1 0:5Þ 2 ¼ 5, which is less than 5.8; ﬁnally, if she contributes 0, she gets 3 þ 0:5 3 ¼ 4:5o5:8. Hence, i 2 C1 also has no incentive to deviate.

Tacit Coordination in Contribution-based Grouping

37

Example 5 (Finding the experimental FEE). In a game with parameters as in Example 1, now let H be unspeciﬁed. We want to ﬁnd an H such that there exists an FEE. According to Eq. (3), H has to satisfy h ¼ 2 ð6=2ðH 1ÞÞ, which solves for H 2:5. Because Eq. (3)-RHS holds when H 2:5, this concludes the calculation. In light of this, in our experimental setup where Lows have an endowment of 80 tokens each and Highs have 120 tokens each, the endowment of the Highs would need to be raised from 120 tokens to at least 200 tokens for an FEE rather than an NEE to emerge. 3.6. Existence of a Near-Efﬁcient Equilibrium (NEE) The NEE exists if and only if player i 2 C 3 \ N L has no incentive to increase her contribution from 0 to 1, player i 2 C 3 \ N H has no incentive to increase her contribution from 0 to 1 þ or H, player i 2 C2 \ N L has no incentive to reduce her contribution from 1 to 0, Player i 2 C1 \ N H has no incentive to reduce her contribution from H to 1 þ or 0. Since Example 1 in Section 3.4.3 already showed an NEE is possible, there is no real existence problem. However, we now provide a general overview of the conditions under which it exists. L Let cH 3 be the count of Highs in C3, and let c3 be the count of Lows in C3. L H þ c of and c ah, otherwise c~1 ¼ 0, which contradicts Then c3 ¼ cH 3 3 3 Lemma A1(a). We have c 1 ¼ nH c H 3 8 < Af þ h cH if cH 3 3 oh ¼ : ðA 1Þf þ h þ f cH if cH 3 3 4h

ð9Þ

and c2 ¼ nL cL3 8 < Bf þ ‘ cL3 if cL3 ‘ ¼ : ðB 1Þf þ ‘ þ n cL3 if cL3 4‘

ð10Þ

L It is obviously impossible that cH 3 4h and c3 4‘ hold simultaneously since h þ ‘ ¼ f. It can also be seen from Eqs. (9) and (10) that there are three

38

ANNA GUNNTHORSDOTTIR ET AL. c2 = nL − cL3

c1 = nH − c3H h − cH 3

l + cH 3

c3 − c3

cH 3

cL3

Group (A +1)

s1 = H

s2 = 1

Fig. 4.

s3 = 0

The Distribution of Players in an NEE.

L H L situations to consider: (1) cH 3 oh and c3 ‘, (2) c3 oh and c3 4‘, and H L (3) c3 4h and c3 ‘. In this chapter we analyze only category (1), which is the simplest case.

cH 3 oh;

cL3 o‘;

L and cH 3 þ c3 of

The other cases can be analyzed in the same manner. We develop our analysis with the help of Fig. 4, which illustrates the distribution of players in an NEE. 3.6.1. Incentives to Deviate for C3 Players in an NEE First, for player i 2 C3 \ N L , her payoff from contributing 0 is U L0 ðC3 Þ ¼ 1 þ mðf c3 Þ.

(11)

If she contributes 1, then there are c2 þ 1 players contributing 1 and player i enters Group A þ 1; . . . ; G with positive probabilities, which are 8 H =ðc2 þ 1Þ; if k ¼ A þ 1 ‘ þ c > 3 < if k ¼ A þ 2; . . . ; G 1 Prðkj1Þ ¼ f=ðc2 þ 1Þ; > : ðf c þ 1Þ=ðc þ 1Þ; if k ¼ G 3 2 H Let S h cH 3 H þ ‘ þ c3 . Thus, player i’s expected payoff from contributing 1 is ( " # ) G1 X Prðkj1Þ f þ PrðGj1Þ ðf c3 þ 1Þ U L1 ðC 3 Þ ¼ m PrðA þ 1j1Þ S þ k¼Aþ2

m 2 ¼ ‘ þ cH 3 S þ ðnL f ‘ Þf þ ðf c3 þ 1Þ c2 þ 1

h1 i

ð12Þ

39

Tacit Coordination in Contribution-based Grouping

where h1i holds because

c2 þ cL3 f ‘ nL f ‘ ‘ þ cH f c3 þ 1 3 ¼ ¼ Prðkj1Þ ¼ 1 c2 þ 1 c2 þ 1 c2 þ 1 c2 þ 1 k¼Aþ1 G1 P

Hence, player i 2 C 3 \ N L has no incentive to deviate from contributing 0 to contributing 1 if and only if U L0 ðC3 Þ U L1 ðC 3 Þ. Second, for i 2 C 3 \ N H , her payoff from contributing si ¼ H is UH 0 ðC 3 Þ ¼ H þ mðf c3 Þ.

(13)

If player i contributes 1 þ , she enters group (Aþ1) and obtains H H lim U H 1þ ðC 3 Þ ¼ lim ðH 1 Þ þ m h c3 H þ ‘ þ c3 1 þ ð1 þ Þ

!0

!0

¼ Dw þ mS

ð14Þ

If player i contributes H, then there are c1 þ 1 players contributing H; player i enters Group 1; . . . ; A þ 1 with positive probabilities, which are 8 ðc1 þ 1Þ; > < f= h cH PrðkjH Þ ¼ 3 þ1 > : ðc þ 1Þ ; 1

if k ¼ 1; . . . ; A if k ¼ A þ 1

Thus, player i’s expected payoff is UH H ðC 3 Þ ¼ m

( A X

½PrðkjH ÞfH þ PrðA þ 1jH Þ

h cH 3 þ1

Hþ

‘ þ cH 3 1

)

k¼1

h cH h cH 3 þ1 3 þ1 ¼m 1 fH þ ðS þ DwÞ c1 þ 1 c1 þ 1 m ðnH hÞfH þ h cH ð15Þ ¼ 3 þ 1 ðS þ DwÞ c1 þ 1 Hence, player i 2 C 3 has no incentive to deviate if and only if the following conditions are satisﬁed: 8 > < Eq: ð11Þ Eq: ð12Þ : i 2 C3 \ N L has no incentive to deviate from 0 to 1 Eq: ð13Þ Eq: ð14Þ : i 2 C3 \ N H has no incentive to deviate from 0 to 1 þ > : Eq: ð13Þ Eq: ð15Þ : i 2 C \ N has no incentive to deviate from 0 to H 3 H (16)

40

ANNA GUNNTHORSDOTTIR ET AL.

3.6.2. Incentives to Deviate for C2 Players in an NEE Recall that C2 consists of Lows. If i 2 C 2 N L contributes 1, she gets m 2 H ‘ þ cH (17) U L1 ðC2 Þ ¼ 3 S þ c2 ‘ c 3 f þ c 3 f þ ð f c 3 Þ c2 if she contributes 0, she gets U L0 ðC2 Þ ¼ 1 þ mðf c3 1Þ

(18)

Thus, i 2 C 2 \ N L has no incentive to deviate if and only if Eq: ð17Þ Eq: ð18Þ :

i 2 C 2 N L has no incentive to deviate from 1 to 0 (19)

3.6.3. Incentives to Deviate for C1 Players in an NEE C1 consists of Highs. For i 2 C1 N H , if she contributes H, her expected payoff is

h cH h cH 3 3 fH þ ð C Þ ¼ m 1 S (20) UH 1 H c1 c1 If she contributes 1 þ , she obtains H H lim U H 1þ ðC 1 Þ ¼ lim ðH 1 Þ þ m h c3 1 H þ ‘ þ c3 þ ð1 þ Þ

!0

!0

¼ mS þ ð1 mÞDw

ð21Þ

A similar argument as in Lemma 2 shows that we need not consider whether i 2 C 1 \ N H has any incentive to contribute 1 if she has no incentive to contribute 1 þ . We can therefore immediately consider the last possible deviation. If player i contributes 0, she obtains UH 0 ð C 1 Þ ¼ H þ m ð f c3 1 Þ

(22)

Thus, i 2 C 1 N H has no incentive to deviate if and only if ( Eq: ð20Þ Eq: ð21Þ : i 2 C 1 N H has no incentive to deviate from H to 1 þ Eq: ð20Þ Eq: ð22Þ : i 2 C 1 N H has no incentive to deviate from H to 0: (23) Theorem 3 summarizes this section’s ﬁndings. Theorem 3. The NEE exists if and only if Eqs. (16), (19), and (23) are all satisﬁed.

Tacit Coordination in Contribution-based Grouping

41

3.7. Coexistence of NEE and FEE? So far we know that in a 2-Type GBM an equilibrium with positive contributions is either an FEE or an NEE. Can these two equilibria with positive contributions ever coexist? We now show with an example that this is possible. Our analysis focuses on the speciﬁc version of the game tested experimentally in Sections 4 and 5. Example 1 (Section 3.4.3) has already demonstrated that this game has a NEE. Example 5 (Section 3.5.3) has shown that this game has an FEE if and only if H 2:5. We now show that if H ¼ 2:5 there exists in addition to the FEE the following NEE: ðhH; H; H; H i; hH; H; 1; 1i; h1; 1; 1; 0iÞ For player i 2 C 3 N L , the equilibrium payoff is U L0 ðC 3 Þ ¼ 1 þ 3=2 ¼ 5=2; if she contributes 1, the expected payoff is U L1 ðC 3 Þ ¼ ð1=2Þ ðð2=6ÞS þ ð4=6Þ 4Þ ¼ ð5=2Þ ¼ U L0 ðC 3 Þ. For player i 2 C 2 N L , the equilibrium payoff is U L1 ðC 2 Þ ¼ ð1=2Þ ðð2=5Þ 7 þ ð3=5Þ 3Þ ¼ 2:3; if she contributes 0, the payoff is U L0 ðC 2 Þ ¼ 1 þ ð1=2Þ 2 ¼ 2oU L1 ðC 2 Þ. Finally, for player i 2 C 1 ¼ N H , she gets U H H ðC 1 Þ ¼ ð1=2Þ ðð4=6Þ 4H þ ð2=6ÞSÞ ¼ 4:5 in equilibrium; if she contributes 1 þ , the payoff is H lim!0 U H 1þ ðC 1 Þ ¼ S=2 þ ðH 1Þ=2 ¼ 4:25oU H ðC 1 Þ; if she contributes H H 0, the payoff is U 0 ðC1 Þ ¼ H þ 2=2 ¼ 3:5oU H ðC 1 Þ. Note however that the unique equilibrium with positive contributions is the FEE if H42:5. Since it is required that c1 44 and c~1 40 in any equilibrium H with positive contributions, cH 3 can only take two possible values: either c3 ¼ H H 1 or c3 ¼ 0. However, c3 ¼ 1 is impossible. This is because if a High has no incentive to contribute 0 in the FEE, she also has no incentive to contribute 0 when there is at least one Low in Group G contributing 0. Hence, we only need to consider the case of cH 3 ¼ 0. By Eq. (11), 4 c 3 6 c3 ¼ 2 2

(24)

4H þ 4 þ ð5 c3 Þ2 14 2c3

(25)

U L0 ðC 3 Þ ¼ 1 þ By Eq. (12), U L1 ðC 3 Þ ¼

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ANNA GUNNTHORSDOTTIR ET AL.

where c3 ¼ 1; 2; 3. Then ð110 Þ ð100 Þ ¼

3c3 þ 4H 13 14 2c3 3ðc3 1Þ 4 14 2c3 40

for any c3 ¼ 1; 2; 3. This means that U L0 ðC 3 ÞoU L1 ðC 3 Þ, that is, any C3 player would like to increase her contribution no matter how many players contribute 0 in Group G. We thus proved that no player contributes 0 if H42:5, and the FEE is the unique equilibrium with positive contributions in this situation.

4. METHOD 4.1. Experimental Game Parameters and Experimental NEE The 2-Type GBM was examined under MPCR m ¼ 0:5. The number of participants per session was 12, group size was four. Six participants were randomly selected as Lows and received L ¼ 80 tokens per round, while the six Highs received H ¼ 120 tokens. Once assigned, a subject’s type did not change over the experiment’s 80 rounds. Most parameters here are the same as in GVSM including the mean endowment over 12 subjects. The only difference is that in GVSM’s study the endowments are uniform. These experimental parameters conﬁguration does not allow a FEE since Ho2.5L (by Theorem 2; see also Example 5, both in Section 3.5). However, there exists the following NEE: f120; 120; 120; 120; 120; 120; 80; 80; 80; 80; 0; 0g. It is calculated in Example 1 (Section 3.4.3). As usual in a GBM, there also exists a risk-dominant equilibrium of non-contribution by all (by Lemma 1, Section 3.4.1).

4.2. Design and Participants Participants were undergraduates at City University of New York, recruited from the general student population for a two-hour experiment with payoffs contingent on the decisions they and other participants made during the experiment. Subjects were seated in front of computer terminals separated

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by blinders. There were four experimental sessions with 12 participants each, 48 subjects in total. Each session lasted two hours. The show-up fee was $10. The exchange rate was 700 tokens for a dollar or conversely, 0.143 cents per token. In addition to the show-up fee, mean earnings of Highs were $25; mean earnings of Lows were $16.

4.3. Procedure 4.3.1. Investment Decision At the beginning of each round, each subject received the type-appropriate amount of integer tokens to be divided between a public account and a private account. For every token invested in the private account, the account returned one token to the investor alone. For every token invested in the public account, the return was 0.5 tokens to everyone in the investor’s group including herself. Appendix B contains the experimental instructions. 4.3.2. Group Assignment In each round, after all subjects had made their investment decisions, they were partitioned in three groups of four. The four highest public account investors were placed together in one group, the ﬁfth through the eighth highest investor into a second group, and the four lowest investors into a third group. Ties were broken at random. After grouping, subjects’ earnings were calculated based on the group to which they had been assigned. Note that group assignment depended only on the subjects’ current contributions in that round, not on contributions in previous rounds. Subjects were regrouped according to these criteria in each decision round (see Appendix B). 4.3.3. End-of-Round Feedback After each round, each subject’s computer screen displayed her private and public investment in that round, the total investment made by the group she had been assigned to, and her total earnings. The screen also displayed an ordered series of the current round’s group account contributions by all 12 participants, with a subject’s own contribution highlighted so that she could see her relative standing. This ordered series was visually split into three groups of four, which further underscored that the participants in the experiment had been grouped according to their contributions and that ties had been broken at random.

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5. RESULTS AND DISCUSSION The main purpose of this analysis is to establish whether the 2-Type GBM is an effective mechanism when abilities to contribute differ, and whether GVSM’s results about the precise coordination of the payoff dominant equilibrium are robust to such inequality. 5.1. Result 1 Observed mean contributions correspond to the NEE mean contribution. The broken lines in Fig. 5 represent the NEE mean contribution per round (86.67 tokens). The solid lines are the observed mean contributions. Mean contributions over all four sessions (solid lines) closely trace their predicted 120 Contribution

100 80 60 40 Mean (s = 83.02)

20 0 20

40 Round

120

120

100

100

80

80

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40 20

20 0

20

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Session 2 (s = 88.57) 20

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40 Session 3 (s = 88.57)

20

0

Session 4 (s = 88.57)

0 20

Fig. 5.

80

40 Session 1 (s = 88.57)

0

20

60

40

60

80

20

40

60

80

Mean Contributions Per Round over Four Sessions and for Each Session.

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value, and trace it particularly closely after Round 20. This pattern also emerges in the single sessions shown in the lower part of Fig. 5. 5.1.1. Adjustment in Initial Rounds There is some adjustment in the initial rounds. In GVSM’s experiments with homogeneous endowments, subjects coordinated the payoff-dominant Nash equilibrium as well, but did so more quickly: GVSM’s subjects reached NEE means by Round 2. Here however, a comparable level of consistent precision is only achieved after Round 20, even though sporadic mean precision is seen as early as Round 6. Since GVSM’s experiments and the present experiment were run at different universities, it is not possible to attribute the slower convergence here to the fact that the NEE of the 2-Type GBM has a more complex structure (three strategies) than the NEE in GVSM’s homogeneousendowment game (two strategies).

5.2. Result 2 Strategies that are part of the NEE are predominantly selected, and selected with precision; there is slightly more precision after about Round 20. The experiment’s NEE consists of the two corner strategies from among a set of 81 choices f0; 1; . . . ; 80g for Lows, and only one of 121 available choices f0; 1; . . . ; 120g for Highs. Fig. 6 shows the strategy space on the horizontal axis and the observed percentages of choices over four sessions on the vertical axis. Solid squares show the NEE proportions. The top graph shows choice frequencies for Rounds 1–80. The middle graph shows the same for Rounds 21–80 only, and once again highlights that the equilibrium strategies are executed with more precision after Round 20. We include a comparable graph from GVSM as the bottom graph of Fig. 6. A comparison of the top two graphs with the bottom graph shows that in both series of experiments the NEE strategy proportions were coordinated quite precisely. 5.2.1. Coding the Data In Fig. 6 and in all subsequent analysis, we classiﬁed choices Z77 as 80, choices Z117 as 120, and choices r3 as zero contribution. We recode the raw data this way since GVSM did the same, so that the two studies can be properly compared. Note however that GVSM report that this minor recoding, while grounded in behavioral theory about prominence Selten (1997) and neighboring strategies Erev and Roth (1998), barely changed their results. The same applies to our data. Table 1 displays the raw frequencies of

%

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50 40 30 20 10 0

%

0

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40

60

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Choice proportions Rounds 21–80, four sessions

50 40 30 20 10 0 0

20

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GVSM choice proportions Rounds 1-80

80

%

60 40 20 0 0

20

40

60

80

100

Fig. 6. Observed Proportion of Choices in the Current Study (Top Two Graphs) and in GVSM’s Experiment (Strategy Space on the Horizontal Axis; NEE Choice Proportions as Red Blocks).

the exact NEE strategies and of their neighboring strategies, separately for Rounds 1-80, Rounds 21-80, and Rounds 1–21. The precision with which the NEE was realized becomes once again clear, as well as the increased precision after Round 20. What is this increased precision in later rounds due to? For this purpose, we next examine choice strategies by type (High or Low).

5.3. Result 3 The aggregate frequencies with which equilibrium strategies were selected by the two different types are close to the NEE. In the experimental game’s NEE, all Highs contribute fully; four of six Lows also contribute fully while the other two Lows contribute nothing.

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Table 1. Strategy

Raw Frequencies of NEE Strategies and Their Neighboring Strategies. Raw %

Strategy

Raw %

(A): Raw frequencies of choices before recoding (Rounds 1–80) 0 8.0 80 32.8 1 1.2 79 0.5 2 0.2 78 0.2 3 0 77 0.0 Totals

9.6

10.5

6.9

120 119 118 117

31.3 0.9 0.5 0.1 32.8

120 119 118 117

34.7

(C): Raw frequencies of choices before recoding (Rounds 1–21) 0 5.9 80 28.8 1 0.7 79 0.8 2 0.1 78 0.3 3 0.1 77 0.2 Totals

Raw %

33.6

(B): Raw frequencies before recoding (Rounds 21–80) 0 8.8 80 34.1 1 1.5 79 0.4 2 0.2 78 0.1 3 0 77 0 Totals

Strategy

30.1

38.4 0.8 0.4 0.2 39.9

120 119 118 117

10.0 0.9 0.3 0.1 11.6

Thus, Lows have a choice between two strategies but Highs must play one speciﬁc strategy. Fig. 7 displays, separately for Highs and Lows, the frequency with which equilibrium strategies were chosen in each round over four sessions. Broken lines show the frequencies of a given strategy as predicted by the NEE over four sessions of 12 subjects each. For example, for Highs the NEE-based prediction is 4 6 ¼ 24 observations of full contribution per round. It can be seen that the number of fully contributing Lows is quite close to the NEE prediction by Round 20. Many Highs, on the other hand, only gradually appear to discover that, since the game is converging to the NEE rather than the alternative equilibrium of non-contribution by all, their optimal strategy is full contribution. Appendix C displays the individual choice path of each subject over 80 rounds. Column headings on top of each page indicate the session. Numbers on the LHS alongside each page identify the subject. Within each

observed frequency

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ANNA GUNNTHORSDOTTIR ET AL. 30 25 20 15 10 5

Choice frequencies: Full contributions by Highs (4 Sessions)

observed frequency

20 30

60

80

Choice frequencies: Full contributions by Lows (4 Sessions)

25 20 15 10 20

observed frequency

40 Round

30

40 Round

60

80

Choice frequencies: Zero contributions by Lows (4 Sessions)

20 10 0 20

Fig. 7.

40 Round

60

80

Frequencies of Full Contributions by Highs, Full Contributions by Lows, and Zero Contributions by Lows, over Four Sessions.

session, Subjects 1-6 are Highs, Subjects 7-12 are Lows. We henceforth refer to subjects by these two numbers, so that for example Subject 4-3 is Subject 4 (a High) in Session 3. The straight horizontal line in each chart shows the endowment; in each graph, the lower line represents the subject’s group contribution; the upper line tracks the associated earnings. A glance over all graphs shows support for the NEE. The contribution paths of Highs, who in the NEE must contribute fully, are ﬂat in particular in later rounds, and often on or close to the straight endowment line. Lows often oscillate between their two NEE strategies of full contribution and non-contribution.14 Appendix C again underscores that a noticeable proportion of Highs experimented in early rounds before settling on their sole optimal strategy. Notice the slow learning of Highs 1-1, 2-3, 4-1, 4-3 and particularly 2-6, and the consistent

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‘‘confusion’’ (Andreoni, 1995) of Highs 2-4, 2-6, 3-6 and particularly 3-2. Among Lows, 4-9 is a slow learner. Notice consistently confused Lows 3-12 and 4-12. Finally, the charts show that no Low is a permanent noncontributor. GVSM similarly found no steady free-riders in their study where the proportion of non-contributors in the NEE is the same as here.

5.4. Result 4 Deviations from the NEE strategies are penalized by lowered earnings. NEE earnings are 227 tokens for Highs, 140 tokens for contributing Lows, and 160 tokens for non-contributing Lows. A subject’s mean earnings over 80 rounds are written on the right edge of her Appendix C chart, either in the upper or lower corner. Overall, individual mean earnings over 80 rounds are close to NEE earnings. The mean earnings of subjects who do not select their NEE corner strategies are lower than the earnings of subjects who do. A similar pattern can be detected by examining the top lines in the Appendix C charts, which show a subject’s earnings per round. See for example confused High 3-2 who consistently does not quite contribute fully and whose mean earnings over 80 rounds are only 197 tokens; see also the lowered mean earnings of Highs 2-4 and 2-6. The reason for their lowered mean earning is that, as long as most other players choose NEE strategies, Highs who contribute W80 and o120 can never enter the High-only top group, and are instead put into the mixed middle group consisting of Highs and Lows, where Lows can free-ride off them. Lows who consistently select strategies from the interior of their strategy space such as Lows 3-12 and 4-12, also make less than they would earn with NEE strategies. Since the NEE is quite consistently played by most participants, Lows who contribute between 0 and 80 are usually placed in the lowest group with certainty, get no chance to free-ride off Highs in the middle group, and get free-ridden by the zero-contributors in the bottom group.

6. CONCLUSION Unequal abilities to contribute are an important feature of real-world societies. We use a formal mechanism to examine the impact of endogenous group formation in the context of mechanism design and rational choice and study the impact of unequal ability to contribute on contribution behavior and efﬁciency. In our game, some players (‘‘Lows’’) are naturally

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disadvantaged due to low endowments. They can never aspire to membership in the most productive and rewarding teams, nor can their earnings ever match those of players with high endowments (‘‘Highs’’). Our theoretical and experimental results show that despite of this, competitive contributionbased grouping is an effective and precise tool to raise social contributions by the advantaged and disadvantaged alike. Not only do our behavioral results indicate that unequal abilities to contribute are not deleterious to efﬁciency, but also our theoretical analysis suggests that when the difference between the high and low endowments increases, efﬁciency can increase until full Pareto optimality is achieved. 6.1. The Predictive Power of the Nash Equilibrium The strategy sets of our experimental subjects are quite large. The payoffdominant ‘‘near-efﬁcient’’ equilibrium (NEE) is asymmetric, and consists of three different strategies. Discovering the NEE analytically is a lengthy process (as reﬂected in the length of Section 3 and Appendix A) consisting of the step-by-step elimination of conﬁgurations involving positive contributions. It is therefore unlikely that subjects can understand or compute the NEE. Yet aggregates of subjects reliably and tacitly coordinate the NEE, seemingly ‘‘magically’’ (Kahneman, 1988, p. 12). It further underscores the predictive power of the Nash equilibrium that (1) aggregate behavior conforms to the NEE even though many Lows, who, in an NEE have a choice between two different corner strategies, oscillate erratically between their strategies over rounds, and (2) the version of the 2-Type GBM experimentally tested here does not lead to full efﬁciency (the latter is not an equilibrium). In their study of a simpler form of the mechanism with homogeneous endowments GVSM, using a different subject pool, also found that the NEE was coordinated with precision. The coordination of the GBM’s asymmetric equilibrium thus appears to be a robust phenomenon. Since this payoffdominant equilibrium predicts aggregate behavior so well, we do not apply explanatory concepts such as reciprocity, competitiveness and the like, which only allow for a directional prediction rather than a point prediction. 6.2. Policy Relevance Our results suggest efﬁciency gains if a system is organized along meritocratic principles rather than privilege. Since the nature of the GBM’s group-based

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output is broadly deﬁned, our theoretical and experimental ﬁndings could apply to a wide variety of settings such as teams, ﬁrms, or academic departments.15 The empirical conﬁrmation that the GBM’s payoff-dominant equilibrium, however complex, is reliabily coordinated in the laboratory even if abilities to contribute vary and an alternative equilibrium of noncooperation by all is available, might add to our understanding of how societies and organizations have become increasingly meritocratic, as evidenced for example by trends away from family ﬁrms and toward professional management, the reduced relevance of gender, race, or class in many industrialized or developing countries, or the gradual disappearance of monarchies. We note however that we have found cases of the mechanism where only an equilibrium of non-contribution by all exists (Example 2, Section 3.4.3). This raises the question whether and how the efﬁciencyenhancing effects of meritocratic organization are dependent on social structure.

6.3. Is a Lag Free Model of Social Grouping Sufﬁciently Realistic? Our model is one of instantaneous, perfect mobility based on current performance, with no lags between performance and grouping, or between grouping and reward. Players decide, get grouped and rewarded, all in the same round. Lags would represent system imperfections in the form of delays, for example, if information needs to be collected over periods that are longer than the reward cycles. In an ideal Group-based Meritocracy, there should be no lags since positions and associated rewards should be instantaneously adjusted based on performance. Individuals’ occasional mistakes would thus be immediately reﬂected in group membership and associated rewards; on the contrary, a slacker could instantaneously redeem herself if she increases her contribution. A trend to shorten employment contracts or to increase the frequency of performance reviews, could be interpreted as a move toward such a model. However, it is clear that our current model remains extreme in this regard since in the real world, grouping and reward is based on past behavior and reputation. Note however that introducing lags into the model would make this game dynamic. The game’s equilibrium structure is already quite involved in the current static version, and introducing reputation, more complex institutional rules, and other complexities would make the model difﬁcult, perhaps even impossible, to solve analytically.

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6.3.1. Giving the Nash Equilibrium its Best Chance We acknowledge that in the current version of the model and in its experimental test, boundedly rational players are not overloaded with information and complications that exist in the ﬁeld such as reputation and lags. We also do not incorporate possible effects of homogeneity of class, race or gender on in-group cohesion and cooperation. Our model thus provides a favorable environment for a payoff-dominant Nash equilibrium to be realized. The impact of lags and other complications merits systematic exploration, but this does not detract from our ﬁnding that in principle, performance-based group mobility makes provision levels of collective goods efﬁcient even if players’ abilities to contribute are not equal. This chapter is part of a research program that studies the rational aspects of endogenous group formation. Although lags and other complicating aspects need at some point to be built into the mechanism, we consider the following extensions more pressing.

6.4. Extensions The main purpose of this chapter’s experiment was to test whether GVSM’s ﬁnding that the GBM mechanism’s NEE is precisely coordinated in the laboratory is robust to inequality and the added complexity that goes with it. The general theoretical analysis of the 2-Type GBM in Section 3 however can form the base for numerous other experimental tests. The sensitivity of the mechanism’s equilibrium structure to a change in parameters, as illustrated in the examples in Section 3, together with the precision with which subjects have so far coordinated the mechanism’s payoff-dominant equilibrium, should yield distinctive experimental results that closely reﬂect the underlying equilibrium structure. 6.4.1. Full Efﬁciency with Sufﬁcient Inequality? The theoretical ﬁnding that if the difference between the advantaged and disadvantaged types is large enough, the disadvantaged, far from getting discouraged, might increase their social contributions even more so that a fully efﬁcient, rather than merely a near-efﬁcient solution results (Theorem 2) invites testing. Payoff dominance (Harsanyi & Selten, 1988) suggests that full efﬁciency should occur in such a case. However, payoff dominance and other theories of equilibrium selection are not entirely uncontested (see, e.g., Binmore, 1989; Aumann, 1988; Crawford & Haller, 1990; Harsanyi, 1995; van Damme, 2002). A useful method to distinguish among a game’s multiple

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equilibria is therefore to test with experiments which of the equilibria subjects actually pick. From a policy viewpoint, could one increase inequality in order to raise efﬁciency? It would all depend on how it is done. Lowering the ability of the Lows to the point where they all contribute fully (leading to an FEE) might be counterproductive. In our experiment for example it would require lowering the low endowment L to only 40% of the high endowment H, from 80 tokens to 48 tokens. This however does not increase overall social contributions or earnings. Subjects’ total earnings per round in the NEE experimentally tested in Section 4 are 2,240 tokens, but would only be 2,016 in the FEE that would result if L were reduced to 48 tokens only. Increasing H, on the other hand, could result in higher overall earnings and full efﬁciency. It remains yet to be seen whether there is a point at which increasingly disadvantaged Lows revolt and gravitate toward the alternative equilibrium of non-contribution by all. An experiment could provide indications. 6.4.2. Type Counts as Critical Elements Type count can be manipulated so that both NEE and FEE disappear (see Example 2, Section 3.4.3). In such a case, will experimental subjects indeed converge to the only remaining equilibrium of non-contribution by all? 6.4.3. Full Heterogeneity Our current model allows for inequality only in the form of a 2-Type society. An obvious further theoretical extension of the current model is to increase the number of types, eventually up to the number of players. 6.5. Concluding Remarks If social stratiﬁcation and grouping based on contributions is to be a credible policy tool for raising cooperation levels, the question of diversity in the form of unequal abilities must be addressed. Our ﬁndings based on a two-type model indicate that when grouping and stratiﬁcation are competitively based on contributions, unequal abilities to contribute are not necessarily detrimental to efﬁciency. Our mechanism of contribution-based grouping applies to the extent that the impact of superﬁcial grouping criteria unrelated to output, such as race, class or gender, is eliminated. Our results suggest that if grouping is based on superﬁcial prejudice rather than contributions, the only stable state is non-contribution by all. A thought experiment, which could also be

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empirically tested, might offer some insight into the effect and mechanics of prejudice on contribution levels. Psychological research on ‘‘minimal groups’’ indicates that similarity along even the most superﬁcial of grouping criteria can cause selective favoritism because people tend to prefer others who resemble them.16 Imagine now a dynamic, lagged version of our model where a randomly selected subset of players faces prejudice: their past free-riding is discounted less over time and their past contributions are discounted more, so that they need to prove themselves more before they can enter a high-performing group with high payoffs. It is a theoretical and empirical question whether and at which point these victims of prejudice stop contributing and become a burden to the system. The remaining contributors can react in one of two ways: (1) Unwilling to support the noncontributors through charitable contributions without reciprocity, they in turn also contribute nothing, and the system reaches a state of noncontribution by all. (2) The remaining contributors segregate into their own cooperative communities, which turn out homogeneous in whatever is assumed to have caused the differential weighing of contributions in the ﬁrst place, and the system reaches a state where a superﬁcial attribute has become a signal of willingness to contribute, even though it was not so at the beginning. Originally unfounded prejudice would thus gain seeming empirical support. The ﬁndings from the static, instant-reward two-type model of contribution-based grouping analyzed in this chapter together with the above thought experiment suggest that if community members know that their contributions are speedily translated into rewards that reﬂect their contribution, then most-including the less capable, contribute as much as they can. If there exist multiple societies with different stratiﬁcation rules and mobile players, a society that rewards contribution relatively quickly and applies the same unprejudiced metric to the output of all members no matter how diverse their superﬁcial characteristics, should therefore attract migrants willing to contribute, and whose contributions are better recognized in the new location.

NOTES 1. See, for example, Ahn, Isaac, and Salmon (2008); Charness and Yang (2009); Croson, Fatas, and Neugebauer (2007); Gu¨th, Levati, Sutter, and Van der Heijden (2007); Cabrera, Fatas, Lacomba, and Neugebauer (2007); Page, Putterman, and Unel (2005); Ga¨chter and Tho¨ni (2005); Cinyabuguma, Page, and Putterman (2005);

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Maier-Rigaud, Martinsson, and Stafﬁero (2005). Endogenous grouping also has an impact if players do not even know that they are being grouped (e.g., Ones & Putterman, 2004; Gunnthorsdottir, Houser, & McCabe, 2007). 2. For example, to increase intellectual competitiveness, over the 20th century Ivy League schools reduced or eliminated non-performance related intake criteria such as legacy preferences, gender, or ethnicity (Karabel, 2005). 3. For example, Singapore, among the most successful Asian countries by most standards, seceded from Malaysia in 1965 because it rejected ethnic quotas in the assignment of social and professional roles in favor of contribution-based hiring. 4. Gunnthorsdottir, Houser, & McCabe (see also Gunnthorsdottir, 2001) use a related game where like-contributors are grouped together. With the goal of identifying player types who vary in reciprocity, Gunnthorsdottir et al. created a purposefully vague and brief version of a VCM with contribution based grouping, so that subjects ignorant of the grouping method project their personality (cooperator or free rider) into the ambiguous situation. Thus, their design and its purpose differ from ours: The current study tests a speciﬁc equilibrium prediction based on a precise game-theoretic model. In established communities and societies the grouping method is usually known, as is the case in the current study. Gunnthorsdottir (2009) found that behavior is quite different when subjects know the grouping method compared to situations where they don’t. 5. Additionally and depending on the parameters, there exist mixed-strategy equilibria. Their existence is brieﬂy discussed by GVSM. Mixed strategies are beyond the scope of the current paper since (1) the pure strategy equilibrium predicts very well here. (2) Mixed strategies are intuitively implausible when there is no stringent need to play unpredictably, and pure equilibrium strategies are available to players (see, e.g., Kreps, 1990, pp. 407–410; Aumann, 1985, p. 19). (3) Even in games with a unique equilibrium in mixed strategies, proper mixing (both the right proportions of choices and their serial independence) is usually beyond regular subjects’ abilities (see, e.g., Palacios-Huerta & Volij, 2008; Walker & Wooders, 2001; Brown & Rosenthal, 1990; Erev & Roth, 1998). (4) GVSM report that their subjects do not play mixed strategies. 6. GVSM denote cR by z. 7. By introducing unequal endowments, we make players’ world less fair even though it is not exactly an ascriptive (Linton, 1936) system. Note though that Rawls (1971) explicitly included differing abilities in the Lottery of Birth. Unequal abilities to contribute still allow players some control over their grouping, but within constraints that are again Lottery of Birth based (exactly what a meritocracy often claims to overcome). In a meritocracy with differential abilities to contribute, ability thus constitutes a ceiling to what an individual can aspire to, even though within these constraints, she determines her contribution levels and through them, her social position. Fair or not, ability to contribute is a signiﬁcant determinant of social position in contemporary societies. For example, IQ is the strongest single predictor of socio-economic status (see, e.g., Grusec, Lockhart & Walters, 1990; Herrnstein & Murray, 1996, Chap. 3). 8. See Section 3.5.3 for exceptions. 9. For illustration purposes we describe a case with three or more groups. The case with two groups only is easily inferred in a similar fashion.

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10. In the experimental test in Sections 4 and 5 L ¼ 80 tokens and H ¼ 120 tokens so that Dw ¼ 0.5. 11. Some simple examples of cases where Assumption 2 is relaxed: nH and nL are divisible by f; nH or nL equals f; nHof; nLof, etc. Relaxing Assumption 1, too, creates a large array of different cases. Many of these cases are interesting and are being developed in separate papers. 12. As originally shown by GVSM, cR, which they denote as z, is MPCRdependent. 13. This corresponds to (/120, 120, 120, 120S, /120, 120, 80, 80S, /80, 80, 0, 0S) in experimental tokens. 14. The focus here is on the 2-Type GBM’s payoff-dominant equilibrium rather than on individual strategies. We note however that Lows’ oscillations between their two equilibrium strategies (1) are similar to what GVSM’s subjects with homogeneous endowments, who thus all had a choice between two NEE strategies, did. (GVSM compute the game’s complete mixed-strategy equilibrium and report that neither the individual choice proportions over 80 rounds nor the sequence of choices is consistent with mixing.) (2) Are similar to what is found in Market Entry Games where individual strategies over rounds oscillate unpredictably but aggregate choice proportions are close to the asymmetric equilibrium (for overviews, see, e.g., Ochs, 1999; Camerer & Fehr, 2006). 15. Usually, a system is considered a meritocracy when each member is rewarded individually according to his output. In a modern organization-based economy, however, a signiﬁcant proportion of rewards are shared, for example: overall ﬁrm salary levels, proﬁt sharing payments, health care coverage, leave policy, and intangibles such as ﬁrm reputation, location, premises, or work atmosphere. 16. See Tajfel (1982) for seminal experiments, and Bourhis and Gagnon (2001) for an overview of the ‘‘minimal group paradigm.’’ At ﬁrst sight, these ﬁnding appear to run counter to our assertion that superﬁcially based grouping is deleterious to group contributions. Based on the minimal-group paradigm, one might instead argue that it would be helpful to group players along superﬁcial characteristics since they tend to cooperate with each other more this way. Two points need to be made in response to such an argument: (1) The cooperation-enhancing effect of superﬁcial in-group favoritism appears to be much weaker than the impact of commonknowledge contribution-based grouping; the relevant psychology experiments show a statistically signiﬁcant, but not necessarily substantial, effect. It is also impossible to predict the exact impact or duration of the ‘‘minimal group’’ effect. Without a theoretical foundation in self-interest, the effect may still dissipate over time. (2) The effect is also selective and only applies to players who share a superﬁcial characteristic. The effect can be strengthened if superﬁcially constructed groups face real conﬂict of interest (see, e.g., Sherif, 1966), but intergroup conﬂict, which in turn might reduce the efﬁciency of the system overall, is not part of our current model. 17. We use a weak inequality here because it is not clear at this stage if there are players from classes after C2 in group D1 þ 1. 18. More precisely, i 2 N H ) ieN L ) ieC 2 [ C3 ) i 2 C 1 , so that N H C 1 . Combining this conclusion with the fact that C 1 N H in Lemma A.1(b) results in C1 ¼ N H .

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ACKNOWLEDGMENTS We thank Jim Andreoni, Carlos Pimienta and our collegaues at the Department of Economics, University of Iceland, for helpful comments. We acknowledge support from the Australian Research Council (ARC).

REFERENCES Ahn, T. K., Isaac, M., & Salmon, T. (2008). Endogenous group formation. Journal of Public Economic Theory, 10(2), 171–194. Andreoni, J. (1995). Cooperation in public-goods experiments: Kindness or confusion? American Economic Review, 85(4), 891–904. Aumann, R. (1985). What is game theory trying to accomplish? In: K. Arrow & S. Honkapohja (Eds), Frontiers of economics. Malden, MA: Blackwell. Aumann, R. (1988). Foreword. In: J. Harsanyi & R. Selten (Eds), A general theory of equilibrium selection in games. Cambridge, MA: MIT Press. Binmore, K. (1989). A general theory of equilibrium selection in games. Journal of Economic Literature, 27(3), 1171–1173. Bourhis, R., & Gagnon, A. (2001). Social orientations in the minimal group paradigm. In: B. Rupert & L. G. Samuel (Eds), Intergroup processes: Blackwell handbook of social psychology. Malden, MA: Blackwell. Brown, J., & Rosenthal, R. (1990). Testing the minimax hypothesis: A reexamination of O’Neill’s game experiment. Econometrica, 58(4), 1065–1081. Buchanan, J. M. (1965). An economic theory of clubs. Economica, 32(1), 1–14. Cabrera, S., Fatas, E., Lacomba, J., & Neugebauer, T. (2007). Vertically splitting a ﬁrm: Promotion and relegation in a team production experiment. Working Paper. University of Valencia. Camerer, C., & Fehr, E. (2006). When does ‘economic man’ dominate social behavior? Science, 311(5757), 47–52. Charness, G., & Yang, C. (2009). Endogenous group formation and public goods provision: Exclusion, exit, mergers, and redemption. Working paper. Available at http://ssrn.com/ abstract ¼ 932251 Cinyabuguma, M., Page, T., & Putterman, L. (2005). Cooperation under the threat of expulsion in a public goods experiment. Journal of Public Economics, 89(8), 1421–1435. Crawford, V., & Haller, H. (1990). Learning how to cooperate: Optimal play in repeated coordination games. Econometrica, 58(3), 571–595. Croson, R., Fatas, E., & Neugebauer, T. (2007). Excludability and contribution: A laboratory study in team production. Working paper. University of Texas, Dallas. Davis, D., & Holt, C. (1993). Experimental economics. Princeton: Princeton University Press. Erev, I., & Roth, A. (1998). Predicting how people play games: Reinforcement learning and experimental games with unique, mixed strategy equilibria. American Economic Review, 88(4), 848–881. Ga¨chter, S., & Tho¨ni, C. (2005). Social learning and voluntary cooperation among likeminded people. Journal of the European Economic Association, 3(2–3), 303–314.

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Grusec, J., Lockhart, R., & Walters, G. (1990). Foundations of psychology. New York: Copp Clark Pittman. Gunnthorsdottir, A. (2001). Determinants of cooperation and competition in single-level and multi-level interactive decision making. Unpublished doctoral dissertation. University of Arizona. Gunnthorsdottir, A. (2009). Equilibrium and type: The crucial role of information. In: R. S. Anderssen, R. D. Braddock & L. T. H. Newham (Eds), Proceedings of the 18th world IMACS congress and MODSIM09 international congress on modeling and simulation (pp. 1450–1456), http://www.mssanz.org.au/modsim09/09/gunnthorsdottir.pdf Gunnthorsdottir, A., Houser, D., & McCabe, K. (2007). Disposition, history, and contributions in public goods experiments. Journal of Economic Behavior and Organization, 62(2), 304–315. Gunnthorsdottir, A., Vragov, R., Seifert, S., & McCabe, K. (2009). Near-efﬁcient equilibria in collaborative meritocracies. Available on SSRN, http://ssrn.com/abstract ¼ 967900 Gu¨th, W., Levati, V., Sutter, M., & Van der Heijden, E. (2007). Leading by example with and without exclusion power in voluntary contribution experiments. Journal of Public Economics, 91(7), 1023–1042. Harsanyi, J. (1995). A new theory of equilibrium selection for games with complete information. Games and Economic Behavior, 8(1), 91–122. Harsanyi, J., & Selten, R. (1988). A general theory of equilibrium selection in games. Cambridge, MA: MIT Press. Herrnstein, R., & Murray, C. (1996). The bell curve. New York: Simon and Schuster. Isaac, M., McCue, K., & Plott, C. (1985). Public goods provision in an experimental environment. Journal of Public Economics, 26(1), 51–74. Kahneman, D. (1988). Experimental economics: A psychological perspective. In: R. Tietz, W. Albers & R. Selten (Eds), Bounded rational behavior in experimental games and markets (pp. 11–20). Berlin: Springer. Karabel, J. (2005). The chosen: The hidden history of admission and exclusion at Harvard, Yale, and Princeton. Boston, MA: Houghton-Mifﬁn. Kreps, D. M. (1990). A course in microeconomic theory. Princeton: Princeton University Press. Ledyard, J. O. (1995). Public goods: A survey of experimental research. In: J. Kagel & A. Roth (Eds), Handbook of experimental economics (pp. 111–194). Princeton: Princeton University Press. Linton, R. (1936). The study of man. New York: Appleton-Century-Crofts. Maier-Rigaud, F., Martinsson, P., & Stafﬁero, G. (2005). Ostracism and the provision of a public good. Mimeo, Max Planck Society. Ochs, J. (1999). Coordination in market entry games. In: D. Budescu, I. Erev, & R. Zwick (Eds), Games and human behavior: Essays in honor of amnon rapoport (pp. 143–172). New York, NY: Erlbaum. Ones, U., & Putterman, L. (2004). The ecology of collective action: A public goods and sanctions experiment with controlled group formation. Working Paper. Brown University Department of Economics. Page, T., Putterman, L., & Unel, B. (2005). Voluntary association in public goods experiments: Reciprocity, mimicry, and effciency. Economic Journal, 115(506), 1032–1053. Palacios-Huerta, I., & Volij, O. (2008). Experientia docet: Professionals play minimax in laboratory experiments. Econometrica, 76(1), 71–115.

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Rawls, J. (1971). A theory of justice. Cambridge: Harvard University Press. Selten, R. (1997). Descriptive approaches to cooperation. In: S. Hart & A. Mas-Colell (Eds), Cooperation: Game theoretic approaches (pp. 289–326). Heidelberg: Springer. Sherif, M. (1966). Group conﬂict and cooperation: Their social psychology. London: Routledge & Kegan Paul. Tajfel, H. (1982). Social psychology of intergroup relations. Annual Review of Psychology, 33, 1–39. van Damme, E. (2002). Strategic equilibrium. In: R. Auman & S. Hart (Eds), Handbook of game theory (Vol. 3, pp. 1522–1596). Amsterdam: Elsevier. Walker, M., & Wooders, J. (2001). Minimax play at Wimbledon. American Economic Review, 91(6), 1521–1538.

APPENDIX A. PROOF OF THEOREM 1 The proof of Theorem 1 relies on the ﬁve auxiliary results summarized in Lemma A1 here below: Lemma A1. If an equilibrium with positive contributions exists, it has the following properties: (a) The count of C1 players is larger than and not a multiple of group size f, and each C1 player contributes fully. Formally, c1 4f; c~1 40, and si ¼ wi if i 2 C 1 . (b) C1 consists of Highs only, that is, C 1 N H . (c) There is no class Cr satisfying 1osr oH. (d) If the equilibrium consists of only two classes, it is an FEE. (e) If the count of CR players is less than or a multiple of the group size, then each CR player contributes nothing. Formally, if cR of or c~R ¼ 0, then sR ¼ 0. Proof. (a) If c~1 ¼ 0, then c1 jC1 j ¼ D1 f by Eq. (2). Consider any player i 2 C 1 . If si ¼ s1 , she is always grouped with (f 1) players contributing s1 and gets wi s1 þ mfs1 ; if she contributes s0i ¼ s1 4s2 where 2 R, she is in Group D1 but is still grouped with (f 1) players contributing s1, and gets wi s1 þ þ m ðf 1Þs1 þ s1 ¼ wi s1 þ mfs1 þ ð1 mÞ 4wi s1 þ mfs1

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since mo1. Thus i has an incentive to deviate. It follows that c~1 40 as claimed. To see that c1 4f, note that if c1 of, player i 2 C 1 is in the ﬁrst group where the total contribution except for player i is S 1i . If she reduces her contribution from s1 to s1 4s2 , she remains in the ﬁrst group, but her payoff increases from wi s1 þ m S 1i þ si to wi s1 þ m S 1i þ si þ ð1 mÞ Thus i has an incentive to deviate. This proves that c1 4f. To verify that each C1 player contributes fully, note that we now have c1 ¼ D1 f þ c~1 , where D1 1 and c~1 40; hence, every C1 player hasa strictly positive probability of entering Group (D1þ1), that is, PrðD1 þ 1s1 Þ ¼ c~1 =c1 40. Given a contribution proﬁle s satisfying si ¼ s1 owi for some i 2 C 1 , let S ¼ fs1 be the total contribution in Group 1; . . . ; D1 , and let S0 c~1 s1 þ ðf c~1 Þs2 be the total contribution in Group D1þ1.17 Then S4S0 since s1 4s2 . Hence, if a C1 player contributes si ¼ s1 owi , her payoff is (" ) # D1 X 0 1 1 ðwi si Þ þ m Pr ks S þ Pr D1 þ 1js S k¼1

¼ wi s1 þ m 1 Pr D1 þ 1s1 S þ Pr D1 þ 1s1 S 0 o wi s1 þ mS

However, if she increases her contribution from s1 to s1 þ owi , she enters the ﬁrst group with certainty and obtains: wi s1 þ mðS þ Þ ¼ wi s1 þ mS ð1 mÞ This deviation is proﬁtable as long as e is small enough. We thus proved that s1 ¼ wi if player i is in the ﬁrst class. (b) We ﬁrst show that there is at least one High in C1. Suppose this is not true, that is, suppose that C 1 N L . Then s1 ¼ 1 since each C1 player contributes fully. We can show that in such a situation any C2 player has an incentive to deviate. There are three cases to consider: (i) c~ 1 þ c2 /; see Fig. A1(i). Since we assume that C1 N L , there are more than nH 4f players outside of C1, so that jCj 3 and s2 40. In such a case each C2 player can reduce her contribution from s2 to s2 4s3 and remain in Group (D1 þ 1). By the same reasoning as in Lemma A1(a), this is a proﬁtable deviation.

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(i)

Group 1 C1

Group 3

Group 2 C2

By contributing s2 +

Group (D1 + 1)

(ii) C1

i C2

(iii) C1

C2

Fig. A1. There Is at Least One High in C1.

(ii) c~ 1 þ c2 4/ and c~ 1 þ c~ 2 ¼ /; see Fig. A1(ii). Consider any player i 2 C 2 . If si ¼ s2 o1, her payoff is wi s2 þ m Pr D1 þ 1s2 c~1 þ ðf c~1 Þs2 þ 1 Pr D1 þ 1s2 fs2 oðwi s2 Þ þ m c~1 þ ðf c~1 Þs2 because c~1 þ ðf c~1 Þs2 4fs2 . However, if she contributes s2 þ os1 , she enters Group (D1þ1) with certainty and obtains wi s2 þ m c~1 þ ðf c~1 Þs2 þ ¼ wi s2 þ m c~1 þ ðf c~1 Þs2 ð1 mÞ which is greater than her original payoff when e is small enough. Thus, player i 2 C 2 has an incentive to increase her contribution. (iii) c~ 1 þ c2 4/ and c~ 1 þ c~ 2 a/; see Fig. A1(iii). This cannot be an equilibrium since any player i 2 C 2 will increase her contribution for the same reason as in (ii). Hence, there is at least one High i in C1. Together with Lemma A1(a) this implies that si ¼ H. We thus conclude that s1 ¼ H and C 1 N H . (c) Suppose there exists a class Cr satisfying 1osr oH. Since r s oH ¼ s1 , class C1 is ranked above class Cr; since sr 41, there is at least one class after Cr and C r N H . A similar argument as in Lemma A1(b) shows that (1) C1 is the immediate predecessor class of Cr, and (2) any Cr player has an incentive to deviate. This proves the nonexistence of a class Cr where 1osr oH.

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(d) Let C ¼ fC1 ; C 2 g. Then s2 1 because of the existence of Lows, and N L C 2 since C 1 N H by Lemma A1(a). Hence, c2 nL 4f, c~1 þ c2 4f and c~1 þ c~2 4f, which is exactly Case (ii) in Lemma A1(b); therefore, s2 ¼ 1 and N H C 1 . This conclusion together with the fact that C 1 N H implies that C 1 ¼ N H , and consequently C 2 ¼ N L . (e) Let cR of and sR 40. Then class CR is in Group G, and each CR player gets ðwi sR Þ þ m SG , where S G is the total contribution in Group G. If i 2 C R reduces her contribution from sR to 0, her payoff becomes wi þ mðS G sR Þ4ðwi sR Þ þ mS G . Therefore, sR ¼ 0 in equilibrium when cR of. Let c~R ¼ 0 and sR 40. Consider any CR player. If she reduces her contribution from sR to 0, she enters the Group G, but is still grouped with (f 1) players contributing sR , so that her payoff increases by deviating this way. &

A.1. Proof of Theorem 1 By Lemma 1, jCj 2 in any equilibrium with positive contributions. Since jCj n in any equilibrium, we can characterise the last class CR, which can only take one of the following three forms: (a) cR ¼ DR f þ c~R ; where DR 1 and c~R 40, (b) cR of, or (c) cR ¼ DR f, where DR 1. Also note that sR 1 in any equilibrium because of the existence of Lows. The proof will be given by the following four claims: Claim 1. If (a) holds, then the equilibrium candidate is an FEE. Let cR ¼ DR f þ c~R 4f with c~R 40 and suppose that sR o1. Since c~R 40 and n ¼ Gf, we have cR an. So there exists at least one class C R1 before CR satisfying sR1 4sR . In this case each CR player has an incentive to increase her contribution so that she can be grouped with the CR1 players with certainty. In equilibrium it must be that each CR player cannot increase her contribution further, that is, sR ¼ 1 and CR \ N H ¼ +. Therefore, C1 is the immediate predecessor class of CR by Lemma A1(c), that is, jCj ¼ 2. Lemma A1(d) implies that this is an FEE.

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Claim 2. If (b) holds, then the equilibrium candidate is an NEE. Suppose that cR of in equilibrium. In this case jCj 3 since jCj ¼ 2 implies that cR ¼ nL 4f by Lemma A1(d). Also note that sR ¼ 0 by Lemma A1(e). Consider class CR1 . There are three cases to consider: (i) cR1 þ cR /; see Fig. A2(i). This is impossible since CR1 is in the last group and any CR1 player has an incentive to reduce her contribution for the same reason as in Lemma A1(e). (ii) cR1 þ cR 4/ and c~ R1 þ c~ R ¼ /; see Fig. A2(ii). With the following two steps we show that in this case sR1 ¼ 1. Step 1. Suppose that sR1 41. Then Lows cannot be in CR1 or the classes, if any, before CR1 since s1 4 4sR1 41, which means that nL cR of. This contradicts Assumption 2 that nL 4f. Step 2. Suppose that sR1 o1 and consider any player i 2 C R1 . If player i contributes si ¼ sR1 o1, her expected payoff is

wi sR1 þ m 1 Pr GsR1 fsR1 þ Pr GsR1 c~R1 sR1 owi sR1 þ mfsR1 because c~R1 of. But if she increases her contribution from sR1 to sR1 þ o minf1; sR2 g, she enters the ﬁrst group in class C R1 , and gets wi sR1 þ m fsR1 þ ¼ wi sR1 þ mfsR1 ð1 mÞ which is greater than her original payoff as long as e is small enough. sR = 0 Group G

(i) CR−2

CR−1

CR

sR−1 = 1

sR = 0

CR−1

CR

(ii) CR−2

sR−1 = 1

sR = 0

CR−1

CR

(iii) CR−2

Fig. A2.

The Last Class CR.

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The above two steps proved that sR1 ¼ 1 when cR1 þ cR 4f and c~R1 þ c~R ¼ f. It follows from Lemma A1(c) that C1 is the immediate predecessor class of CR1 , that is, jCj ¼ 3. The fact that [3r¼1 C r ¼ N implies: n ¼ c 1 þ c2 þ c3 ¼ ðD1 þ D2 þ D3 Þf þ ðc~1 þ c~2 þ c~3 Þ h1 i

¼ ðD1 þ D2 þ D3 Þf þ ðc~1 þ fÞ ¼ ðD1 þ D2 þ D3 þ 1Þf þ c~1 where h1i holds because c~2 þ c~3 ¼ f. The above equation implies that n is not a multiple of the group size f because 0oc~1 of from Lemma A1(a). This contradicts the assumption at the beginning of Section 3.1 that n ¼ Gf, where G 2 N. (iii) cR1 þ cR 4/ and c~ R1 þ c~ R a/; see Fig. A2(iii). In this case sR1 ¼ 1 and C R1 N L , otherwise any CR1 player will increase her contribution so that she can be grouped with C R2 players and avoid entering the last group. Lemma A1(c) implies that C1 is the immediate predecessor class of CR1 , that is, jCj ¼ 3. We know the composition of the ﬁrst two classes in terms of their members’ endowments but we do not know for sure the composition of the third class, thus cannot exclude the possibility that N H \ C 3 a+ or that N L \ C3 a+, so that C 1 N H and C3 N H [ N L . Claim 3. If (c) holds, then there is an equilibrium candidate termed Eu, which is not an equilibrium. Suppose that cR ¼ DR f. We ﬁrst verify that jCja2: if jCj ¼ 2, then c1 ¼ n c2 ¼ ðG D2 Þf, which implies that c~1 ¼ 0, and contradicts Lemma A1(a). We next show that jCj ¼ 3 if cR ¼ DR f. Note that jCj 3 and sR ¼ 0 [Lemma A1(e)] imply c~R1 40 and cR1 4f, else any C R1 player has an incentive to reduce her contribution, which further implies that sR1 ¼ 1 and C R1 N L since each C R1 player wants to be grouped with C R3 players. Once again, Lemma A1(c) implies that C1 is the immediate predecessor class of CR1 ; thus, the equilibrium structure is as in Fig. A3. We will prove in Claim 4 that Eu is not an equilibrium, but for now, we content ourselves with proving that C 3 N L . Suppose there exists a player i such that i 2 C 3 \ N H . It follows that her payoff is H. But if she deviates and contributes 1 þ e, she enters group (D1 þ 1), and since there exists at

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C1

C2

Fig. A3.

C3

c~R ¼ 0.

least one player contributing H in Group (D1 þ 1) by Lemma A1(a), player i can guarantee ðH 1 Þ þ m½H þ ðf 2Þ þ ð1 þ Þ4H þ ðmf 1Þ ð1 mÞ4H when oðmf 1Þ=ð1 mÞ, where the ﬁrst strict inequality holds because HW1, and the second one can hold because mf41. This proves that C 3 N L . Because [3r¼1 Cr ¼ N H [ N L ¼ N, C 2 N L , and C 3 N L , we thus have C1 ¼ N H and C2 [ C 3 ¼ N L .18 Claim 4. Eu is not an equilibrium. Eu is an equilibrium if and only if: Player i 2 C3 N L has no incentive to increase her contribution from 0 to 1; Player i 2 C2 N L has no incentive to reduce her contribution from 1 to 0; and Player i 2 C 1 ¼ N H has no incentive to reduce her contribution from H to 1 þ , 1, or 0, where ! 0. Here we examine the incentives of all players starting with the last class and show that there exists no equilibrium satisfying all these constraints. Recall from Claim 3 that if Eu is an equilibrium, we must have (a) c3 ¼ D3 f and (b) c2 þ c3 ¼ nL since C 2 [ C 3 ¼ N L . Let b ðB D3 Þf. This allows us to write c2 as follows: c2 ¼ nL c3 ¼ ðBf þ ‘Þ D3 f ¼ b þ ‘ A.1.1. Incentives to Deviate for C3 Players in E u Consider any player i 2 C 3 N L . Her payoff from contributing 0 is U L0 ðC 3 Þ ¼ 1. If i wants to deviate, she should contribute si ¼ 1; then there would be (c2 þ 1) players contributing 1, and i would enter

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ANNA GUNNTHORSDOTTIR ET AL.

Group A þ 1; . . . ; A þ D2 þ 2 with positive probabilities, which are: 8 ‘=ðc2 þ 1Þ; > < Prðkj1Þ ¼ f=ðc2 þ 1Þ; > : 1=ðc þ 1Þ; 2 Because

PAþD3 þ2 k¼Aþ1

if k ¼ A þ 1 if k ¼ A þ 2; . . . ; A þ D2 þ 1 if k ¼ A þ D2 þ 2

Prðkj1Þ ¼ 1, we have

AþD 3 þ1 X

Prðkj1Þ ¼ 1 PrðA þ 1j1Þ PrðA þ D3 þ 2j1Þ

k¼Aþ2

c2 ‘ c2 þ 1 b ¼ bþ‘þ1

¼

Recall that S Aþ1 hH þ ‘, so that player i’s expected payoff from contributing 1 is ( U L1 ðC 3 Þ

¼ ð1 1Þ þ m PrðA þ 1j1ÞS Aþ1 " þ

AþD 3 þ1 X

#

)

Prðkj1Þ f þ PrðA þ D3 þ 2j1Þ

k¼Aþ2

‘ c2 ‘ 1 SAþ1 þ fþ ¼m c2 þ 1 c2 þ 1 c2 þ 1 Aþ1 m ‘S þ bf þ 1 ¼ bþ‘þ1 Therefore, player i 2 C3 has no incentive to deviate if and only if U L0 ðC 3 Þ U L1 ðC 3 Þ, that is b

‘ þ 1 m‘S Aþ1 m mf 1

(A.1)

Eq. (A.1) shows that there cannot be too many players in class C2 (recall that c2 ¼ b þ ‘), else some players in class C3 will have an incentive to try to go to C2.

Tacit Coordination in Contribution-based Grouping

67

A.1.2. Incentives to Deviate for C2 Players in E u Consider any player i 2 C 2 N L . If i contributes 1, she enters Group A þ 1; . . . ; A þ D2 þ 1 with positive probabilities, which are: ( ‘=c2 ; if k ¼ A þ 1 Prðkj1Þ ¼ f=c2 ; if k ¼ A þ 2; . . . ; A þ D2 þ 1 Her expected payoff is ‘ Aþ1 c2 ‘ S þ f U L1 ðC 2 Þ ¼ m c2 c2 m ‘S Aþ1 þ bf ¼ bþ‘ If i 2 C 2 wants to deviate, she will contribute ! 0 to stay in Group (A þ D2 þ 1), and her expected payoff is lim U L ðC 2 Þ ¼ lim½1 þ mðf 1Þ ð1 mÞ

!0

!0

¼ 1 þ mðf 1Þ Therefore, i 2 C 2 has no incentive to deviate if and only if U L1 ðC 2 Þ lim#0 U L ðC 2 Þ, that is, b

m‘SAþ1 ð1 þ mf mÞ‘ 1m

(A.2)

The reason why b cannot be very large is as follows: Consider i 2 C 2 ; if b is large, her probability of entering Group (Aþ1) is small and her expected payoff from contributing 1 is small, so that her incentive to deviate is large. Note that by Claim 3, we also require b f, else i 2 C 2 will reduce her contribution. Combining this requirement, (A.1), and (A.2), we observe that m has to satisfy the following conditions:

‘S

Aþ1

fþ‘ fþ‘þ1

m Aþ1 ‘f þ f þ ‘ þ f2 þ 1 ‘S

(A.3)

The intuition behind Eq. (A.3) is as follows: m is the return from the group investment, so it cannot be very small because if it is very small C2 players will have no incentive to contribute. At the same time m cannot be

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ANNA GUNNTHORSDOTTIR ET AL.

very large because this would give C3 players an incentive to contribute. These two constraints determine the bounds of m in Eq. (A.3). For ease of expression deﬁne

‘S

Aþ1

fþ‘ fþ‘þ1 m; and m Aþ1 ‘f þ f þ ‘ þ f2 þ 1 ‘S

Eq. (A.3) implies that m m; thus given all other parameters, SAþ1 must satisfy SAþ1

‘2 ‘f þ ‘2 f f2 þ 2‘f2 þ f3 ‘

Substituting SAþ1 in the above inequality making use of the deﬁnition of m, one obtains m

1þ‘þf 1 ‘ ‘f þ ‘2 f þ 2‘f2 þ f3 2

(A.4)

A.1.3. Incentives to Deviate for C1 Players in E u C 1 ¼ N H in Eu. We have shown in Section 3.5.2 that a C1 player has no incentive to reduce her contribution from H to 1 þ e if and only if: M (A.5) h nH 1 ‘ It can be seen that if Eq. (A.5) holds, then 1 M=‘40, which means that m4

1 ‘þ1

(A.6)

Eu is not an equilibrium because Eqs. (A.4) and (A.6) are incompatible: If Eu were an equilibrium, m must satisfy 1=ð‘ þ 1Þom m, so we must have 1=ð‘ þ 1Þom; however, m

1 ‘ðf 2Þ ðf2 fÞ o0

‘ þ 1 ð1 þ ‘Þ½1 þ ‘ðf 1Þ þ f2 f

which is a contradiction. Conclusion: Equilibrium candidate Eu is not a equilibrium.

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APPENDIX B. EXPERIMENTAL INSTRUCTIONS This is an experiment in the economics of group decision-making. You have already earned $10.00 for showing up at the appointed time. If you follow the instructions closely and make decisions carefully, you will make a substantial amount of money in addition to your show-up fee. Number of Periods and Endowments There will be many decision-making periods. In each period, you are given an endowment of experimental tokens. You receive the same endowment in each round of the experiment. By a random process, half of the participants receive 80 tokens per round, and half receive 120 tokens per round.

The Decision Task In each period, you need to decide how to divide your tokens between two accounts: a private account and a group (public) account. The latter account is joint among all members of the group that you are assigned to in that period. See below for the group assignment process and for how earnings from your accounts are calculated. How Earnings from Your Two Different Accounts are Calculated in Each Period Each token you place in the private account stays there for you to keep. All tokens that group members invest in the group (public) account are added together to form the so-called ‘‘group investment.’’ The group investment gets doubled before it is equally divided among all group members. Your group has four members (this includes yourself).

A Numerical Example of the Earnings Calculation in Any Given Period Assume that your endowment per period is 80 tokens. In a given period, you decide to put 30 tokens into your private account and 50 tokens into the

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group (public) account. The other three members of your group together contribute an additional 300 tokens to the group (public) account. This makes the total group investment 350 tokens, which gets doubled to 700 tokens (350 2 ¼ 700). The 700 tokens are then split equally among all four group members. Therefore, each group member earns 175 tokens from the group investment (700/4 ¼ 175). In addition to the earnings from the group (public) account, each group member earns 1 token for every token invested in his/her private account. Since you put 30 tokens into your private account, your total proﬁt in this period is 175 þ 30 ¼ 205 tokens. How Each Decision-Making Period Unfolds and How You are Assigned to a New Group in Each of the Periods First, you make your investment decision. Decide on the number of tokens to place in the private and in the group (public) account, respectively. To make a private account investment, use the mouse to move your cursor to the box labeled ‘‘Private Account.’’ Click on the box and enter the number of tokens you wish to allocate to this account. Do likewise for the box labeled ‘‘Public Account’’ entries in the two boxes must sum up to your endowment. To submit your investment click on the ‘‘Submit’’ button. Then wait until everyone else has submitted his/her investment decision. Second, you are assigned to the group that you will be a member of in this period. Once every participant has submitted his or her investment decision, you will be assigned to a group with four members (including yourself). The group assignment proceeds in the following manner: All participants’ contributions to the group (public) account are ordered from the highest contribution to the lowest contribution. Participants are then grouped based on this ranking: The four highest contributors are grouped together (e.g., if four of the participants all contributed 120 tokens, they are all put together into one group). Participants whose contributions rank from 5 to 8 form the second group. The four lowest contributors form the third group. As said, you will be grouped based on your public account investment. If there are ties for group membership because contributions are equal, a random draw decides which of these equal-contributors are put together into one group and who goes into the next group below. For example, if ﬁve participants each contributed 120 tokens, a random draw determines which

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four participants form a group of like-contributors and who is the one participant who goes into the next group below. Recall that group membership is determined anew in each period based on your public contribution in that period. Group membership does not carry over between periods! After the group assignment, your earnings for the round are computed. Experimental earnings from a given round are computed after you have been assigned to your group. See the numerical example above for details of how earnings are computed after you have been assigned to a group. End-of period message. At the end of each period, you will receive a message with your total experimental earnings for the period [total earnings ¼ the earnings from the group (public) and from your private account added together]. This information also appears in your Record Sheet at the bottom of the screen. The Record Sheet will also show the group (public) account contributions of all participants in the experiment in a given round in ascending order. Your contribution will be highlighted. A new period begins after everyone has acknowledged his or her earnings message. At the end of the experiment your total token earnings will be converted into US$ at a rate of 700 tokens for 1 US$.

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APPENDIX C. INDIVIDUAL GRAPHS WITH EARNINGS Session 2 50 100 150 200 250 40

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74 ANNA GUNNTHORSDOTTIR ET AL.

Session 3 Session 4

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THE EFFICIENCY-EQUALITY TRADEOFF IN PUBLIC SECTOR CHARITY PROVISION Daniel T. Hall ABSTRACT Purpose – We investigate the outcomes of public sector charity provision, which relies on income redistribution. Increasing the level of redistribution can result in an efﬁciency-equality tradeoff. We investigate whether the efﬁciency-equality tradeoff can be explained by lowered work incentives. Methodology – The chapter uses the methodology of laboratory experiments. We remove the administration costs of redistribution to see if a signiﬁcant source of the tradeoff can be explained by lower work incentives. Findings – We ﬁnd a signiﬁcant efﬁciency-equality tradeoff between lowand high-tax groups explained by lowered work incentives. Labor supply decisions are motivated by strategic and cooperative preferences which vary the size of the tradeoff. Limitations – Our analysis is limited to measuring the size and distribution of labor income. We discuss avenues such as allowing for crowding out and volunteerism, to further explore the impact of public sector charity provision. Charity with Choice Research in Experimental Economics, Volume 13, 77–111 Copyright r 2010 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0193-2306/doi:10.1108/S0193-2306(2010)0000013006

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Practical and social implications – Charity can be provided by the public, private, and independent sector. The public sector must redistribute income to provide charity, which leads to an efﬁciency-equality tradeoff. This calls for a reconsideration of increasing dependence on public sector charity provision. Originality – The efﬁciency-equality tradeoff traditionally focuses on the labor supply response to taxation. We allow subjects to respond to how their taxes are being used as well. Subjects are also given feedback on whether they are net taxpayers into redistribution or net recipients from it.

INTRODUCTION The welfare of the unfortunate continues to be a concern to society. Many people help those less fortunate by donating time, money, and/or other resources through various independent sector organizations; but, sometimes voluntary efforts for the provision of public goods such as poverty alleviation do not have satisfactory scale. On that basis some people advocate for government provision.1 The government provision of public goods has the advantage that it can compel the acquisition of capital through taxation. But, government cannot ratchet up taxes without limit. Economic theory, as well as empirical and experimental evidence, suggests that the government has diminishing and perhaps even negative returns over some levels of taxation. This study assesses the inefﬁciency of public sector charity provision; speciﬁcally, the inefﬁciencies of redistribution of income from an effort-based task.

BACKGROUND AND LITERATURE One type of charitable redistribution commonly used by the public sector is income redistribution. For example, some people pay positive federal income taxes, and others receive federal earned income tax credits. Income redistribution, however, can lead to inefﬁciencies. This indicates that there can be a tradeoff between efﬁciency and reductions in poverty and inequality. We must decide how much efﬁciency we are willing to sacriﬁce for a given reduction in poverty and inequality (Okun, 1975). What is the source of the inefﬁciency? Some of it comes from the administration costs of redistribution. Administration costs include the

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resources used by the government to collect and redistribute income, as well as the compliance costs of net taxpayers and application costs of net recipients. A second source of inefﬁciency is those distortions in work incentives caused by redistribution ﬁnanced by an income tax. Theory tells us that people who are ‘‘net tax payers’’ work less when the substitution effect (a negative labor supply response to higher taxes on wages) dominates the income effect (a positive labor supply response to maintain the same standard of living). Such a reduction in work effort results in inefﬁciency (Okun, 1975; Break, 1957; Brown, 1980). Income redistribution can also result in allocative inefﬁciency. The public may at ﬁrst advocate for the public sector to increase redistribution to provide a social safety net. Redistribution funds can be used for other purposes instead (Mueller, 2003). In particular, redistribution funds can be captured by groups with outside interests through rent-seeking activities (Stigler, 1971; Linster, 1993). The effectiveness of the public sector in reducing poverty is mitigated by the problems associated with income redistribution: administration costs, disincentives to work, and the misallocation of redistribution funds. The beauty of laboratory experiments is that a controlled and simpliﬁed environment can be set up to analyze one problem at a time. This research asks, ‘‘Assuming zero administration costs and proper allocation of redistribution funds, does redistribution still result in an efﬁciency loss due to lowered work incentives?’’ I build upon previous experiments that give predictions on how redistribution may affect the labor supply of taxpayers and recipients. The Laffer Curve states that tax revenue will rise, peak, and fall as the tax rate increases (Laffer, 2004). Naturally, the public sector’s capacity for charity provision follows this pattern.2 Field studies have looked at the effects of income redistribution on the recipients’ labor supply. The most famous and expensive studies were the negative income tax (NIT) experiments. The NIT experiments provided in-cash transfers to households, which fell below a speciﬁed minimum income level. The transfers decreased in size as the recipient’s household income approached the maximum level of eligibility. This created dynamic income and substitution effects. Five separate NIT experiments were conducted in the 1960s and 1970s. Four of the ﬁve programs found signiﬁcant reductions in labor supply (Brown, 1980).3 Although the variance of tax rates in the ﬁeld is limited, laboratory experiments have the advantage of looking at all possible tax rates. Some have in fact replicated the Laffer Curve (Ottone & Ponzano, 2007; Swenson,

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1988; Le´vy-Garboua, Masclet, & Montmarquette, 2009; Sutter & WeckHannemann, 2003). I set up an experiment with low- and high-tax rate treatments to look for changes in efﬁciency, equality, and labor supply. Subjects allocate their time between performing a labor task and taking leisure each period. Subjects’ labor earnings were taxed and redistributed equally at the end of each period, making subjects who earned above (below) the group average net taxpayers (net recipients). We ﬁnd a signiﬁcant efﬁciency-equality tradeoff. The primary efﬁciency loss comes from reduced output following subjects’ reduced labor supply. Subjects reduce their labor supply by allocating more time toward leisure activities. I also ﬁnd that the efﬁciency-equality tradeoff does not always hold: if labor productivity and cooperation is high enough to keep inequality low, intensive redistribution can reduce both efﬁciency and equality. A higher level of income redistribution signiﬁcantly reduces income inequality, but fewer funds are available for charity provision when there are large reductions in labor supply.

EXPERIMENTAL DESIGN4 The experimental design consists of two treatments differing only in the tax level used to carry out redistribution. Subjects participate in only one of the two tax treatments: a 20% tax treatment or an 80% tax treatment. The experiment is designed to test the following hypotheses: (1) efﬁciency will be lower in the 80% tax treatment; (2) inequality after redistribution will be lower in the 80% tax treatment; (3) labor supply will be lower in the 80% tax treatment; and (4) the signiﬁcance of the tradeoff will depend on withingroup cooperation as subjects compare their labor participation and output to other group members. Key features of the experimental design include (1) zero administration costs in the redistribution process; (2) homogeneous labor task and leisure options; (3) subjects make labor–leisure choices in real time; (4) subjects receive feedback on whether they gain or lose money from income redistribution; and (5) subjects receive information on their opportunity cost of labor (their potential leisure earnings). These features are important for testing the efﬁciency-equality tradeoff effectively. Administration costs are removed such that efﬁciency is only a measure of subject output. Subjects have homogeneous labor and leisure tasks to allow inequality to arise naturally: inequality comes only from heterogeneity in the ability and effort levels subjects bring to the laboratory.

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Homogenous labor and leisure tasks also remove fairness considerations external to the fairness considerations surrounding redistribution. Allowing subjects to allocate his or her time between labor and leisure removes friction from the process of self-selecting into and out of the labor force. Subjects are given feedback on whether they gain or lose from redistribution so we can test whether net taxpayers and net recipients behave differently. Subjects are also given information on their potential leisure earnings because this information will also play a role in their decision to substitute labor for leisure. Both treatments of this experiment involve subjects performing a repetitive labor task. Subjects perform the labor task on a computer using a program created in Visual Basic. The labor task is to type, exactly as shown on the screen, a random sequence of ﬁve single-digit numbers between 0 and 9. Fig. 1 shows a screenshot of the labor task. Each time a subject copies the sequence of characters correctly, a conﬁrmation of ‘‘CORRECT!’’ ﬂashes on their screen and the subject receives a piece-rate payment. Each time a subject copies the sequence of characters incorrectly, a conﬁrmation of ‘‘WRONG!’’ ﬂashes on their screen, but there is no penalty, only the

Fig. 1.

Screenshot of a Subject’s Labor Task.

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opportunity cost of forgone leisure earnings he or she could have made instead while typing the incorrect sequence. This work task follows a similar work task used by Dickinson (1999) where subjects were paid a piece-rate each time they copied a paragraph (Dickinson, 1999). There are 13 periods in each treatment: one Double Pay Period followed by 12 Regular Pay Periods. Each period lasts 5 minutes and 30 seconds. The last 30 seconds of each period give subjects time to review their earnings. The Regular Pay Periods last a total of one hour plus six minutes of review time. In the Double Pay Period subjects earn a piece-rate of $0.06 for each correctly typed sequence. This is double the piece-rate subjects are paid for the remaining Regular Pay periods. We double the pay to give subjects extra incentive to work at their productivity threshold. The number of correct sequences a subject types during the Double Pay Period gives a raw measure of ability. We use subjects’ ability measures to control for heterogeneity in ability, since changes in effort are of greater interest. The Double Pay Period also ranks subjects on their productivity to build groups of ﬁve for the Regular Pay Periods. We rank subjects on their productivity to create groups with similar compositions of low, medium, and high productivity members. The rank-to-group matching procedure is taken from Blumkin, Rufﬂe, & Ganun (2008) and is shown in Table 1 (Blumkin et al., 2008). This group formation procedure serves two major purposes: (1) to ensure that a wide initial income distribution exists in each group given similar effort levels and (2) to reduce variation in total productivity across groups for better intergroup comparison. The Regular Pay Periods introduce more complex work incentives because subjects now make real labor–leisure decisions. At any time during the Regular Pay Periods subjects can switch from labor to leisure and back by clicking the Labor and Leisure Tabs shown on their computer screen. Subjects can make labor earnings and leisure earnings but not both at the same time, so they must allocate their time between receiving labor and leisure earnings. We induce subjects’ value for the leisure task: subjects earn 1 cent for every two seconds the Leisure tab is active. Induced values of leisure are used instead of homegrown values because Esarey, Salmon, and Barrilleaux (2007) found that the redistributive tax rate had no signiﬁcant impact on productivity in their experiment. The explanation they offer is ‘‘subjects had nothing else to do but produce’’ (Esarey et al., 2007). Fig. 2 shows a subject screenshot of the leisure task. When the Leisure tab is active, there is no real leisure activity for subjects to take part in. Subjects could rest their head, daydream, or read quietly, but no suggestions for leisure activities are made.

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The Efﬁciency-Equality Tradeoff in Public Sector Charity Provision

Table 1.

Group Assignment According to Rank in Double Pay Period.

Rank in Double Pay Period

Group Number

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1 2 3 3 2 1 1 2 3 3 2 1 1 2 3

Fig. 2.

Screenshot of a Subject’s Leisure Task.

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This is done to remove any positive or negative framing for taking leisure over labor. External validity lies in favor of homegrown values of leisure, but homegrown values are difﬁcult to measure. In addition homegrown values are too low in the laboratory because subjects participate with intentions to make money and can delay taking leisure until after the experiment. The objective is to take a step closer toward external validity by allowing subjects not only to endogenously choose their productivity output, but also self-select into and out of the taxed labor sector freely. The Regular Pay Periods have the same labor task as the Double Pay Period except subjects receive a lower pay and face redistribution. First, they earn a lower piece-rate of 3 cents for each correct labor task. Second, their labor earnings are subject to redistribution. Subjects’ leisure earnings are free from taxation, so they simply keep their leisure earnings. Subjects’ labor earnings are subject to redistribution as shown in the following equation: B pA i ¼ ð1 tÞpi þ

S 1X tpB 5 i¼1 i

At the end of each Regular Pay Period, pBi represents the labor earnings before taxation and redistribution, and pA i represents the labor earnings after. Here t is the tax rate or the proportion of labor earnings to collect each period for redistribution. The collected labor earnings are put into a Group Account, which is split equally among all members of the group. The redistribution equation keeps subjects from trading positions on the income distribution due to redistribution, so position changes will only occur if a subject becomes relatively more productive (or another subject becomes relatively less productive) in the next period. Subjects receive feedback on how the choices of others in their group affect their earnings through income redistribution. Subjects receive feedback information, shown in Fig. 3, on the right side of their screen. During a period, subjects receive constant feedback on what their labor earnings are before redistribution and how much labor earnings they are transferring to the Group Account. Subjects’ leisure earnings increase continuously whenever their Leisure tab is active. At the end of each period, subjects are given their 20% or one-ﬁfth share of the Group Account. Their total earnings at the end of each period equal: Total earnings ¼ Labor earnings Labor earnings transferred to the group account þ 20% share of the group account þ Leisure earnings

The Efﬁciency-Equality Tradeoff in Public Sector Charity Provision

Fig. 3.

85

Subject’s End of Period Earnings Information.

Subjects are told that if the amount they transfer to the Group Account is larger (smaller) than their 20% share of the Group Account then (1) they have completed more (fewer) sequences than the average member of their group and (2) have contributed more (less) to the Group Account than at least one other member. Also given at the end of each period is additional information on ‘‘Earnings if the entire period was spent taking leisure.’’ This gives subjects their opportunity cost of labor under income redistribution, which is simply their forgone leisure earnings plus their share of the Group Account (without their labor earnings transfer). We tell subjects that this number represents what their earnings could have been if they spent the entire period with the Leisure tab active. Subjects see how this number is calculated in the instructions. It is the maximum leisure earnings of $1.50 (equal to 300 seconds $0.005) plus their 20% share of the Group Account after excluding their transfers. We remind subjects that this is hypothetical earnings and that if everyone in the group spent the entire period in leisure

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then the Group Account would be zero and each member would make $1.50 for the period. Subjects receive this information to help them recognize the incentives present in the design and to lower their decision making cost. The Double Pay Period is the same for both treatments. The Regular Pay Periods differ across treatments only in the tax level. Two treatments are run: a 20% tax rate (t ¼ 0.2) and an 80% tax rate(t ¼ 0.8). Using an acrosssubjects treatment design does have the drawback of sample heterogeneity across treatments, but using a within-subjects treatment design can cloud treatment effects because order effects can arise as productivity and cooperation vary over time with any given tax rate. In all treatments, subjects’ earnings are the sum of their Double Pay Period earnings and Regular Pay Periods earnings. This design creates incentives quite similar to those present in voluntary public goods provision experiments, which also have important implications for charity (Ledyard, 1995; Isaac & Walker, 1988): (1) the pool of funds collected for redistribution are in fact a public good; (2) income earned from leisure provides a pure private return; (3) income earned from leisure provides a private and public return; (4) the supply of labor becomes a 100% contribution to the public good as the tax rate approaches 100%; and (5) subjects are given feedback at the end of multiple periods which allows them to compare their contribution to the public good (labor productivity in this experiment) to other group members’ contributions. There are major differences, however, between this experiment and other voluntary public goods experiments. First, the activity (labor) which increases provision of the public good (the Group Account) yields both a public (taxed labor earnings) and a private return (untaxed labor earnings). The marginal per-capita return from typing one correct sequence differs across tax treatments: 1. The marginal per-capita return from the Group Account is 0.2 0.2 0.03 ¼ $0.0012 for the 20% tax rate and 0.8 0.2 0.03 ¼ $0.0048 for the 80% tax rate. Here the return is 4 times larger in the 80% tax treatment. 2. The marginal after-tax return is 0.8 0.03 ¼ $0.024 for the 20% tax rate and 0.2 0.03 ¼ $0.006 for the 80% tax rate. Here the return is 4 times larger in the 20% tax treatment. 3. The marginal total return to labor is $0.0012 þ $0.024 ¼ $0.0252 for the 20% tax rate and $0.0048 þ $0.006 ¼ $0.0108 for the 80% tax rate. Here the return is 2.333 times larger in the 20% tax rate.

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Leisure yields a 100% private return of $0.005 per second. Effort is not directly observable. Each correctly typed sequence is a function of an individual’s ability, effort, and time supplied to labor, which cannot be perfectly separated. Subjects’ labor time and effort are observable to the experimenter, but subjects do not know other members’ exact time and effort placed into increasing the Group Account. Subjects have to infer what each group member’s labor supply is by comparing their share of the Group Account with their transfers to the Group Account. Finally, the individual returns to labor and leisure are dependent not only on the contributions of others but also on the individual’s productivity. Therefore the endowment of productive ability is endogenous, thus making the ability to contribute asymmetric across subjects.

RESULTS The 20% and 80% tax treatments each consisted of two sessions. All four sessions were conducted using undergraduate students at Georgia State University. Each session included 15 subjects, who were split into three groups of ﬁve for the Regular Pay Periods. Table 2 labels the six 20% tax groups 1–6 and the six 80% tax groups 7–12. Efﬁciency is measured in terms of productivity so the loss of efﬁciency will be measured by the reduction in number of correct tasks completed. Fig. 4 shows the mean number of tasks completed by treatment. Period 0 represents the mean number of correct sequences typed in the Double Pay Period, which shows that on average the latent ability to type sequences is the same across treatments. Periods 1 through 12 represent the Regular Pay Periods. Here the mean of all individual correct tasks completed equals the mean of the group means for each tax rate. Under the 20% tax, production is relatively stable and increases toward the later periods. Under the 80% tax production is more erratic and declines as subjects approach later periods. The mean number of correct tasks performed in the Regular Pay Periods is 50.69 for groups facing a 20% tax with an 8.36 standard deviation across the group means. For groups facing an 80% tax the mean number of sequences typed correctly is 32.32 with an 8.24 standard deviation across the group means. This is a 36.3% average productivity loss for each period. Using a t-test with unequal variances to compare the mean of the group means for each tax level, the null hypothesis that the means of the six group means for the two tax levels are the same is rejected at the 1% level (p-value ¼ 0.0024), with the 20% tax groups being more efﬁcient (p-value ¼ 0.0012).

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Table 2. Group Number 1 2 3 4 5 6 7 8 9 10 11 12

Group Treatment and Session Assignment. Treatment 20% 20% 20% 20% 20% 20% 80% 80% 80% 80% 80% 80%

Fig. 4.

tax tax tax tax tax tax tax tax tax tax tax tax

Treatment Session 1st session 1st session 1st session 2nd session 2nd session 2nd session 1st session 1st session 1st session 2nd session 2nd session 2nd session

Efﬁciency Measured in Productivity by Treatment.

Fig. 5 breaks down the mean number correct by session into four graphs. Each graph shows the mean productivity of each group in the session. Average performance in the Double Pay Period is very close across groups in each session. Production under the 20% tax level is relatively the same for

The Efﬁciency-Equality Tradeoff in Public Sector Charity Provision

Fig. 5. Efﬁciency Measured in Productivity by Session and Group.

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DANIEL T. HALL

Fig. 5.

Continued.

The Efﬁciency-Equality Tradeoff in Public Sector Charity Provision

91

all groups, and the null hypothesis that they are the same cannot be rejected at the 10% level of statistical signiﬁcance. Production under the 80% tax level does vary across sessions as the second session does not have as dramatic decay in productivity as the ﬁrst. This is because the groups in the second 80% tax session choose to be more productive. Using a t-test with unequal variances to compare the mean of the group means for each 80% tax session, the null hypothesis that the mean of the three group means for each 80% tax session are the same is not rejected at the two-tailed test (p-value ¼ 0.2837). Fig. 6 shows the percentage loss in mean productivity over periods. The percentage loss in mean productivity increases over periods. If subjects were merely responding to the decrease in wage from the tax, then the response should happen rather quickly since the changes in wages from the tax are very salient. Subjects are responding to something else, perhaps subjects learn about their productivity and the size of the Group Account over time and decide that leisure is a more attractive option in the 80% tax treatments. Cooperation may play an important role in differences in productivity across groups. The results show a signiﬁcant loss in efﬁciency (productivity) over time when the tax is increased from 20% to 80%. Following Okun’s

Fig. 6.

Efﬁciency Loss Measured in Percentage Change.

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Leaky-Bucket test, is there a gain in equality that would make us tolerant of this efﬁciency loss? There are many ways to measure the inequality of an income distribution. We use the GINI coefﬁcient because it carries the beneﬁt of scale invariance so the inequalities can be compared across treatments. GINI coefﬁcients of labor income inequality and productivity inequality are the same due to scale invariance and the piece-rate pay. The GINI coefﬁcient measures the dispersion of distributions giving a score of 0 for a perfectly equal distribution to 1 for a perfectly unequal distribution. What was the level of inequality in the Double Pay Period, before redistribution was introduced? In the ﬁrst Double Pay Period, the 20% tax groups’ GINI coefﬁcients are 0.081, 0.086, 0.089, 0.117, 0.128, and 0.141 (average 0.107), and the 80% tax groups’ GINI coefﬁcients are 0.111, 0.112, 0.113, 0.118, 0.118, and 0.125 (average 0.116). As the GINI coefﬁcients demonstrate, inequality of productivity in performing the labor task starts low, a consequence of the group procedure designed to create groups similar in distribution of raw ability and the low difﬁculty of performing the labor task. In the Regular Pay Periods, the inequality of labor earnings after redistribution is of central interest for this is the ﬁnal income distribution. The 80% tax is designed to reduce inequality more than the 20% tax, but by how much? Fig. 7 shows how inequality within groups changed during the Regular Pay Periods. Again, period 0 represents the Double Pay Period. Looking at the graphs, there is greater separation in GINI coefﬁcients over periods in the 20% tax sessions. The average of the GINI coefﬁcients for each group over all periods is taken and averaged with the other groups of the same tax rate. This gives an average GINI coefﬁcient of 0.212 for the 20% tax and a GINI coefﬁcient of 0.094 for the 80% tax. GINI coefﬁcients were quite low in both treatments on average, which is likely because labor was homogeneous across tasks leading subjects to become more equal in ability with practice. What are the efﬁciency-equality tradeoffs across groups? Fig. 8 maps the average efﬁciency and inequality averaged over all Regular Pay Periods for each group. It is clear from the graph that there is an overall efﬁciencyequality tradeoff when the redistribution level is increased by increasing labor taxes. However, the tradeoff varies depending on which groups are paired for comparison. If the least efﬁcient 80% tax groups are paired with the most efﬁcient 20% tax groups, a much larger tradeoff (a large drop in productivity for a small gain in equality) is observed. If the most efﬁcient 80% tax groups are paired with the least efﬁcient 20% tax groups, a much smaller tradeoff is observed. Some may argue that the real tradeoff is measured in the long run because individuals learn how redistribution

The Efﬁciency-Equality Tradeoff in Public Sector Charity Provision

Fig. 7.

Changes in Inequality of Labor Earnings by Session and Group.

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Fig. 7.

Continued.

The Efﬁciency-Equality Tradeoff in Public Sector Charity Provision

Fig. 8.

95

The Efﬁciency-Equality Tradeoff (All Periods Averaged).

affects them, and they reduce their labor over time in response to the incentives created by redistribution. In consideration of this argument Fig. 9 shows three graphs of group tradeoffs in the 1st, 6th, and 12th Regular Pay Periods. After the 6th Regular Pay Period, the inequality of labor earnings after redistribution for the two most productive 20% tax groups are actually lower than all the 80% tax groups. The results suggest that it is possible to lose both efﬁciency and equality over time if the tax rate is high enough. If groups are only compared with other groups facing the same tax then there is no tradeoff because efﬁciency and equality move in the same direction. This can be seen in Figs. 8 and 9. This is likely because inequality was already low in the Double Pay Period, so if everyone is working then efﬁciency is high and inequality stays low. Can the tradeoff found be explained by a reduction in work incentives? Although a subjects’ exact effort level cannot be measured, changes in effort can be inferred from: (1) changes in time allocation between labor and leisure and (2) changes in work intensity while performing labor. Changes in time allocation are the primary measure of the effect of income redistribution on work incentives. Fig. 10 shows the mean number of seconds per period spent on leisure. The ﬁgure clearly shows that the

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Fig. 9.

Tradeoff in the 1st, 6th, and 12th Regular Pay Periods.

The Efﬁciency-Equality Tradeoff in Public Sector Charity Provision

Fig. 9.

Fig. 10.

Continued.

Leisure Seconds Taken by Treatment.

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reduction in productivity is coming primarily from subjects spending more of their time in leisure under an 80% tax. Comparing Fig. 10 with Fig. 4, which shows the changes in productivity over periods, one can see that changes in average productivity are almost a horizontal reﬂection of changes in average leisure time. It is because of this strong correlation that graphs showing the breakdown of leisure seconds for each group and each session are not included. Fig. 11 shows histograms of the leisure seconds taken by subjects in the 1st, 6th, and 12th Regular Pay Periods of each tax. The histograms conﬁrm how strongly time allocation is driving the majority of changes in productivity as the vast majority of decisions made involve subjects working the entire time or not at all for both tax treatments. The mean number of leisure seconds is 81.46 (31.63 standard deviation across group means) under the 20% tax and 154.27 (37.36 standard deviation across group means) under the 80% tax. Using a t-test with unequal variances to compare the mean of the six group means of leisure seconds taken over all Regular Pay Periods for each tax level, the null hypothesis that the mean leisure seconds for each treatment are the same is rejected at

Percent 10 20 30 40 50

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Leisure Seconds Taken by Subjects (Bar Width ¼ 30 Seconds).

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the 1% level (p-value ¼ 0.0035) with leisure time being signiﬁcantly less for 20% tax groups (p-value ¼ 0.0018). What happens across treatments when subjects are working? Does work intensity also vary? Work intensity is deﬁned as the number of sequences correctly typed per minute of labor time. The mean number of correct sequences per minute of labor is 13.32 under the 20% tax and 12.43 under the 80% tax. Fig. 12 shows that work intensity is the same under the 20% and 80% tax treatments across periods. Subjects also become more productive in performing the labor task over time in both treatments. Why is there no difference? One explanation is time is money in this experiment: it is rational for a subject to work at their maximum ability even if he or she intends to spend part of the period on leisure. The correlation between work intensity and leisure seconds overall is 0.455, but the correlation is weak (0.092) if you only include observations with leisure seconds less than 270 and strong (0.856) if you only include observations with leisure seconds greater than or equal to 270. Perhaps subjects spending 30 seconds or less on the labor task do not have enough time to get into the groove of typing fast, or are typing slowly because they are already considering switching to leisure. Although insignificant, intensity is slightly less on average in the 80% tax, which could be due to the higher number of subjects spending almost all of their time on leisure.

Fig. 12.

Work Intensity by Treatment.

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How can overall work effort be measured? It is a function of labor time supplied and work intensity. The number of sequences typed correctly serves as their measure of productivity, but the differences in ability must be controlled for. Ability is exogenous in the Double Pay Period, but endogenous thereafter because ability can increase through learning by doing. The effort proxy variable is generated by taking the number of sequences typed correctly in the current period and dividing it by the maximum number of sequences typed thus far in any period. The Double Pay Period is included in case a subject puts forth little effort in the Regular Pay Periods. If an individual scores a 0, then they are not working at all. If an individual’s score equals 1, then they have reached their maximum productivity threshold established in this period or in a previous period. This effort proxy only measures a decrease in effort relative to a revealed maximum productivity level, for increases in effort are confounded with increases in ability. During the Regular Pay Periods, the average work effort measure for any given individual in any given period was 0.75 for the 20% tax treatment and 0.49 for the 80% tax treatment. Fig. 13 shows histograms of the work effort variable for the 1st, 6th, and 12th Regular Pay Periods of each tax rate. The majority of subjects in the 20% tax treatment continue to establish new or come close to their maximum over the periods. 20% Tax 12th Period

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Fig. 13.

0 .2 .4 .6 .8 1 effortproxy = correct/max correct

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Effort Proxy by Subjects (Bar Width ¼ 0.1).

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The majority of subjects in the 80% tax treatment decrease effort in later periods. At the end of each period, subjects are told their hypothetical earnings if they had spent the entire last period on leisure. Some could argue that this information is too salient and encourages subjects to perform leisure if it pays more than labor. Maybe so, but this salient information was given to subjects so the following question can be asked: ‘‘Do subjects follow the myopic best response, or do they have strategic and/or other regarding preferences?’’ A choice is consistent with the myopic best response if they see that they would have been better off (worse off) switching to leisure in one period and, subsequently, they spend the better half of the next period in leisure (labor). Over all decisions made after the ﬁrst Regular Pay Period, 430 of 660 (65.15%) are consistent with myopic best response. However, 230 of 660 (34.85%) are not, including 80 of 330 choices from the 20% tax treatment (24.24%) and 150 of 330 choices from the 80% tax treatment (45.45%). Of the decisions inconsistent with myopic best response, 221 of 230 (96.09%) cases occurred where the subject learned that he or she could have earned more by performing only leisure in the previous period yet chose to spend the majority of the following period on labor instead of leisure. This 34.85% of decisions inconsistent with myopic best response need to be explained. Subjects receive feedback at the end of each period. They are told whether their transfers to the Group Account are above or below the group average. They are told their opportunity cost of labor in terms of their hypothetical ‘‘earnings if entire period was spent on leisure.’’ Finally subjects are told that if everyone takes leisure then the Group Account will be zero for the period and everyone will only make $1.50. Subjects are aware of the non-excludability of income collected for redistribution and are told that the size of the Group Account is conditional on the productivity of the other group members as well as their own. How does this feedback affect individual time allocation between labor and leisure? Fig. 3 shows the feedback given to subjects at the end of each regular pay period. Here they can compare their transfers to the group account (or tax payments) with their share of the group account to see if they contributed more than the group average (themselves included) to the group account. They can also compare their total earnings with their hypothetical ‘‘earnings if entire period was spent taking leisure’’ to see whether they would have been better off not working at all that period. Both of these comparisons are highly dependent on how many sequences the other four members’ type and the amount of labor income they transfer into

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the group account. As seen from Fig. 11, the vast majority of labor–leisure time allocations involved subjects spending the entire period on labor or on leisure. This calls for a tobit random-effects estimation of the panel data which sets limits for the dependent variable, the number of leisure seconds taken in a period, from the left at 0 leisure seconds and from the right at 300 leisure seconds. Table 3 shows results of three separate two-limit tobit estimations of the panel data. The ﬁrst tobit regression includes both 20% tax and 80% tax data for the Regular Pay Periods. The tax dummy variable, equal to 0 for 20% tax data and 1 for 80% tax data, came up highly signiﬁcant and increased the leisure seconds by a large amount. The remaining explanatory variables are lagged because they are the feedback from the previous period Table 3.

Tobit Analysis of Leisure Seconds Taken.

Dep Var: Leisure Seconds

20% and 80% Tax Data

20% Tax Data Only

80% Tax Data Only

n-obs n-groups n-obs per group n-left-censored n-uncensored n-right-censored

660 60 11 167 361 132

330 30 11 97 203 30

330 30 11 70 158 102

Constant

97.536 [35.16] (0.006)

33.022 [88.69] (0.710)

259.94 [58.83] (0.000)

Tax dummy (1 ¼ 80% tax, 0 ¼ 20% tax)

147.896 [43.15] (0.001)

Leisure seconds (lagged)

Others’ mean transfer to GA (lagged and in cents) (Others’ mean transfer to GA)^2 (lagged and in cents)

–

–

0.226 [0.07] (0.001)

0.109 [0.08] (0.192)

0.318 [0.11] (0.003)

2.48 [0.82] (0.002)

1.959 [5.74] (0.733)

3.204 [1.17] (0.006)

.0121 [0.00] (0.017)

0.0414 [0.10] (0.667)

0.0166 [0.01] (0.021)

Notes: Variables signiﬁcant at the 10% level are in bold. Standard errors are in brackets []. P-values are in parentheses ().

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which subjects respond to. The ﬁrst variable, the leisure seconds (lagged one period), is included to control for the possibility that subjects who spend the majority of their time on leisure are more likely to do so in later periods. This variable is signiﬁcant in the tobit regression of all data and the tobit regression of the 80% tax data. The second variable, the others’ mean transfer to the Group Account (lagged one period and in cents), is calculated as the Group Account minus the subject’s transfer to the Group Account with the difference divided by 4. This variable was included to see whether individuals responded to how much the other four members contributed to the Group Account, which they could determine indirectly by comparing the feedback information given to them at the end of each period. The third variable is the second variable squared, which is included to capture a possible quadratic relationship of the second variable to leisure seconds in the current period. Overall, other group members’ transfers to the Group Account were found to signiﬁcantly decrease the number of leisure seconds taken at a signiﬁcantly decreasing rate. The marginal effect of this variable calculated at the mean of the variable is 2.484 þ 2 (0.0121) (55.03) ¼ 1.152. This variable does not come up signiﬁcant when only the 20% tax data is used, but it is signiﬁcant when only the 80% tax data is used (the marginal effect is 3.204 þ 2 (0.0166) (79.93) ¼ 0.55. An alternative dependent variable may be overall work effort as deﬁned previously and shown in the histograms of Fig. 13. How does this information and feedback affect individuals’ overall work effort? Table 4 shows a tobit regression censored from the left at 0 and at the right at 1. Using all of the data there were 157 left-censored observations, 351 uncensored observations, and 152 right-censored observations. The tax dummy shows a signiﬁcant effect on reducing effort. The lagged leisure seconds variable has a negative and signiﬁcant effect on the effort proxy using all of the data and using only 80% tax data. Other group members’ transfers to the Group Account were found to signiﬁcantly increase effort but at a signiﬁcantly decreasing rate. The marginal effect of this variable calculated at the mean of the variable including all data is 0.0079 þ 2 (0.00004) (55.03) ¼ 0.0035. The marginal effect is 0.0111 þ 2 (0.00006) (79.93) ¼ 0.0015 using all data. In both measurements of labor supply, there is some evidence that individuals are responding to the contributions of other members to the Group Account, where the stronger responses are found in the 80% tax treatment. It is also shown that efﬁciency in the 80% tax groups decay over periods in a manner similar to the decay of contributions in voluntary public goods experiments. Recall that at a tax level of 100%, performing labor

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Table 4. Dep Var: Effort Proxy

n-obs n-groups n-obs per group n-left-censored n-uncensored n-right-censored Constant

Tobit Analysis of Effort Proxy. 20% and 80% Tax Data

20% Tax Data Only

660 60 11 157 351 152 0.648 [0.11] (0.000)

330 30 11 38 195 97 0.679 [0.30] (0.025)

330 30 11 119 156 55 0.047 [0.20] (0.815)

Tax dummy (1 ¼ 80% tax, 0 ¼ 20% tax)

0.519 [0.13] (0.000)

Leisure seconds (lagged)

0.0007 [0.00] (0.009)

0.0002 [0.00] (0.605)

0.0009 [0.00] (0.014)

0.008 [0.00] (0.007)

0.0083 [0.02] (0.675)

0.0110 [0.00] (0.008)

0.00004 [0.00] (0.029)

0.0001 [0.00] (0.661)

0.00005 [0.00] (0.021)

Others’ mean transfer to GA (lagged and in cents) (Others’ mean transfer to GA)^2 (lagged and in cents)

–

80% Tax Data Only

–

Notes: Variables signiﬁcant at the 10% level are in bold. Standard errors are in brackets []. P-values are in parentheses ().

tasks becomes a 100% contribution to the public good (the Group Account). If the tax rate is 0%, or if there is no Group Account, then there is no public good and subjects will simply select the activity which pays them more. This means that the 80% tax treatment is more comparable to the standard voluntary public goods provision experiment.

CONCLUSION The results demonstrate the potential for a signiﬁcant efﬁciency-equality tradeoff in government-mandated income redistribution. The tradeoff can be explained by lower work incentives in the high tax treatment. If the

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primary goal of the public sector is to reduce income inequality, they will be successful; income inequality is lower under the high-tax treatment. However, this comes with a signiﬁcant reduction in efﬁciency; output in the high-tax treatment is 36.3% lower than the low tax treatment on average. There will be less income available for charity if the efﬁciency loss from redistribution becomes sufﬁciently large. Signiﬁcant reductions in labor time and overall work effort supplied occurred in the high tax. This supports the hypothesis that lowered work incentives are an unavoidable consequence of income redistribution based on wage taxation. Most of the efﬁciency loss comes from the lower labor time supplied in the high-tax treatment. Subjects in the high-tax treatment are also no less productive when they are working, as long as they spend more than 10% (30 seconds on the Leisure tab) of the period performing the labor task. Constructing a work effort proxy, we ﬁnd that on average subjects work at half of their revealed output capacity in the high-tax treatment. If the public sector implements an intense redistribution program, we might expect fewer charitable goods and services if people signiﬁcantly reduce their labor supply. We ﬁnd some evidence of strategic and other-regarding preferences. 34.85% of subjects’ decisions cannot be explained as myopic best responses to the relative returns to labor and leisure. Since tax revenue was redistributed as a public good, a comparison of this experiment to other public goods experiments was included. The level of cooperation within a group can have a profound effect on group efﬁciency. Here labor participation is the signal of cooperation. One surprising result was that the two most cooperative low tax groups had greater efﬁciency and more equality than all of the high-tax groups. This peculiar result suggests that, if a group is very cooperative, redistribution can do more harm than good regardless of whether your objective is efﬁciency, equality, or providing charitable goods and services. Results from this experiment are based solely upon the size and distribution of labor income. Outside the laboratory, there are of course other measures that go into evaluating the impact of redistribution. For example, although crowd out of charitable public goods is often incomplete, there may be quality effects if government feedback mechanisms are weaker than in the independent sector. On the contrary, some positive unintended consequences may occur. In this experiment, labor activity yielded both a public and a private return, whereas leisure only provided a private return. Outside this experiment, leisure may provide both a private and a public return. People who already spend some of their leisure time volunteering will

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volunteer more as they reduce their labor supply. In fact, volunteerism may increase more than proportionately with leisure time taken if volunteers grow dissatisﬁed with the quality of public charity provision and decide to offer competing alternatives. Future research may want to take account of the quality dimension of charitable goods as well as the unintended consequences of tax policy on the volunteer labor supply.

NOTES 1. The private sector consists of all for-proﬁt ﬁrms, the public sector consists of all government entities, and the independent sector consists of households, nonproﬁt businesses, individual volunteers, and donors (Cornuelle, 1965). 2. Unlike the Laffer Curve, the efﬁciency-equality tradeoff only requires an overall negative labor supply response to higher taxes. 3. The New Jersey Experiment (or Urban Income Maintenance Experiment) showed an insigniﬁcant household labor supply response. 4. Subject instructions for the experiment are located in the Appendix.

ACKNOWLEDGMENTS The experiment was programmed using the Visual Basic Express 2008 software. I thank Jason Delaney, William Holmes, Sarah Jacobson, Todd Swarthout, and Krawee Ackaramongkolrotn for research assistance. I also thank James Cox, Vjollca Sadiraj, Ragan Petrie, Kurt Schnier, David Dickinson, Tim Salmon, Enrique Fatas, and Jean-Louis Rullie`re for helpful comments. I also thank the referee and editors Mark Isaac and Doug Norton for helpful ﬁnal comments. I also acknowledge the generous support from James C. Cox and the Experimental Economics Center at Georgia State University. I hold myself responsible for any remaining errors.

REFERENCES Blumkin, T., Rufﬂe, B. J., & Ganun, Y. (2008). Are income and consumption taxes ever really equivalent? Evidence from a real-effort experiment with real goods. CESifo Working Paper Series. Break, G. F. (1957). Income taxes and incentives to work: An empirical study. The American Economic Review, 47, 530–549. Brown, C. V. (1980). Taxation and the incentive to work. New York: Oxford University Press. Cornuelle, R. C. (1965). Reclaiming the American dream. New York: Random House.

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Dickinson, D. L. (1999). An experimental examination of labor supply and work intensities. Journal of Labor Economics, 17, 638–670. Esarey, J., Salmon, T. C., & Barrilleaux, C. (2007). What motivates political preferences? Selfinterest, ideology, and fairness in a laboratory democracy. Working Paper, Florida State University. Isaac, R. M., & Walker, J. M. (1988). Group size effects in public goods provision: The voluntary contributions mechanism. Quarterly Journal of Economics, 103, 179–199. Laffer, A. B. (2004). The Laffer curve: Past, present, and future, executive summary backgrounder. The Heritage Foundation (1765), 1–18. Ledyard, J. O. (1995). Public goods: A survey of experimental research. In: J. H. Kagel & A. E. Roth (Eds), The handbook of experimental economics. Princeton, NJ: Princeton University Press. Le´vy-Garboua, L., Masclet, D., & Montmarquette, C. (2009). A behavioral Laffer curve: Emergence of a social norm of fairness in a real effort experiment. Journal of Economic Psychology, 30, 147–161. Linster, B. G. (1993). A generalized model of rent-seeking behavior. Public Choice, 77, 421–435. Mueller, D. C. (2003). Public choice III. Cambridge, UK: Cambridge University Press. Okun, A. M. (1975). Equality and efﬁciency: The big tradeoff. Washington, DC: The Brookings Institution. Ottone, S., & Ponzano, F. (2007). Laffer curve in a non-Leviathan scenario: A real-effort experiment. Economics Bulletin, 3(47), 1–8. Stigler, G. J. (1971). The theory of economic regulation. Bell Journal of Economics and Management Science, 2, 3–21. Sutter, M., & Weck-Hannemann, H. (2003). Taxation and the veil of ignorance – A real effort experiment on the Laffer curve. Public Choice, 115, 217–240. Swenson, C. W. (1988). Taxpayer behavior in response to taxation: An experimental analysis. Journal of Accounting and Public Policy, 7, 1–28.

APPENDIX These are the instructions used in the 80% tax treatment. The 20% tax treatment instructions are identical after the ‘‘20% of Your Labor Earnings are Transferred to the Group Account’’ replacement is made oINSTRUCTIONS HANDED OUT BEFORE THE DOUBLE PAY PERIODW No talking allowed Now that the experiment has begun, we ask that you do not talk. We ask that you remain in your seat for the entire time. If you have any questions, please raise your hand and the experimenter will approach you and answer your question in private

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Your labor task You are going to participate in a labor task. Your earnings will be determined by how many times you complete the task correctly Your labor task is to type a sequence of single-digit numbers exactly as they are displayed on a computer screen. Each sequence consists of ﬁve numbers, which are determined randomly. Once you have copied your entire sequence of numbers you will click the ‘‘Submit Your Sequence’’ button A Correctly Typed Sequence

An Incorrectly Typed Sequence

The ﬁgure on the left shows a correctly typed sequence, and the ﬁgure on the right shows an incorrectly typed sequence. Notice that there is no room for error as the incorrect sequence has only one incorrect number (6 is typed in the last box instead of 5) Every time you submit a sequence correctly, your earnings will increase by 6 cents

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If you enter an incorrect sequence, you will not be penalized, but your earnings will not increase when you perform the task incorrectly After you have viewed your results, click the ‘‘Type Another Sequence’’ button to repeat the labor task Periods There are 13 periods in this experiment. Each period lasts 5 minutes and 30 seconds. For the last 30 seconds of each period, you cannot type any sequences. This is done to give you time to review your earnings information The ﬁrst period is called the Double Pay Period. You will be paid 6 cents for each correct task during this period only. This is twice the amount you will be paid for each correct task for the 12 remaining Regular Pay Periods, so take advantage. Your earnings will be displayed in the ‘‘Total Earnings’’ box when the Double Pay Period Summary is displayed oINSTRUCTIONS HANDED OUT AFTER THE DOUBLE PAY PERIODW The regular pay periods You will keep your earnings from the Double Pay Period. You will have the exact same labor task in the next 12 Regular Pay Periods, but your earnings will be determined differently Groups of ﬁve All participants in this session have been assigned to a group with ﬁve members. You will stay in the same group for all of the Regular Pay Periods. Please note that you will not be interacting with any of the other groups in the experiment Earnings calculation for the Regular Pay Periods The third page shows a sample screen shot of your earnings information at the end of a Regular Pay Period. Use this picture as a guide while the remaining instructions describe the types of earnings information displayed. When you are ﬁnished reading instructions, the experimenter will demonstrate how your earnings are calculated each period with examples

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Your labor earnings You will be paid 3 cents for each correct task in the Regular Pay Periods. You will receive continuous feedback on your labor earnings during each period 80% of your labor earnings are transferred to the group account 80% of your labor earnings will be automatically transferred into the group account. This happens to every member of your group. You will receive continuous feedback on your transfers to the group account during each period Your 20% share of the group account Your 20% share of the group account will be revealed at the end of each period once all transfers to the group account are summed together. The group account is then split evenly such that each member of the group receives 20% of the group account Your leisure earnings You may want to take a leisure break after completing the labor task a number of times. If you take a leisure break, you will receive payment for your leisure activities: 1 cent for every 2 seconds of leisure time spent. These earnings are private to you, and none of your leisure earnings will be transferred to the group account Taking a leisure break is easy. Click on the tab labeled ‘‘Leisure’’ to start your leisure break. A blank screen will open up and you will immediately begin to collect leisure earnings. When you are ready to complete more labor tasks click the tab labeled ‘‘Labor’’ Your total earnings Your total earnings will be revealed at the end of each period. Your total earnings are equal to your labor earnings MINUS your transfers to the Group Account PLUS your 20% share of the Group Account PLUS your leisure earnings Earnings if entire period was spent taking leisure This shows information on what your hypothetical earnings would have been if you spent the entire period with the ‘‘Leisure Tab’’ active. This information is revealed at the end of each period.

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Reviewing Your Earnings Information For the last 30 seconds of each period, you will be prohibited from making any labor or leisure earnings. You should take this time as an opportunity to review and interpret what has happened to your earnings this period. Your cumulative earnings for this experiment can also be viewed during this time. Once the 30 seconds are over, a new period will start and you may continue typing sequences or making leisure earnings SAMPLE SCREEN SHOT OF EARNINGS INFORMATION

RETAINED EARNINGS MAXIMIZING NONPROFIT ENTERPRISES Douglas A. Norton ABSTRACT Purpose – The purpose of this chapter is to present a new business model called the Retained Earnings Maximizing (REM) Nonproﬁt Enterprise. Speciﬁcally, the chapter details the nature of the REM enterprise’s motivation, organizational control, market interaction with other ﬁrms, and obstacles to the growth for the REM enterprise. Additionally, the chapter outlines a research agenda for experimental and empirical inquiries into nonproﬁt organizations and the REM enterprise. Methodology – This chapter utilizes standard industrial organization theory in a nonmathematical approach to explaining the nature of the REM enterprise. Findings – The chapter seeks to establish the business model of the REM. By inquiring into the nature of the REM enterprise, the chapter provides the basis for future research. Research Limitations – The research was limited in terms of potential case studies because this is a new business model that is being proposed.

Charity with Choice Research in Experimental Economics, Volume 13, 113–129 Copyright r 2010 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0193-2306/doi:10.1108/S0193-2306(2010)0000013007

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Practical Implications – The chapter could have large practical implications for increased and more consistent revenues to philanthropic organizations. Since writing the chapter, we tried to implement our own REM business model in an on campus coffee shop. Other ventures are being established in a similar vein. Value of the Chapter – The adoption of the L3C legal structure by a handful of states demonstrates the desire to establish new business models with charitable ends. Likewise, the REM business model hopes to increase levels of philanthropy while spurring innovative thought about the Independent Sector which has been underrepresented in economic research.

1. INTRODUCTION The history of monastic beer brewing reaches back into the middle ages and because Benedictine ‘‘rules’’ required monks to produce all things they needed to live, many monasteries have been ﬁnanced by a smooth ale. Beer was a popular and proﬁtable drink then and continues to be popular today; but, many monastery beers are not widely distributed and are produced only to the extent that monks cover the costs of their essentials. One exception to this zero-proﬁt constraint however comes from the Abbey of Scourmont that still produces Chimay Ale. Like other Trappist Orders, the monks at the Abbey of Scourmont make a vow of celibacy, live life in community under an abbot and renounce all claims on personal possessions. But, they still earn ‘‘proﬁt’’ from the sale of their brew and other agricultural products. With that surplus of money however they supply a public good to the nearby city of Chimay, Belgium. According to their website, ‘‘The heart of their life is their work and they try hard by these means to secure aid for the poorest people’’ (Chimay, 2008). This may seem somewhat dissonant with the way economists have been conditioned to think about nonproﬁt organizations because the beer is not actually the public good. Rather, the beer is a private good that competes in the private marketplace with other private goods, but whose earnings will be channeled in a different direction than perhaps the earnings of Budweiser. Early economic work on nonproﬁt organizations developed the notion of quantity maximization subject to a zero proﬁt constraint because that work focused on nonproﬁt hospitals (Newhouse, 1970). In this case the output of nonproﬁt hospitals is the provision of a public good.

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Moving along the continuum, others after Newhouse identiﬁed that nonproﬁts could be quite commercial in nature receiving the bulk of their funds from donations while also selling private goods (Hansmann, 1980). Since then, the addition of commerce to enhance the mission components in nonproﬁts has increased. New independent sector scholarship has commented on the murky distinction between the commercial and the mission-based nonproﬁt models (Dees & Anderson, 2006). Moreover, Dennis R. Young investigates many of the characteristics and emerging blends of nonproﬁt organization and private enterprise that have typically been termed ‘‘social enterprises’’ (Young, 2007). Many of those new emerging nonproﬁt organizations operate in the private marketplace and simultaneously provide a public good. Again, these types of organizations have been termed social enterprises, a term which applies broadly to the many facets in which nonproﬁts operate in the marketplace. Such nonproﬁts include ‘‘New Horizon’’ an Atlanta, Georgia based lawn maintenance company that works for proﬁt while also supplying jobs to people recently released from the prison system. New Horizon provides an environment for these men and women to develop a better reputation and thus open the door for more future job opportunities (ibid.). Another example of this type of social enterprise is Cafe´ Reconcile in New Orleans, Louisiana. Cafe´ Reconcile provides jobs to at-risk youths and trains them in various hospitality jobs at the restaurant, so that they can better compete in the extensive hospitality job market in New Orleans (Jones, 2007). These are just a set of the new and emerging nonproﬁt business models. Also under the social enterprise umbrella are nonproﬁts that are almost indistinguishable in any way from a for proﬁt ﬁrm. Given the inherent instability of voluntary contributions many nonproﬁt organizations are headed towards the marketplace to establish steadier streams of revenue.1 In 2007 the Wall Street Journal published an article titled ‘‘Proﬁts on the Side’’ that discusses the increasing phenomena of ‘‘social franchises.’’ Nonproﬁt organizations such as Share Our Strength who combat world hunger have negotiated with chains such as WineStyles to purchase a franchise. The difference between any other WineStyles and the WineStyles owned by Share Our Strength is not noticeable and the business generates surplus for the beneﬁt of the traditional nonproﬁt organization (DeBaise, 2007). Now we have reached the edge of the continuum of social enterprise, which the Abbey of Scourmont and a ﬁctional business we will call RemMart occupy. The businesses started (Chimay Ale) and will start with their roots as nonproﬁt organizations. Also, they produce private goods, for private enjoyment, but the money retained from the sale of those goods is

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intended for another nonproﬁt and has an obvious public goods component. The nondistribution constraint of the nonproﬁt organization prohibits redistribution to residual claimants and to opportunistic payment of agents inside the nonproﬁt (Hansmann), but it says nothing of the way a nonproﬁt must operate in the marketplace. In fact, the importance of social and commercial combinations for the increase and beneﬁt of mission activity has been discussed in the context of ancillary fee income (James & Young, 2006). Many nonproﬁt organizations are seeing their roles expanding; but, their donations are shrinking or holding constant (Wasley, 2009). The nonproﬁt business type that is proposed here exists for their beneﬁt and is called a ‘‘Retained Earnings Maximizing Nonproﬁt Enterprise’’ (REM).2 The hope is to introduce the REM enterprise as a legitimate and emerging business model that can offer a proﬁtable pipeline from the private sector to undercapitalized philanthropy with more mission-based objectives. The remainder of the chapter is devoted to raising key questions regarding the nature and growth of the REM enterprise, especially with regard to some conjectures and/or questions that admit the need for empirical and experimental testing.3

2. COMMAND AND CONTROL The established economic wisdom of command and control in an organization viewed shareholders as disciplinarians for the actions of managers in a corporation. But, the possibility that shareholders would be uninterested in day-to-day operations called into question their effectiveness as agents of control in an organization (Berle & Means, 1932). Although it may be costly for any individual to organize action against a misbehaving manager (Olson, 1965), there are some stories of pension funds such as TIAA CREF and other companies (most notably Disney) indicating that, if the interests of shareholders and the larger pension funds are aligned, effective action can take place (Deutsch, 2003).4 Nevertheless, in more decentralized setting where interest is high, individual shareholders (or people in a parallel role) may be effective agents of control. However, it is unlikely that interest alone will equip individuals with the knowledge to form their support or criticism of an organization. They must be provided with the information. Individual Americans collectively gave 222.89 billion dollars to philanthropic organizations in 2006. Like publicly traded companies, nonproﬁt organizations are growing toward understanding the importance of information provision to their donors, especially as the stakes have increased (Beatty, 2007).

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To provide that information, organizational transparency has been made a center-piece topic in the discussion for nonproﬁts. Since the emergence of nonproﬁt ‘‘watch dogs’’ such as Charity Navigators and Wall Watchers the cost of withholding information for nonproﬁts has increased.5 In 2007 Business Week said that Charity Navigators was ‘‘revolutionizing the process of giving’’ by providing efﬁciency ratings on their fellow nonproﬁt organizations (Charity Navigators Overview, 2008). Those ratings are based in part on each charity’s IRS Form 990 and several ﬁnancial and performance ratios. But, even though the ratings are useful, they are not without debate because there is the possibility for widely different objective functions among nonproﬁts. We may assume here that the average customer at an REM would not see the lack of one uniform performance measure as a looming issue. There is signiﬁcant evidence that people follow expert advice and people see Charity Navigators as both expert and credible. Whether or not people incorporate Charity Navigators into their charitable gift decisions could motivate future empirical studies.6 Nevertheless, if consumers are willing to accept that the REM chooses to support a nonproﬁt that rates well on the system used by Charity Navigators and that particular charity carries credibility with customers then the residual questions for customers must be about the level at which the REM gives to those charities. The objective function of the REM ought not to be obscure to customers given that it is identical to a proﬁt maximizing ﬁrm. Instead, there are two types of questions of control that might be of interest to customers of a REM. First, there are questions of organizational efﬁciency – the ‘‘reasonableness’’ of executive compensation at an REM is a good example. Second, customers may be interested in how much of the retained earnings are kept to fund internal growth, and how much is actually paid out to recipient nonproﬁts. My conjecture is that, in the absence of shareholders and with organizational transparency, REM customers will act as the agents of control. A general experimental study testing the conjecture is included later in this volume (Norton & Isaac, 2009).7 Questions about the speciﬁc levels of giving necessary to differentiate the product from the average socially responsible ﬁrm and the impact choice of charity has on REM patronage remains untested. Imagine two stores side by side, one store is a local store with a sterling brand reputation that advertises its social responsibility, and another store is local and established as a nonproﬁt organization that advertises its donations, at some level of its retained earnings, to charity. If all other characteristics of the two stores are held constant, will customers, on average, prefer to buy goods from the

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REM (as long as the amount the REM gives is above the social responsibility of the for-proﬁt ﬁrm)? The answer for many people would likely go in favor of the REM. Although purchasing a good they would ordinarily buy, they make a larger contribution to digging clean water wells in Africa or educating orphans. I return to these good deeds later on in the section on market interaction. But, if the perception of the REM is that it does not give ‘‘enough’’ of its retained earnings to charity, the customers may choose to discipline the REM by buying goods at the other store. What this represents in standard economic theory is a principal–agent problem in which each customer implicitly writes a contract with the REM over the level of charitable gift. The question of size ‘‘How much is enough?’’ is an empirical question that could be addressed. Again, the lynchpin feature of the customers as the agents of control in an REM enterprise is the transparent environment where the level of giving, the recipient of the gifts, and the efforts (whether success or failure) of the organization are known. Without the transparent environment, the agent (ﬁrm) will be unable to signal to the principal (customer) that they are making the appropriate charitable decisions.

3. DONATIONS AND QUASI-RENTS There are different expectations for the way people interact with for-proﬁt and nonproﬁt ﬁrms. One signiﬁcant difference is the receipt of donations which are foundational to many nonproﬁt organizations whether or not they chieﬂy procure capital from the sale of goods. If the nonproﬁt is sufﬁciently small, they may be able to receive physical donations from other surrounding businesses, volunteer labor, or lower cost rental space. Some of these donations reduce ﬁxed costs, whereas the potential for volunteer labor effectively reduces the marginal cost for the REM enterprise compared to its for-proﬁt counterpart. Another way to consider size of the REM is the proportion of the market that operates from the REM business model. With small amounts of REMs, we can imagine that these cost-reducing donations will persist. However, the support of for-proﬁt businesses to REMs may dwindle as the proportion of REMs in the market increase. Imagine you are a paint store owner who has already donated paint buckets to three REMs this month. The fourth REM may cross the threshold of your willingness for to pay for charitable activity. With a critical mass of REMs in the market for-proﬁt businesses may be less inclined to donate.

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The idea of the REM as the inframarginal ﬁrm with a lower marginal cost due to input subsidies strikes at the heart of what Marshall called ‘‘quasirents.’’ Marshall took Ricardo’s concept of rents as returns from nature (‘‘the free gifts of nature’’) and focused on the transitional state of the market before complete adjustments. Those extra proﬁts were called quasirents, and he said they would disappear in the long run as all costs became variable (Blaug, 1968). Likewise I will soon discuss how these quasi-rents gained in the short-run picture will evaporate in the long-run as the REM enterprise grows in size. To be clear, the receipt of donations is an important characteristic of the REM enterprise, but it is not imperative. The receipt of donations simply helps the REM enterprise to more quickly cover its costs. That also quickens the ability of the REM enterprise to give its retained earnings to charity which from the aforementioned section is what customers will demand (all else equal).

4. ECONOMIC GROWTH AND THE REM ENTERPRISE Before we discuss why or how REMs may grow, it will be useful to step back and think about the general topic of ﬁrm growth. And to do this, I brieﬂy digress from the ideas of why a ﬁrm, any ﬁrm, exists, and ask whether or not there are any problems with thinking about the REM enterprise in particular. The REM enterprise is an organization that sells typical consumer goods in established markets using inputs for which there are well-known prices. On the basis of this description, it might appear that there is very little Knightian uncertainty to provide returns to the REM entrepreneur.8 However, there may be more uncertainty upon second glance. In the earlier sections, I wrote that the small-scale REM entrepreneur may have an entrepreneurial function like (a) gathering the quasi-rents from donated inputs and (b) capturing demand that is based not only (in part) on price but also on customers’ desires to support, and also see through, the charitable purpose of the REM. Furthermore, there may be even more uncertainty on these issues for the path-breaking entrepreneur who seeks to extend the REM to a larger scale. Because the REMs have not developed into large-scale operations, we say that there is some Knightian uncertainty that goes along with increased size. But, because the REM entrepreneur is working in a well-developed market

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with signiﬁcant certainty in input costs (if the ﬁrm is large), we can regard the REM entrepreneur more as a Coasian manager.9 The Coasian manager organizes the inputs and input quantities in a manner that minimizes cost while seeking other strategies to maximize proﬁts. Thus, the REM entrepreneur is a participant in both Coasian and Knightian theories of the ﬁrm. With these models in mind, I identify three possible barriers to scale expansion of the REM. First, there seems to be a fairly substantial barrier to an increase in the size (or even scope) of the REM due to the evaporation of the procurement of quasi-rents from subsidized or donated inputs. Few people, if anyone, would sign up to work at Wal-Mart as a volunteer or at below-market wage.10 Why is there no willingness to volunteer for Wal-Mart? Is it Wal-Mart’s size, forproﬁt status, public perception or all of the above? Suppose we consider a not-for-proﬁt REM of equivalent scale to Wal-Mart, we call it Rem-Mart. As the ‘‘social distance’’ grows between Rem-Mart and company volunteers, the incentive to free-ride may increase.11 Even with willing volunteers, the coordination of volunteers may become much more difﬁcult at a larger scale. Also, the amount of donated paint needed for a small enterprise is typically less than the paint needed for a large enterprise and therefore is more costly to the owner of the paint store. Thus, my working hypothesis is that quasi-rents are likely to evaporate as the size of the REM increases. The disappearance of those quasi-rents does not mean that a Rem-Mart could not exist. In the previous section, I noted that quasi-rents were an important bonus but not necessarily an imperative for the REM. There is at least one recent historical example of a functional and somewhat successful Rem-Mart albeit the context is atypical. Formed in 1868 in Salt Lake City, Utah, ‘‘Zion’s Co-operative Mercantile Institution’’ was the fulcrum of the co-operative movement in the LDS (Latter Day Saints) church. These smaller retail co-operatives however required a large wholesale storehouse and so ZCMI was built for their distribution. The ﬁnancial success of ZCMI as a wholesaler was immediate and lucrative. Within two years they dispatched many of their competitors who were viewed by LDS leadership as ‘‘opposed to the true interests of Utah’’ (Arrington, 1958). Other smaller retailers wilted or were bought out by private investors. Throughout the transition from the co-operative movement toward private enterprise ZCMI maintained and parlayed their success as a wholesaler into also being a retailer. This lasted until ZCMI was purchased by May Department Stores Company in 1999 after two years of negative proﬁts (ZCMI Sold to May Company, 2008).

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The construction and execution of this project by the LDS church make it atypical for a number of reasons, but it is proof of the existence of a large REM at least for some time. Like ZCMI, an REM may become large, but, after the evaporation of the quasi-rents it will be subject to the same market forces of competition as any other ﬁrm. A second barrier to REM growth exists with regard to customer expectations. Earlier I stated that the objective of the REM was to provide money to other charities. And, I mentioned that the quasi-rents of inputs moved the point of REM proﬁtability (the point at which the earnings are transferred to charity) forward in time. This had the additional effect of allowing an early demonstration of the success of the REM to the customers. If quasi-rents for the REM disappear, the REM may take longer to achieve the point at which their donations to other charities occur. Without being able to observe these donations in an earlier time period, it is unclear how consumers of goods at the larger REM will adjust their expectations. Consumers must be willing to continue to purchase goods at the REM until it is able to rise above the up-front costs and begin to donate retained earnings. There are two methods that may prove useful for larger REMs to signal to customers about correct expectations for the time-frame of transfers. One method is for the manager to advertise this fact by communicating with customers directly: at ground level upon start-up or by an advertising campaign. Another method that may prove useful in retaining the REM’s credibility is the existence of Charity Navigators and Wall Watchers. If the growing REM is open and transparent to these organizations, their statements and rankings may correctly reﬂect the progress of the REM toward future transfers. The third potential barrier for REM growth is capital to ﬁnance growth. A fundamental characteristic of entrepreneurs seeking to grow their businesses is that the funds required for expansion typically exceed the capabilities of what can be ﬁnanced internally (Cooper & Carleton, 1979). But, this is increasingly not an obstacle for nonproﬁt organizations because prudent and passionate nonproﬁt entrepreneurs are able to attract money from venture capitalists. The incidence of venture capitalists involved in business with social rather than proﬁt maximizing goals has increased in past years. And, there is no reason to believe that they would not welcome a hybrid that is commercial in nature but supports donative models. For example, Jeff Skoll, former President of eBay, developed the Skoll Foundation because, ‘‘[he] believes that strategic investments in the right people can lead to lasting social change,’’ (Skoll Foundation, 2008). But, what type of investing is preferred?

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The venture capitalist that deals with nonproﬁt organizations can only invest on a debt basis because there is no equity investment to be had.12 Even if equity investments were available there is much literature that suggests that some debt ﬁnancing is preferred to 100% equity ﬁnancing for the venture capitalist (Cooper and Carleton). For the REM, whose objective is to give their retained earnings to charity, debt ﬁnancing is good news because as it became larger, it would not have to send a larger absolute amount of their retained earnings to the venture capitalist. However, 100% debt ﬁnancing creates an incentive for the social entrepreneurs to engage in more risky ventures. Venture capitalists may see this as either a good or a bad thing. (But, if they’re like the Skoll Foundation description of betting on people, giving the social entrepreneur more liberty may be preferred.) Laboratory economics ought to be able to provide more insight into the nature of contractual arrangements between social entrepreneurs/nonproﬁts and venture capitalists.13 Before completing this section on growth in the REM, let us return to the Coasian manager discussed earlier. One of the chief characteristics of the Coasian manager is that they scan the choice set and make decisions for the ﬁrm that reduce transaction costs and increase proﬁts. Speciﬁcally, here, I discuss two considerations for the Coasian manager of the REM enterprise who must choose between markets or hierarchies. If the REM uses an internal salary lower than the market wage, which is common practice for nonproﬁts (Ruhm & Borkoski, 2003), the employee may be signaling two different kinds of information. The ﬁrst signal is one of alignment where the employee signals that their values are aligned with the values of the nonproﬁt. This is consistent with a literature that suggests trade-offs nonproﬁt employees make with lower salaries for providing a social good (Bacchiega & Borzaga, 2001). The second signal is one of incompetence where the employee signals that they are low skilled and have not or can not succeed in the for-proﬁt world. This is particularly harmful to the nonproﬁts since not having a quality manager increases the ex-ante production function because they cannot efﬁciently allocate inputs. In an effort to shield themselves from the second type of signal, nonproﬁts may be led to choose a hierarchy, developing an internal ‘‘farm system’’ for upper management. I am aware of at least one local example of adverse selection into a lower paying nonproﬁt job and a more formal study could be interesting for future empirical study. One area where the market may be more useful than the hierarchy for the REM is in the promotion of transparency. But, the additional strength of the market may be in the strength of the signal to potential donors.

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Signaling is about perception. For instance, despite the informational advantage inherent in the hierarchy, there may be a stronger signal to the customer if the REM hires a recent MBA from Wharton. Undoubtedly, nonproﬁts experience the tension between the adverse selection problem caused by lack of information and the type of signal they send to donors in their promotions as well as contracting of technical services.

5. REM ENTERPRISE AND MARKET INTERACTION The output of the REM enterprise is not itself the public good. Rather the sale of a private good generates the revenue that allows the nonproﬁt to cover costs and donate the retained earnings to charity. This requires the REM enterprise to compete in a market with other for-proﬁt ﬁrms. From the previous discussion about quasi-rents, we know that the inframarginal REM enterprise may possess some marginal cost advantage over a for-proﬁt ﬁrm. Also, I noted that there may be positive sentiments for shopping at the REM enterprise because the retained earnings are channeled toward helping the impoverished in local and/or international communities. Therefore, the REM enterprise, although selling an identical good may have a differentiated product due to its ﬁrm structure. Even with the differentiated product based on ﬁrm structure I believe we should assume as a working hypothesis that the product is identical in other respects. The attractiveness of the identical goods assumption is that the REM enterprise is subject to the same market forces as other ﬁrms. Even if customers shop at an REM enterprise because of the way the retained earnings are distributed, they will most likely not shop there while simultaneously settling for a signiﬁcantly lower quality product. The products must be at least on par with the competitors. So what is the evidence? There is some evidence that consumers are willing to pay a higher price for a good where a portion of the proceeds are given to charity (Elfenbein & McManus, forthcoming). However, the frequency of purchase and the level of the greater price they are reported to pay lead me to conjecture that, on average, people cannot be counted upon to pay signiﬁcantly higher prices for goods associated with charity. Thus, the idea that an REM could exercise monopoly power, charging a substantially higher price to maximize proﬁts in order to supply the greatest amount of capital to charity (Eckel & Steinberg, 1993) is unlikely.

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However, if customers have some modest preferences over ﬁrm goals, products differentiated on levels of charitable giving could cause increased competition among ﬁrms where each ﬁrm competes over who is most charitable in order to win customers. This would create a market where at the limit even a for-proﬁt ﬁrm approaches the ‘‘social responsibility’’ of an REM enterprise.14 The opposite outcome is segmentation of ﬁrm responsibilities where all for-proﬁt ﬁrms assume the Friedman charge of ﬁduciary responsibility (Friedman, 1970). Then, the REM enterprise is the only type of business the public expects to deliver a portion of its earnings to charity (although this is less likely if we consider charitable acts to be a form of advertising). Notice that the REM business model does not invalidate traditional Industrial Organization theory. The public goods component to the sale of a good that is private in character differentiates the product. The intellectual structure therefore is the same as competition among differentiated products.

6. CONCLUSION The Retained Earnings Maximizing Nonproﬁt Enterprise is a structural and operative speciﬁcation among the set of commercial nonproﬁts termed social enterprises. The REM is physically indistinguishable from the average for-proﬁt ﬁrm save the ‘‘nonproﬁt’’ that might be scripted across the entry doors, but in operation there are several differences. Such differences are most easily visible in table format (Table 1). To summarize the table the REM contains a mixture of a standard commercial ﬁrm and a traditional donative nonproﬁt. Like the traditional nonproﬁt the REM beneﬁts from the quasi-rents received in the form of volunteer labor and donated materials. Likewise, because of its charitable mission the REM may, like the donative nonproﬁt, also receive donations from social entrepreneurs. Venture capitalists may also choose to invest in the REM enterprise; however, if the REM were considering the need for capital formation beyond the amount it could receive from a social entrepreneur it may consider changing to an L3C legal arrangement. The beneﬁt would be the ability to accumulate capital via shareholders with small rates of return. The drawback however to an L3C arrangement would be that the donations would no longer be tax exempt. This is an empirical question about how much those individual donations would likely decrease.

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Table 1.

Similarities and Differences between REM and Others. Commercial

REM Enterprise

Donative Nonproﬁt

Motivation

Proﬁt Maximization for Shareholder Beneﬁt.

Proﬁt Maximization for Supported Nonproﬁt Beneﬁt.

Quantity Maximization for most quality coverage.

Competition

Other Firms

Other Firms

Other Nonproﬁts

Obstacles to Growth of the Firm

Entrepreneurial loss of control.

Difﬁcult to manage consumer expectations, lack of equity investment and quasi-rent loss are associated with growth.

Increased problems with coordination.

Organizational Discipline

Shareholders, Large Funds, Board of Directors and Customers

Customers and Board of Directors

Donors and Board of Directors

Capital Formation

Venture Capitalists and Shareholders

Venture Capitalists, Social Entrepreneurs and Donors

Social Entrepreneurs and Donors

Labor

Hired

Volunteer and Hired

Volunteer and Hired

In other ways the REM has an objective similar to its traditional commercial counterpart, proﬁt maximization. Also, its competitors are other ﬁrms selling products in a private market. All three types of ﬁrms have board of directors as control over the organization. The customers receiving the goods in the REM and the standard for-proﬁt ﬁrm also represent a control of the organization due to the discipline they bring to the market. Similarly, donors in the REM and donative nonproﬁt bring discipline to the actions of organizations. This chapter constructs a foundation for both ﬁeld and laboratory empirical testing of theories about the organization growth and market performance of the REM. Such conjectures include the impact of organizational transparency, contractual arrangements between social entrepreneurs and venture capitalists, and the tension between hierarchy and the market. The prospects for growth in the REM enterprise are exciting because REMs have the potential to increase overall levels of charity and funding to independent sector activity. Moreover, if successful in their increase in the overall level of charity, the REM enterprise may be a crucial catalyst for a

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reversal in government provision of various welfare goods and services, a phenomenon called ‘‘reverse crowd out’’ (Norton and Isaac). Finally, why is this better than a for-proﬁt company like Newman’s Own? In the long run, there are potential problems with both Newman’s Own and the REM. The destiny of a for-proﬁt company is in the hands of shareholders which may change across generations. Meanwhile, the nonproﬁt organization could be prone to mission drift. But, problems exist in any kind of organizational structure. Because the nonproﬁt is legally bound with a nondistribution constraint this may represent stronger and more reliable signal in the marketplace.

NOTES 1. In fact, Community Wealth Ventures, Inc. was founded in 1997 ‘‘on the premise that every organization can increase its social impact by building its own internal assets, rather than relying on support from external organizations.’’ For more information, see Austin and Pearson (1998). 2. The REM has been discussed in the nonproﬁt literature on nonproﬁt organizations but has been broadly deﬁned as a ‘‘social enterprise.’’ The name REM hopes to specify one particular business model among the social enterprise classiﬁcation. 3. The L3C legal arrangement or low-proﬁt limited liability company is also an up-coming model that provides beneﬁts of both a limited liability corporation and more options to raise capital. As of September 2009 these legal structures are only available in a handful of states. For a more extensive discussion of the L3C legal structure, see Americans for Community Development (2009). 4. Shareholder interaction with the Disney Corporation is a well-documented example. 5. This increased cost of withholding information has a simple explanation based on the concept of signaling. As more nonproﬁts provide information, the nonproﬁts that do not provide information transmit a more negative signal in terms of their resource stewardship quality. 6. One recent study in the Rand Journal posed the question of whether people responded to Medicare report cards issued to consumers by the government. Despite large market-based learning the authors ﬁnd a separate effect of those government report cards on plan selection (Dafny & Dranove, 2008). A similar study could be conducted on the importance of Charity Navigators and other so-called watch dog nonproﬁts. 7. The Isaac and Norton experimental design employs the standard voluntary contributions mechanism for public goods and consists of one manager and four customers. The manager chooses the production technology (or the group multiplier), whereas the customers allocate a stock of tokens between their individual and group exchanges. The two treatments of interest are the presence of information

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to the customers in the style of a quarterly report and the importance of an outside option in signaling managerial credibility. 8. Knightian uncertainty represents immeasurable or extremely difﬁcult to measure risk under which an entrepreneur inventing a market must operate (see Knight, 1921). 9. For a discussion of the difference between entrepreneurs as seen by Frank Knight and managers as seen by Ronald Coase, see Boudreaux and Holcombe (1989). 10. Perhaps except for the special case of retired persons who enjoy being greeters. 11. Surprisingly, to my knowledge, there has been little experimental public goods research with respect to social distance. There are some reasons to believe increased social distance negatively effects the level of voluntary contributions to the group exchange. For instance, group size increasing (which is a form of social distance) may be associated with a decrease in lower marginal per capita returns (people beneﬁt less on average from contributions) which induce free riding (Isaac & Walker, 1988a, 1988b). Other partial glimpses at the effect of social distance are increased contributions from face to face strategic communication (Isaac & Walker, 1988a, 1988b) and public goods games with an intentional Christian community (Norton and Isaac, 2009). 12. The Economist magazine (2008) recently featured a short article that discussed the idea of ‘‘philanthropic equity.’’ People buy shares of a nonproﬁt organization and hold onto the shares as they produce ‘‘a signiﬁcant social return on investment.’’ For the venture capitalist this should not change their preference. 13. The third barrier (ﬁnancing for increased expansion of the REM size) could also be handled through an L3C legal structure which would allow for shareholder investment (with small returns) if size does reduce the likelihood of pure charitable donations as conjectured. 14. Firms are becoming more ‘‘socially responsible’’ in terms of their level of giving to charity. One question for publicly traded ﬁrms is how shareholders respond to the increases in socially responsible activity. The question of whether this increased charitable activity by ﬁrms causes a decrease in individual charitable gifts through more traditional avenues has been addressed at least theoretically (Baron, 2007).

ACKNOWLEDGMENTS Thanks to the John and Hallie Quinn Eminent Scholar Chair, Dewey F. Bartlett Fellowship, and the Charles G. Koch Foundation for their support of my academic work. Thanks to session attendants at Southern Economic Association meetings 2008, with a special thanks to Brian McManus for his comments. Thanks to Kurt Schnier for his editorial duties with this chapter and to the anonymous referee for providing some insight on nonproﬁt studies. Finally, thanks to Mark Isaac for my academic development. This is a modiﬁed version of my thesis in which Mark served as my advisor. Any errors in the chapter are my own.

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REFERENCES Americans for Community Development. (2009). Available at http://www.americansforcommunitydevelopment.org. Retrieved on December 7, 2009. Arrington, L. (1958). Great Basin Kingdom: An economic history of the latter-day saints, 1830–1900. Cambridge, MA: Harvard University Press. Austin, J. E., & Pearson, M. D. (1998). Community Wealth Ventures, Inc., Harvard Business School Case 399-023. Bacchiega, A., & Borzaga, C. (2001). Social enterprise as incentive structures. In: C. Borzaga & J. Defourney (Eds), The emergence of social enterprises (pp. 273–295). London: Routledge. Baron, D. P. (2007). Corporate social responsibility and social entrepreneurship. Journal of Economics and Management Strategy, 16(3), 683–717. Beatty, S. (2007). How charities can make themselves more open. The Wall Street Journal, December 10, 2007, Philanthropy, 1–4. Berle, A. A., & Means, G. C. (1932). The modern corporation and private property. New York: The Macmillan Company. Blaug, M. (1968). Economic theory in retrospect. Homewood, IL: Richard D. Irwin, Inc. Boudreaux, D. J., & Holcombe, R. G. (1989). The Coasian and Knightian theories of the ﬁrm. Managerial and Decision Economics, 10(2), 147–154. Charity Navigator-Overview. (2008). Charity navigator-America’s largest charity evaluator| Home. Available at http://www.charitynavigator.org/index.cfm?bay ¼ content.view&cpid ¼ 628. Retrieved on December 10, 2008. Chimay – History, Origin, and Secular Traditions of the Abbey of Scourmont. (2008). Chimay: The art of Trappist cheese and beer. Available at http://www.chimay.com/en/ the_origins_110.php. Retrieved on December 10, 2008. Cooper, I. A., & Carleton, W. T. (1979). Dynamics of borrower lender interaction: Partitioning ﬁnal payoff in venture capital ﬁnance. The Journal of Finance, 34(2), 517–529. Dafny, L., & Dranove, D. (2008). Do report cards tell consumers anything they didn’t already know? The case of Medicare HMOs. RAND Journal of Economics, 39(3), 790–821. Debaise, C. (2007). Proﬁts on the side: Charities and franchises. The Wall Street Journal, July 25. Available at http://www.franchise-hit.com/articles-and-stories/Proﬁts-on-the-Side:Charities-and-Franchises-6657.htm. Retrieved on May 13, 2008. Dees, G., & Anderson, B. B. (2006). Framing a theory of social entrepreneurship: Building two schools of thought. Research on social entrepreneurship, R. Mosher-Williams. ARNOVA Occasional Paper Series, 1(3), 39–66. Deutsch, C. A. (2003). Revolt of the shareholders. New York Times. Available at http:// query.nytimes.com/gst/fullpage.html?res ¼ 9906EEDC133DF930A15751C0A9659C8B63 &sec ¼ &spon ¼ &pagewanted ¼ 3. Eckel, C., & Steinberg, R. (1993). Cooperation meets collusion: Antitrust and the non-proﬁt sector. In: D. C. Hammack & D. R. Young (Eds), Non-proﬁt organizations in a market economy: Understanding newroles, issues, and trends. San Francisco, CA: Jossey-Bass Press. Elfenbein, D. W., & McManus, B. (forthcoming). A greater price for a greater good? Evidence that consumers pay more for charity linked products. American Economic Journal: Economic Policy. Friedman, M. (1970). The social responsibility of business is to increase its proﬁts. New York Times, September 13, pp. 32–33, 122, 124, 126.

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Hansmann, H. B. (1980). The role of nonproﬁt enterprise. Yale Law Journal, 89(5), 835–901. Isaac, R. M., & Walker, J. (1988a). Group size effects in public goods provision: The voluntary contributions mechanism. Quarterly Journal of Economics, 103(1), 179–199. Isaac, R. M., & Walker, J. (1988b). Communication and free riding behavior: The voluntary contribution mechanism. Economic Inquiry, 26(4), 585–608. James, E., & Young, D. R. (2006). Financing nonproﬁts: Putting theory into practice. Walnut Creek, CA: AltaMira Press. Jones, S. A. (2007). Serving up hope. Southern Living Magazine, (October). Knight, F. H. (1921). Risk, uncertainty, and proﬁt. New York, NY and Boston, MA: Houghton Mifﬂin Company. Newhouse, J. P. (1970). Toward a theory of nonproﬁt institutions: An economic model of a hospital. American Economic Review, 60(1), 64–74. Norton, D. A., & Isaac, R. M. (2009). The role of trust, endogenous institutions, and the possibility of grace. Working Paper. Florida State University, Tallahassee, FL, USA. Olson, M. (1965). The logic of collective action: Public goods and the theory of groups, second printing with new preface and appendix (Harvard Economic Studies). Cambridge, MA: Harvard University Press. Ruhm, C. J., & Borkoski, C. (2003). Compensation in the non proﬁt sector. The Journal of Human Resources, 38(4), 992–1021. Skoll Foundation. (2008). About the skoll foundation. Available at http://www.skollfoundation. org/aboutskoll/index.asp. Retrieved on December 10, 2008. The business of giving|Non-proﬁt capitalism|Economist.com. Economist.com. September 11, 2008. Available at http://www.economist.com/research/story_id ¼ 12208564. Retrieved on December 10, 2008. Wasley, P. (2009). Giving takes a beating. Chronicle of Philanthropy, (June). Young, D. R. (2007). A uniﬁed theory of social enterprise. Nonproﬁt Studies Program Working Paper ZCMI Sold to May Company. (2008). Sunstone Magazine, 73. Available at http://www. sunstonemagazine.com/pdf/117-73-79.pdf. Retrieved on May 29, 2008.

ENDOGENOUS PRODUCTION TECHNOLOGY IN A PUBLIC GOODS ENTERPRISE Douglas A. Norton and R. Mark Isaac ABSTRACT Purpose – Motivated by new models of nonproﬁt organizations, we study a voluntary contributions environment in which the productivity of the public goods process is chosen endogenously by a manager. The experimental treatments incorporate two institutions of transparency in the organization, which we conjecture will assist the manager in achieving an outcome superior to the standard free-riding prediction. Methodology – The chapter uses the methodology of laboratory experimental economics. Findings – The ﬁndings demonstrate that transparency institutions can be important for assisting the manager and the stakeholders achieve relative stable and efﬁcient outcomes. Limitations – We discuss obvious areas for further investigation including environments in which ﬁrm productivity is only stochastically related to the decisions of the manager. Practical and Social Implications – The chapter is oriented to real-world issues in the organization of nonproﬁt enterprises, which were a once Charity with Choice Research in Experimental Economics, Volume 13, 131–163 Copyright r 2010 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0193-2306/doi:10.1108/S0193-2306(2010)0000013008

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ubiquitous and now re-emerging source of charitable activity. The chapter is written so that it should be accessible to informed practitioners in nonproﬁt organizations. Originality – The study of endogenous environments and institutions in the provision of charitable and public goods is a relatively new advance and is indeed the theme of Research in Experimental Economics, Volume 13, ‘‘Charity with Choice.’’

INTRODUCTION Too many charities fail to make information about their accomplishments, struggles, boards and executive staff available online. As a ﬁrst step charities should offer detailed ﬁnancial information on their websites. (Sally Beatty, The Wall Street Journal, 2007)

Historically, not-for-proﬁt organizations were viewed as nonproﬁt organizations; that is, their unique status derived not only from the absence of shareholders as the residual claimants on proﬁts but also from a nontraditional objective function, such as output maximization subject to a zero-proﬁt constraint (Newhouse, 1970; Lakdawalla & Philipson, 2006). Both Weisbrod (1977) and Hansman (1980) characterize the production of certain collective or public goods as an important feature of the nonproﬁt organization. New models of nonproﬁts such as the retained earnings maximizing nonproﬁt enterprise (REM) do not themselves produce a public good. Instead, the REM, whose output is not itself the public good, produces and sells private goods for the purpose of donating those retained earnings to other nonproﬁt organizations that produce public goods (Norton, Chap. 4, this volume). The idea of cross-subsidization of different mission activities in a multi-product nonproﬁt (Weisbrod, 1998) is different from the REM which can exist as a freestanding location apart from other mission activities (Norton).1 For example, the nonproﬁt status commits the REM to channel retained earnings from the sale of coffee into other charitable organizations or activities such as digging clean water wells in Africa. The objective function of such a ﬁrm (maximizing retained earnings) resembles that of the traditional for-proﬁt ﬁrm. However, the nonproﬁt status of the REM enterprise raises issues concerning control inside the organization. A long-standing debate in the industrial organization literature is the comparative role of boards of directors compared with shareholders in controlling a for-proﬁt ﬁrm (Berle & Means, 1932). The hypothesis of this research is that, although most nonproﬁts have some sort of board of

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directors, in the absence of shareholders, it is other stakeholders who exercise an alternate locus of control over the nonproﬁt enterprise. These stakeholders could be customers of the product of a retained earnings maximizing nonproﬁt, donors, or volunteers. For purposes of this chapter, we refer to these economic actors as the ‘‘customers.’’ Similarly the donors of donative nonproﬁt organizations are approximately equal to our customers; thus, this has broader application. We believe that crucial tools for customers or donors (customers hereafter) to exercise that command and control are transparency and openness. These hypotheses admit of experimental testing; speciﬁcally, we utilize the well-calibrated environment of the linear voluntary contributions mechanism. Although this is not an environment that perfectly replicates the transactions of the REM business model the linear voluntary contributions mechanism (VCM) is an extremely well-calibrated environment in which we can clearly study the marginal impacts of different information. We characterize the REM enterprise as essentially a proﬁt maximizer (although nothing requires the market to be one of perfect competition). If enough customers have even the smallest preference for shopping at a ﬁrm whose retained earnings will be donated to a charitable activity, then we argue that these customers can become the agents of control over the nonproﬁt managers. We further argue that this control requires two types of transparency: 1. Historical information: We see the customer as an agent of accountability. The manager produces monetary or operational information in the form of ﬁnancial reports to the customers. 2. Outside option: The other concept of transparency evaluates disclosure by the appearance of the manager’s personal credentials admitting a possible outside employment option.2 The manager’s preference for employment in the nonproﬁt ﬁrm is an indication that her values are aligned with the customers.3 In this case, the customers are signal receivers that will decide their level of involvement.4

EXPERIMENTAL DESIGN A laboratory environment capturing all the market features of an REM would be complex: a seller with something akin to a nondistribution constraint to the management but with retained earnings transferred to a charitable activity; customers with valuations over both the product of the seller and over the charitable activity; and an explicit or induced market

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environment. The complexity of such an environment is not its only drawback. This environment is so different from previously examined laboratory markets that a great deal of baseline calibration would be required to evaluate the effects of the experimental treatments. To circumvent these problems, we decided to focus not on the industrial organization aspects of this environment, but rather upon the transparency treatments themselves. Our argument is that if we study behavioral effects of the transparency treatments in a similar but simpler and more calibrated environment, then we will have established a foundation for further research. Thus, our experimental design builds upon the standard linear economic model of public goods provision dating to Isaac, Walker, and Thomas (1984). We describe the experimental design in two stages. First, we set out the decisions and incentives facing the participants without the institutions of transparency. Then, we explain the standard pessimistic hypothesis of behavior. Second, we describe the two institutions of transparency, which comprise the experimental treatments of this research. Our ‘‘public goods enterprise’’ consists of ﬁve individuals: four ‘‘customers’’ and one ‘‘manager.’’ From the point of view of each of the customers, the public goods enterprise looks like a standard linear public goods experiment. Each customer begins each period with 50 tokens. His task is to allocate those tokens between an individual account (returning one experimental dollar per token) and a group enterprise, whose return is the same to all customers regardless of how many tokens each customer invested. Each customer earns from the group enterprise: G ðsum of all investments in the group enterpriseÞ Note that because the return from the private investment is one, ‘‘G’’ is the same as the familiar marginal per capita return (MPCR), but for brevity we continue with the shorter notation. The novel features of our design begin at this point. First, G is unknown to the customers at the time they make their investment decisions. What the customers know is that G is chosen by the manager and that the two possible choices for G are .3 and .75 (these correspond to the low and high MPCRs from Isaac, Walker, and Thomas). The manager also begins each period with 50 tokens, worth one experimental dollar each. In addition, the manager also consumes the return from the public goods enterprise at the same level as provided to any one of the customers. This is true even though the manager has no option of adding tokens to the group enterprise. The manager is permitted to inﬂuence the return from the group enterprise

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by choosing the value of G (.3 or .75) for each period. In each period, a choice of the .75 MPCR can be made at a cost of 30 tokens to the manager, whereas .3 is the default MPCR with no cost. Customers must make their decisions before knowing whether the manager has set G equal to .3 or .75. The customers cannot communicate with one another, nor can any customer communicate with the manager. Furthermore, the decisions are strategically simultaneous; no participant (customer or manager) knows the current-period decision made by any other participant. In our baseline experiments, we reveal another difference from previous public goods research. The only information provided to participants about the public enterprise is their earnings. They are not told how those earnings are determined by the components of customer investment decisions and the manager’s choice of G. Thus, a low level of earnings could come from low investment by other customers, or by a manger choosing G equal to .3, or by some combination thereof.5 The managers, however, have information that reveals the aggregate contributions of the customers, although they do not receive a vector of the individual decisions. Clearly, a standard argument supports a suboptimal outcome as a Nash Equilibrium. Zero investment in the enterprise is a stage game dominant strategy regardless of whether G equals .3 or .75. If the customers follow this dominant strategy, then the best response of the manager based on such expectations of customer free riding is to choose G equal to .3. This is although the group optimum is for the manager to choose G equal to .75 and for each customer to invest all tokens in the enterprise. Over decades of similar public goods experiments, it has become obvious that subjects do not play the linear public goods game as perfectly selfinterested game theorists. Contributions seldom are equal to the pure freeriding prediction. However, even if subjects depart from formal game theoretic models, empirically a pessimistic outlook may be supported. Most public goods experiments begin with some positive level of contribution by at least some agents, with a characteristic decline before a ﬁnite end period. Part of this standard result is there is less provision of the public good with a low MPCR. A pessimistic, suboptimal scenario for this new environment would have customers expecting the manager to set G ¼ .3, responding with relatively low investment. A Pareto-superior outcome for the group would be for the manger to choose G ¼ .75 and for the customers to provide high levels of contribution. The problems in achieving this more efﬁcient outcome are both the coordination and free-rider problems in the absence of any explicit communication, given that customers must make their decisions without

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knowing the choice of the manager. Providing institutions though which these superior outcomes can be obtained is where our two concepts of transparency come into play. Transparency is our primary experimental treatment, and it consists of two distinct channels of information. First there is historical information on what the manager has actually chosen. This allows at least the potential for a manager to engage in reputation-building. We have made a design choice that when historical information is available, it is not available instantaneously. Speciﬁcally, every three periods the experimenter reveals the manger’s choices of G for the previous three periods (akin to a quarterly report). Second, we enact an experimental treatment in which the manger is offered an outside option. The manager may choose to take that outside option which closes the enterprise for that one period and receive her 50 existing tokens plus an additional ‘‘salary’’ of 25 tokens. If the manager accepts the salary from the outside option and closes the enterprise for the period, the customers each earn only their 50 tokens automatically deposited in their individual exchange. The motivation for the outside option is as follows. Nonproﬁt organizations will typically receive donations in the course of their operations. This often includes managers whose skills, education, and credentials would justify a higher salary in the for-proﬁt sector. Through information channels such as the Internet, customers of a nonproﬁt can observe which organizations’ managers are, in fact, forgoing such an ‘‘outside option.’’ The manager may be able to use the fact that she has foregone an outside option to signal that her values line up with those of the customers of the enterprise. This would involve our managers forgoing the outside option to signal that they intend to choose G equal to .75. By modeling the choice of the manager as a best response to the expected behavior of the customers, choosing G ¼ .3 is never optimal once we add the outside option. If the manager expects low levels of contributions (fewer than 74 tokens), the best response is to take the outside option. For higher levels, the optimal choice is to set G ¼ .75. (It must be noted that around the level of 73 tokens, the managerial proﬁt of setting G ¼ .3 is not far below those of the other two options.) In principle, this provides for a 2 2 experimental design based on historical data (yes or no) and availability of an outside option (yes or no). Table 1 denotes the notation we employ in discussing the treatments, as well as the number of experiments conducted. For practical and budgetary reasons, we began this research with the Baseline, No Info, and No O/O sessions. Each session lasted 24 periods. Subjects were recruited through the

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Roadmap to Sessions.

Manager Has Outside Option

Manager Does Not Have Outside Option

Historical information

Baseline (7 sessions: 1–7)

No O/O (7 sessions: 15–21)

No historical Information

No Info (7 sessions: 8–14)

No Transparency

standard XS/FS protocol at Florida State University and were paid their known exchange rate calculation of their experimental earnings on top of a $10.00 show-up fee.6

EXPERIMENTAL RESULTS In this chapter, we focus on aggregate behavior, not the individual results.7

Results from Baseline Experiments Charts displaying the data from all seven Baseline experiments are included as Figs. 1–4. A data point denotes the number of tokens invested in the group enterprise. When a data point has no marker next it, that indicates that the manager opened the enterprise and chose G ¼ .75. A ‘‘.3’’ next to a data point indicates that the manager opened the enterprise with G ¼ .3, and an ‘‘X’’ indicates that the manager chose the outside option. The reference line at GRPX ¼ 73 indicates the point at which the best response of the manager changes from shutting down to opening and choosing G ¼ .75.8 Result: Managers Usually Choose G ¼ .75 Five of seven managers exclusively chose the high MPCR. One manager chose the low MPCR 8 of 24 periods in an intermittent and perhaps even random fashion and another chose the low MPCR in a majority of periods in which the enterprise was open. Result: Although the Outside Option Was Available, It Was Seldom Used by Most Managers Four of the seven managers never used the outside option. It was taken only once by a ‘‘high quality’’ manager who experienced a brief regime of steady

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Sessions 1 and 2 (Baseline).

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SESSION 3 200 180 160

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Sessions 3 and 4 (Baseline).

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Sessions 5 and 6 (Baseline).

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SESSION 7 200 180 160

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Fig. 4.

Session 7 (Baseline).

decay (see Session 2).9 It was taken twice by the manager who chose G ¼ .3 eight times, and it was taken 14 times by the manager who almost never chose G ¼ .75. Result: The Traditional Result of Decay across Periods Is Less Prevalent than Expected in a Standard VCM Environment Table 2 presents the results of simple regressions in which the dependent variable, the aggregate number of tokens invested in the group enterprise, is explained solely by a constant and the period number (1 through 24). In four of the sessions (2, 4, 6, and 7), there is no signiﬁcant decay across periods. Of note, two of the sessions with a signiﬁcant decay coefﬁcient (1 and 5) are the two sessions with managers who chose G ¼ .3 frequently. Although contributions in Session 1 began a late decay in period 22, they were at 75% of the group optimum (equal to the level of period 1) as late as periods 19 and 21. Session 5 had low investment in the group enterprise throughout. Although the typical VCM may be quickly explained by decay across periods, these experiments indicate there is much not being explained by the passage of time. Obviously, something else is going on with these data, and the logical question is whether our concepts of command and control can

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Table 2. Session (Adj R2) 1 2 3 4 5 6 7 a

(0.21) (0.05) (0.45) (0.02) (0.19) (0.03) (0.06)

Constant (t-Statistics) 154.41 92.45 193.47 137.05 26.58 163.62 161.94

(14.00) (6.67) (19.46) (23.61) (4.06) (14.42) (15.95)

Regression Results: Baseline Sessions. Period (t-Statistics) 2.10 0.19 3.06 .29 1.16 0.48 1.13

(2.57) (0.20) (4.41) (.71) (2.53) (0.60) (1.59)

Final Value

Outside Option Taken?

Periods of MPCR ¼ .75

80/200a 85/200 120/200 140/200 12/200b 140/200 125/200

Yes (2 ) Yes (1 ) No No Yes (14 ) No No

14/22 23/23 24/24 24/24 3/10 24/24 24/24

Final value is for period 23. This manage took the outside option in period 24. Final value is for period 17 for the same reason.

b

serve as useful explanations. We decided to ask whether the actions of the manager provided any explanatory power on the aggregate contributions. We believed two aspects of the manager’s behavior contained potential explanations: choice of the outside option and the frequency and pattern of choices of MPCR. Consider the effects of the outside option taken infrequently by two but quite frequently by another of the managers. Perhaps the manager believes that the customers have forgotten that in order to open the enterprise she has forgone the outside salary. By taking the outside salary, she restores her credibility with the customers and signals her quality and future cooperation. Another possibility is that taking the outside option serves as a kind of punishment that only changes behavior in the short run, and it may be for this purpose that it was so frequently employed by the manager in Session 5. Another impact on the time series of tokens produced through the group exchange would seem to be the manager’s selection of the MPCR. As we mentioned, choosing the low MPCR is never a simple best response to expectations about the customers. If a manger’s expectations are sufﬁciently pessimistic, she should take the outside salary. Yet one manager chose the low MPCR one third of the time. Was this use of the low MPCR a clever strategy, or was it ultimately a mistake? We posit that there are three avenues (in addition to the best response argument) by which choosing the low MPCR could be judged to be a mistake for the manager. First, using the low MPCR immediately lowers customer proﬁts. Customers can see the low return from the group enterprise even in periods in which there is no information about the manager’s choice of MPCR. How do subjects respond to this negative hit on proﬁts? It is possible that they respond by lowering their contributions in subsequent periods.

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Second, it would seem to us that a prudent manager would want to develop a reputation for choosing the high MPCR, especially because the choice of the MPCR is revealed to the customer across three periods. A manager who frequently chooses MPCR equal to .3 may develop a reputation that suggests a low likelihood of choosing MPCR ¼ .75 in the future. Finally, we think that a third mistake that a manger might make is switching back and forth from an MPCR of .3 to .75. frequently. Such a manager creates an environment of uncertainty and a reputation of being unreliable. A manager who has chosen a low MPCR and wishes to change directions should probably do so for more than one or two periods to reestablish a reputation of consistently choosing the high MPCR. Conjecture: It Appears that the Manager Plays a Signaling or Co-ordination Role (Beyond the Simple Effect of Choosing a High MPCR) that Favors Increased Cooperation among the Customers The source of this conjecture can be found in the data in Fig. 5. In the top panel, we compare the average level of contributions to the group enterprise to an extrapolated prediction based upon the four-person, .75 MPCR experiments from Isaac and Walker. However, the data from the current experiments are unconditional in that they include observations from periods with G ¼ .3 and in which the enterprise was closed. It is remarkable that even including these observations the current averages are typically at or above this one measure of expectations. An even more interesting comparison comes from the bottom panel which is the average data from the current experiments conditional upon the observation being in Sessions 2, 3, 4, 6, or 7 (the uniformly .75 MPCR managers). It is seen that these sessions are well above the expectations from the .75 MPCR IW data both in level and in lack of decay. Our earliest impressions led us to attempt within-session econometric analysis of the data, but, upon further reﬂection, we concluded that only a between-session analysis could separate the effects of the outside option and information. For example, in Session 2 the manager endured low cooperation in the ﬁrst two periods followed by ten periods of moderate and stable cooperation. But, the 13th period saw the beginning of a slow decay towards free riding and ﬁnally in 18th period the manager took the outside salary, closed the enterprise, and re-opened in 19th period to a more cooperative group over several periods. Visually we can see that there appear to be two regime changes. One occurs around 11th period when the customers exhibit a more pronounced decay, and the second regime change

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Fig. 5.

Comparisons between Baseline Session Means and Isaac and Walker QJE .75 MPCR Results.

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follows the manager’s choice of the outside option in 18th period. Because the manager’s choice of the outside option essentially served to return the group to their earlier pattern of behavior, simple regression analysis shows ‘‘no signiﬁcant effect’’ of the decision of the manager. Also, the incredible stability, at high contributions no less, of some of our observations renders it difﬁcult to separate our hypotheses about manager decisions from the data inside a single session. For example, the data from Session 4 shown below may have suggested that the constant choice of the high MPCR is reputation building/preserving but it may also be that the customers are responding instead to the existence of the outside option. Furthermore, a legitimate hypothesis could be that the customers are not responding to either the information or the presence of the outside option but to the simple existence of the manager. It is with this in mind that we turn to an across-group analysis, ﬁrst with the seven sessions with no information transparency.

Results from the ‘‘No-Information Sessions’’ The data from the seven ‘‘No Info’’ sessions, denoted as Sessions 8–14, are displayed in Figs. 6–9. And, in Table 3 we present the same default regression analyses that we performed for the baseline sessions. Result: There Are More Sessions with a Statistically Signiﬁcant Rate of Decay in the No Info Condition than in the Baseline Condition Six sessions in No Info present with signiﬁcant decay, versus three in Baseline. In addition, only 2 of the 5 mangers always choose G ¼ .75 when open, compared with 5 of the 7 managers in the baseline condition. Again, only three of the managers actually used the outside option. Result: In Comparing the Unconditional Means of Investment in the Group Enterprise, We Find that the Average from the Baseline Condition is Almost Always Greater than No Info Condition, often Signiﬁcantly So The top panel Fig. 10 exhibits the comparison. The Baseline mean is greater in 21 of 24 periods, and a proposed treatment effect is statistically signiﬁcant (critical p ¼ .082 using a Wilcoxon rank sum test) in 8 of those 21 periods (marked with ‘‘S’’). There are a couple of intriguing facts that can be observed from this comparison. First, the data are almost identical in the ﬁrst two periods, but they separate following period 3, when the Baseline customers receive their

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Fig. 6. Sessions 8 and 9 (No Info).

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Sessions 10 and 11 (No Info).

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DOUGLAS A. NORTON AND R. MARK ISAAC SESSION 12 200 180

.3

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Fig. 8.

8

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9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Period

Sessions 12 and 13 (No Info).

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Endogenous Production Technology in a Public Goods Enterprise SESSION 14 200 180 160 140

.3 .3

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80

.3

60

.3

.3 .3

40 .3

20 0

X X X X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Period

Fig. 9. Session 14 (No Info).

Table 3. Session (Adj R2) 8 (0.46) 9 (0.03) 10 (0.33) 11 (0.19) 12 (0.20) 13 (0.14) 14 (0.42)

Regression Results: No-Information Sessions.

Constant (t-Statistics) 102.94 107.77 140.41 114.24 159.11 81.88 114.90

(8.81) (12.85) (19.46) (18.48) (4.06) (5.03) (13.50)

Period (t-Statistics) 4.09 0.77 1.69 1.09 0.86 2.45 3.97

(4.56) (1.32) (3.54) (2.50) (2.62) (2.15) (4.20)

Final Value 50/200 61/200 85/200 82/200 150/200 60/200 125/200

Outside Option Taken? Yes (7 ) No No No No Yes (7 ) Yes (4 )

Periods of MPCR ¼ .75 5/17 24/24 24/24 20/24 21/24 8/17 10/20

ﬁrst quarterly report. Second, notice that the gap closes in the last three periods, perhaps indicating an end-of-experiment effect that transcends any effect of the information condition (in the last three periods, there will be no effective use for the information for periods 22–24). Making a comparison of means conditional upon the manger being one who always opens with G ¼ .75 is difﬁcult because there are only two sessions in the No Info condition that meet this criterion. However, the data

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DOUGLAS A. NORTON AND R. MARK ISAAC AVERAGE GROUP INVESTMENT: BASELINE VS. NO INFORMATION 200 180 160

GRPX

140 120

S S

S

S

S S

S S

BASELINE

100 NO INFO

80 60 40 20 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 PERIOD AVERAGE GROUP INVESTMENT: BASELINE VS. NO INFO (CONDITIONAL ON MPCR = .75)

200 180 160

BASELINE

GRPX

140 120 100 80 60

NO INFO

40 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Period

Fig. 10. Means Comparisons of Baseline vs. No Info. (In the Top Panel, ‘‘S’’ Signiﬁes a Statistically Signiﬁcant Difference for that Period Based Upon a Nonparametric Test.)

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are presented, with no signiﬁcance calculations, in the bottom panel of Fig. 10. The direction of the result is that the lack of the quarterly report reduces investment in the group enterprise even conditional upon being in a .75 MPCR group.

No-Outside-Option Sessions The data from the seven No-Outside-Option sessions, denoted Sessions 15–21, are displayed in Figs. 11–14 (the comparison line, however, in these ﬁgures is 68 tokens, the number of tokens in the group exchange at which the manager earns more money by choosing MPCR ¼ .75 rather than .3). And, in Table 4 we present the results of the same default regression analysis as before. Result: The Data from the ‘‘No-Outside-Option Sessions Look more Like the ‘‘No-Information’’ Sessions than the ‘‘Baseline’’ Sessions This is true in terms of number of sessions with statistically signiﬁcant negative coefﬁcients on period decay (ﬁve in ‘‘No-Outside-Option’’ versus six in ‘‘No-Information’’ and three in ‘‘Baseline’’). It is true in terms of number of managers who always choose MPCR ¼ .75 when open (zero versus two in ‘‘No-Info’’ and ﬁve in ‘‘Baseline’’). From a purely subjective perspective, a graphical comparison of periodby-period mean levels of investment in the group enterprise (GRPX) across all three treatments is instructive (Fig. 15, top panel). Result: In a Direct Comparison between the Baseline Sessions and the NoOutside-Option Sessions, One Finds that the Mean Investment in the Group Enterprise is Higher in the Baseline Sessions in All 24 Periods, and a RankSum Test Finds a Statistically Signiﬁcant Difference in the Two Samples in 10 of 24 Periods (Fig. 15, Bottom Panel) Statistically, the simple partial effect of removing the outside option is equally harmful to the provision of the public good as the partial effect of removing the quarterly information. Like the previously explained treatments, this treatment, on average, begins with moderate contributions. Over time, no outside option tracks closely with no information, and both are below the baseline treatments where both information and the outside option are present. We were somewhat surprised that the ‘‘No-Outside-Option’’ condition proved to be indistinguishable from the ‘‘No-Information’’ condition. The ‘‘No-Information-Condition’’ appeared to us to place customers in a more

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DOUGLAS A. NORTON AND R. MARK ISAAC SESSION 15: NO OUTSIDE OPTION 200 180 160

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Fig. 11.

Sessions 15 and 16 (No Outside Option).

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Endogenous Production Technology in a Public Goods Enterprise SESSION 17 200 180 160 140 GRPX

120 100 .3 80

.3

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.3

60 40

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200 180 160

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60 40

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Fig. 12.

Sessions 16 and 17 (No Outside Option).

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DOUGLAS A. NORTON AND R. MARK ISAAC SESSION 19 200 180 160

GRPX

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60 40 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Period

Fig. 13.

Sessions 19 and 20 (No Outside Option).

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Endogenous Production Technology in a Public Goods Enterprise SESSION 21 200 180

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100 80 60 40 20 0

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Fig. 14.

Table 4. Session (Adj R2) 15 (0.48) 16 (0.25) 17 (0.15) 18 (0.30) 19 (0.17) 20 (0.00) 21 (0.04)

Regression Results: No-Outside-Option Sessions.

Constant (t-Statistics) 95.16 105.20 73.95 94.50 142.28 97.81 141.44

Session 21 (No Outside Option).

(9.10) (8.86) (11.43) (7.33) (12.33) (11.00) (15.84)

Period (t-Statistics) 3.22 2.42 1.00 2.99 1.95 0.59 0.10

(4.64) (2.91) (2.21) (3.31) (2.41) (0.95) (0.17)

Final Value

Outside Option Taken?

Periods of MPCR ¼ .75

10/200 51/200 55/200 22/200 60/200 80/200 68/200

NA NA NA NA NA NA NA

7/24 16/24 16/24 5/24 21/24 19/24 15/24

uncertain environment, both with regard to the manager’s past and future actions. The lack of information obscures the manager’s past choices. The presence of the outside option provides another choice to the manager which would seemingly create more customer uncertainty about the manager’s future behavior. Instead, it appears that taking either transparency condition away from the baseline has similar effects on the provision of the public good.

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DOUGLAS A. NORTON AND R. MARK ISAAC COMPARISON OF MEAN INVESTMENT IN GROUP ENTERPRISE ACROSS THREE TREATMENTS 200 180 160

GRPX

140 120 BASELINE

100 80 NO O/O

60

NO INFO

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140 GRPX

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S S

S

S

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100 80 60

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40 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Period

Fig. 15. Comparison of Means (In the Bottom Panel, ‘‘S’’ Signiﬁes a Statistically Signiﬁcant Difference for that Period Based On a Nonparametric Test).

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CONCLUSIONS AND THOUGHTS ABOUT FUTURE RESEARCH The world in which a group enterprise has access to two transparency conditions (historical information and the presence of an outside option) supports levels of public goods provision that are greater and more stable than would be expected in a traditional voluntary contributions process. Provision of the public good suffers when either of the transparency conditions is removed. The question is why? There may be a temptation to reduce explanations for the lower levels of public goods provision solely to the mechanical choice of production technology since both of the partial conditions feature a more frequent choice of G ¼ .3. But, there are some obvious behavioral reasons for this fact. In the absence of historical information, the manager may take the anonymity as a license to ‘‘shirk’’ without the customers’ knowledge that it was the manger’s actions that led to the souring of the public goods provision. Without the outside option the manager has only one means, rather than two, by which she can intervene in the public goods process. If customer contributions fall, the manager’s only options are either to do nothing or to change the MPCR. But, whereas using the outside option is a sequential and an immediately advertised decision, there appear to be signiﬁcant coordination issues with the manager’s ability to use the simultaneous and delayed-information tool of changing MPCR as a spur to increase contributions. On the contrary, we found some indication that customers are more ‘‘cooperative’’ in the Baseline condition even when standardizing on the manager’s choice of MPCR.10 This indicates that the two transparency conditions are inﬂuencing both customer and manager behavior in a simultaneous fashion in a way that will require more work to disentangle. One possible avenue of future research along this line could be to select the managers on a pre-speciﬁed criterion.11 In any event, the lesson for REM and other nonproﬁt organizations is clear. Transparency matters. Manager credentials and employment paths can be posted and kept current on websites. Boards of Directors can disseminate reliable performance measures, either independently or through nonproﬁt rating services such as Charity Navigators. The conclusions above are strikingly similar to those of a Wall Street Journal article (Beatty, 2007) on charity transparency. Such activities may be costly to nonproﬁts, but this research suggests that they have the potential to support a behavioral equilibrium that beneﬁts both the organization and its customers.

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In contrast to our claims that the presentation of ﬁnancial, management, and other information would be advantageous, some nonproﬁt managers continue to be wary of transparency. Beatty captures this reluctance to transparency as follows: ‘‘Charities worry that too much candor about their struggles could cause donors to take their money elsewhere.’’ Our experimental environment features managers with certainty over their choice of the public goods production technology. Implicit, however, in Beatty’s description of the managerial perspective is the notion that managers do not have perfect control over the production technology. An interesting variation on the current design would be to make the actual production technology dependent upon the manager’s choice, but, stochastic in realization. This would capture one kind of ‘‘noisiness’’ in nonproﬁt decision-making. An obvious treatment would be to distinguish between information that reports only the realized outcome of a noisy production technology to one in which transparency reveals both the outcome and the manager’s choice.

NOTES 1. The REM nonproﬁt business model is under a larger banner of nonproﬁt social enterprises. For further reading about social enterprises see Young (2007). 2. This information could easily be referenced on the REM’s website. 3. ‘‘Finding Leaders for America’s Nonproﬁt Reports’’ (The Bridgespan Group, 2009) lists inability to compensate as the leading reason for not being able to ﬁnd a suitable leader. The willingness of most leaders to take less money at a nonproﬁt versus a for-proﬁt is due to alignment with the values of the nonproﬁt and was noted in a previous Bridgespan report (Tierney, 2006). 4. We have found that Espinola-Arrendondo and Munoz-Garcia (2007) have developed a game-theoretic model of an almost identical phenomenon. It appears that they posit a follower’s utility function incorporating a ‘‘concern’’ about whether a leader has declined an outside option; the source of the concern is not speciﬁed, but it does not appear to be inconsistent with the signaling motivation we report here. 5. There are higher levels of provision that will signal a manger’s decision. If customers see that the return from the group enterprise exceeds 60 experimental dollars, they have information to conclude that the manager must have chosen an MPCR equal to .75. Likewise, customers may, in certain situations, be able to ﬁgure out bounds on the behavior of other customers (an extreme example would be if earnings from the group enterprise were zero). 6. Each session was preceded by eight ‘‘practice’’ periods. The subjects were paid for those periods, but at a lower rate. Before the actual 24-period experiment began,

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subjects were reassigned roles and groups. In one case in the Baseline condition, we were able to conduct an experiment with only one group of ﬁve subjects. Because this created a potentially unique information condition (there was no possible reassignment of groups), we balanced each of the remaining treatments to include exactly one single-group observation. Also, in the treatment lacking the outside option, the possibility of an outside option was removed from the instructions. Likewise, in the treatment lacking the quarterly reports, all reference to the possibility of historical information was removed from the instructions. This means that subjects in the ‘‘no-outside-option’’ condition are in a different information condition than those in the baseline condition who know that an outside option is a possibility, but don’t see their manager choosing it. 7. In prior discussion of this research, we reported the results of four additional sessions with this same design. In re-initializing the computer program for additional sessions, we discovered an error in the way subject proﬁts were reported to the subjects. Although the results of those ﬁrst experiments are quite consistent with the ones reported here, we decided to be cautious and remove them as research sessions. The data from these sessions are available upon request. 8. The GRPX ¼ 73 line is included as a broad-brush reference. In the stage game, managers do not know customers’ decision when they make their decision on the MPCR, so there is not an actual ‘‘best response’’ choice. A stage game in which managers knew customer decisions before they made their MPCR choice would have a different game theoretic structure than the one in this research. 9. When we refer to a manager as ‘‘high quality,’’ we mean that the manager consistently chooses a G equal to .75. 10. In using the term ‘‘cooperative,’’ we are not intending to make a choice among any one of the numerous hypotheses about individual preferences and/or behavior that have grown out of the public goods literature. 11. We were thinking of a pre-selection based on an understanding of the coordination issues involved in the choice of the outside option and the MPCR. Others have suggested pre-selection based on a criterion such as altruism (behavior in a prior dictator game, for example).

ACKNOWLEDGMENTS The program for this research was constructed on z-Tree (Fischbacher, 2007). We thank Austin Boyle and Sean Collins for research assistance, and Kurt Shnier for serving as editor on the chapter. We also acknowledge the generous support of the John and Hallie Quinn Eminent Scholar Chair, the National Science Foundation (SES-0849272), and the Charles Koch Foundation. The comments of seminar participants at Florida State University and Georgia State University are greatly appreciated, but we are alone responsible for any remaining errors.

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REFERENCES Beatty, S. (2007). How charities can make themselves more open. Wall Street Journal, December 10 (special section ‘‘Philanthropy’’). Berle, A. A., & Means, G. C. (1932). The modern corporation and private property. New York: The Macmillan Company. Espinola-Arrendondo, A., & Munoz-Garcia, F. (2007). The importance of foregone options: Generalizing social comparisons in sequential-move games. Working Paper. Department of Economics, University of Pittsburgh. Fischbacher, U. (2007). z-Tree: Zurich toolbox for ready-made economics experiments. Experimental Economics, 10, 171–178. Hansman, H. (1980). The role of non-proﬁt enterprise. Yale Law Journal, 89, 835–901. Isaac, R. M., Walker, J. M., & Thomas, S. (1984). Divergent evidence on free riding: An experimental examination of possible explanations. Public Choice, 43, 113–149. Lakdawalla, D., & Philipson, T. (2006). The non-proﬁt sector and industry performance. Journal of Public Economics, 90, 1681–1698. Newhouse, J. (1970). Toward a theory of non-proﬁt institutions: An economic model of a hospital. American Economic Review, 60, 64–74. The Bridgespan Group. (2009). Finding leaders for America’s nonproﬁts. Available at http:// www.bridgespan.org/ﬁnding-leaders-for-americas-nonproﬁts.aspx Tierney, T. J. (2006). The nonproﬁt sector’s leadership deﬁcit. The Bridgespan Group. Available at http://www.bridgespan.org/LearningCenter/ResourceDetail.aspx?id ¼ 948 Weisbrod, B. (1977). Not-for-proﬁt organizations as providers of collective goods. In: Weisbrod, et al. (Eds), The voluntary non-proﬁt sector. Lexington, MA: Lexington Books. Weisbrod, B. (1998). To proﬁt or not to proﬁt: The commercial transformation of the nonproﬁt sector. Cambridge, UK: Cambridge University Press. Young, D. R. (2007). A uniﬁed theory of social enterprise. Georgia State University, Nonproﬁt Studies Program Working Paper.

APPENDIX These sample instructions are from the Baseline condition. The No-Information and No-Outside-Option conditions followed the same pattern, with appropriate modiﬁcations. The ﬁnal version of the instructions also included screen prints, and a one paragraph introduction to the eight practice periods. Introduction This is an experiment in the economics of decision making. If you follow the instructions carefully, you could earn a considerable amount of money, which will be paid to you in a check at the end of the experiment. You and four other participants are members of a ﬁve-person group. Throughout this session, four of you will be customers of a group enterprise

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and one of you will be the manager of the same group enterprise. Whether you will be a customer or the manager will be determined randomly by the computer. The proﬁt opportunities for the customers and the manager are different and will be explained in turn. In today’s experiments there are 24 periods. From this point on, everything on your screen is your own private information, and there should be no communication with any other participant except as you are directed in these instructions. All costs, proﬁts, and so forth during the experiment today are denominated in experimental dollars. You will be paid one U.S. dollar for every 100 experimental dollars that you earn.

Instructions for Customers Each customer begins each decision period with 50 tokens. The decision for each customer is how many tokens to invest in his/her individual account and how many tokens to invest in the group enterprise. Each customer may invest all 50 of his/her tokens in the individual account, or all 50 tokens in the group enterprise, or any combination in between. The only restriction is that the sum of the two must equal 50 tokens. Tokens may not be carried over from one period to the next. Tokens invested in a customer’s individual exchange earn 1 experimental dollar per token with certainty. Tokens invested in the group enterprise earn proﬁts for each customer in a different fashion. Each customer earns proﬁts in experimental dollars from the group enterprise based on the total number of tokens invested by all four customers in the group enterprise, according to the following rule: Customer earnings from the group enterprise ¼ G times S where G will be explained in the next paragraph, and S equals the sum of all of the tokens invested in the group enterprise. In today’s experiment, G will be either .3 or .75, depending on the decision of the manager. Customers will not know whether G equals .3 or .75 at the time they make their investment decisions. Notice that this part of each customer’s earnings depends only on the total of all of the tokens invested by all four customers. Whether a single customer invested zero, one, twoyor 50 tokens is irrelevant once the sum is determined. All customers earn an equal amount from the group enterprise.

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Instructions for the Manager The manager in each group begins a decision period also with 50 tokens. The manager, just as the customers, earns a proﬁt in experimental dollars from the group enterprise based upon the following rule: Manager earnings from the group enterprise ¼ G ðsum of all tokens invested by customersÞ It is important to notice that managers do not have the opportunity to invest tokens in the group enterprise. The sum of all tokens invested refers only to tokens invested by the customers. What the manager does choose, however, is the value of G, which can be either .3 or .75. If the manager keeps all of his tokens in his/her individual exchange, then the value of G is .3. However, the manager may make a ‘‘management investment decision’’ to increase G to .75. This involves paying 30 tokens out of the manager’s individual account. Tokens retained in the manager’s individual account earn the manager one experimental dollar per token. The manager has the opportunity to choose G at the beginning of each period.

Instructions for Everyone Managers have, at the beginning of each period, the option of closing the enterprise for that period. If a manager closes the enterprise, no customer has any opportunity to invest tokens, and no one receives any payment from the group enterprise. Each person, both customer and manager, receives 50 experimental dollars for their stock of tokens which are automatically invested in the private exchange. The manager, however, by closing the group enterprise, also receives a certain ‘‘outside salary’’ of 25 tokens. In such an instance, the manager’s total earnings for that period are 50 þ 25 ¼ 75 experimental dollars.

How Each Period Proceeds At the beginning of each period, the manager must decide whether to close or open the enterprise for that period. If the manager decides to close the enterprise and take the additional outside salary of 25 tokens, the customers will be so notiﬁed. If the manager decides to open the enterprise he/she will have to choose whether G ¼ .3 or .75. If the manager chose G ¼ .75, he/she

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will be charged 30 tokens. The customers do not initially know whether the G chosen is .3 or .75, although as we will discuss below, they will be told later. If the manager chooses to open the enterprise, the customers will make their investment decisions. After all of the investment decisions are made, all participants will be shown their earnings. The customers will be told their earnings from their individual exchange and from the group enterprise. They will not know the total number of tokens invested in the group enterprise. The manager will be told the total number of tokens invested in the group enterprise. Additional Information Every three periods, the customers will receive a ‘‘quarterly report’’ that reveals the manager’s choice of G for the previous three periods. Final Summary Customer tokens invested in the individual exchange earn a certain return of one experimental dollar. Customer tokens invested in the group enterprise earn for each customer and for the manager an amount of experimental dollars based upon both (1) whether the manager choose G ¼ .3 or to .75 and (2) the total number of tokens invested in the group exchange by the customers. The manager earns one experimental dollar for each token kept in his/her individual exchange. The manager can spend 30 tokens to increase G from .3 to .75. The manager has the option of closing the enterprise and taking an additional outside salary option of 25 experimental dollars for that period (which is in addition to the 50 experimental dollars in his/her individual exchange).

WHAT CAN SOCIAL PREFERENCES TELL US ABOUT CHARITABLE GIVING? EVIDENCE ON RESPONSES TO PRICE OF GIVING, MATCHING, AND REBATES Linda Kamas and Anne Preston ABSTRACT This chapter investigates the relationship between heterogeneous social preferences and charitable giving under alternative prices of giving and types of subsidies. Using 10 allocation decisions, we categorize participants’ social preferences as self-interested, inequity averse, or social surplus maximizing. In subsequent charitable giving treatments, analysis of within-person decision-making gives support for several predictions consistent with social preference types: social surplus maximizers are most likely to give to a charity that increases production; inequity averters give more to charity than do other groups; all preference types give more when the price of giving declines; and social surplus maximizers are more responsive to the price of giving than are inequity averters.

Charity with Choice Research in Experimental Economics, Volume 13, 165–199 Copyright r 2010 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0193-2306/doi:10.1108/S0193-2306(2010)0000013009

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INTRODUCTION Social preferences, or concern for the welfare of others, play a key role in inﬂuencing individuals’ charitable giving. Therefore, if people differ in the type of social preferences they hold, the amounts given, charities chosen, and responses to incentives to donate may vary among individuals in predictable ways. In previous work (Kamas & Preston, 2009), we found that preferences are heterogeneous and two-thirds of the participants make allocation decisions consistent with self-interest, inequity aversion, or social surplus maximization. The current study examines whether behaviors that are associated with these social preference categories cross over to a different giving situation, that is, we compare within-person giving in different environments. Using a 10-question exercise, where the participants are asked to allocate money among themselves and two other people in the room, we categorize individuals as inequity averters, social surplus maximizers, or primarily self-interested. We also give them the opportunity to donate money to one of two charities (America’s Second Harvest, recently renamed Feeding America, or ACCION USA) under various matching or rebate subsidies. We investigate whether people in particular social preference categories behave in ways predicted by economic theory when they select a charity, choose a donation amount, and respond to changing prices of giving.

IDENTIFYING SOCIAL PREFERENCES AND THEIR IMPLICATIONS FOR CHARITABLE GIVING Social Preferences Following recent literature on social preferences, we specify a general utility function that can represent preferences of self-interested individuals, inequity averters, and social surplus maximizers:1 ( ) ai X bi X U i ðpÞ ¼ pi di max½pj pi ; 0 þ max½pi pj ; 0 ðn 1Þ jai ðn 1Þ jai X þ ri lij pj ð1Þ j

where p is a vector of income of individuals i ¼ 1, y, n, and aiZ0, 1WbiZ0, and lijZ0 for all ai, bi, and lij. The Fehr and Schmidt (1999) speciﬁcation of

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inequity aversion is imbedded in the second full term of the utility function and is weighted by di. Social surplus maximizers value the total income or surplus as well as their own income and their preferences are included in the third term and weighted by ri. Letting pH if pj 4pi and pLj ¼ pj if pj opi j ¼ pj

hdi ai ldi bi di ai X H þ ri lii pi U i ðpÞ ¼ 1 þ p ðn 1Þ ðn 1Þ ðn 1Þ jai j (2) X di b i X L þ pj þ ri lij pj ðn 1Þ jai jai where h is the number of others with income higher and l the number of others with income lower than that of person i. X X X U i ðpÞ ¼ g1 pi þ g2 pH pLj þ g4 lij pj (3) j þ g3 jai

jai

jai

where g1 ¼ 1 þ hdiai/(n 1) – ldibi/(n 1) þ rilii g2 ¼ diai/(n 1) for pjWpi g3 ¼ dibi/(n 1) for pjopi g4 ¼ r i The self-interest category corresponds to the usual assumption in which the person cares only about own payoff so that incomes of others do not affect utility. Therefore di ¼ ri ¼ 0, g1 ¼ 1, and g2 ¼ g3 ¼ g4 ¼ 0. Preferences of the purely self-interested are: U i ðpÞ ¼ pi

(4)

The true inequity averter cares about income to self and inequity. Therefore di ¼ 1 and ri ¼ 0.2 Preferences for the inequity averter are: X X pH pLj U i ðpÞ ¼ g1 pi þ g2 j þ g3

hai lbi ai X H bi X L (5) pi ¼ 1þ pj þ p ðn 1Þ ðn 1Þ ðn 1Þ jai ðn 1Þ jai j For the inequity averter, g2 r 0 and g3 Z 0. The relative values of the individual’s ai and bi, determine person i’s relative preferences for disadvantageous inequality (individual i’s own payoff is less than others) and advantageous inequality (individual i’s own payoff is higher than others).

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If, for example, ai W bi, individual i prefers advantageous inequality to disadvantageous inequality.3 The pure social surplus maximizer cares only about own income and total surplus, so di ¼ 0 and ri ¼ 1 and preferences are: X X lij pj ¼ ð1 þ lii Þpi þ lij pj (6) U i ðpÞ ¼ g1 pi þ g4 jai

jai

where g4Z0 for all j. An increase in income to others (increasing the size of the economic surplus) increases the individual’s welfare even if he or she does not receive more. If the individual values the social surplus, but does not care whether an increase in surplus goes to better-off or worse-off people (or lij ¼ lik for all j and k and lij r 1), we identify the individual as ‘‘efﬁciency maximizing.’’4 In the special case of lij ¼ 1 for all i6¼j and l11 ¼ 0, giving to self and others are perfect substitutes and the person cares only about the P size of the total surplus regardless of who receives the income: U1(p) ¼ pj.5 However, some individuals who have greater concern for those who are worse-off may prefer seeing income going to those who have the lowest incomes, so that lijWlik for pjopk.6 Therefore, we decompose social surplus maximizers into pure efﬁciency maximizers and compassionate social surplus maximizers; the latter temper their desire to increase the surplus with concern for those who are worse-off. We provide graphs of the different social preference categories in Figs. 1–3. Here utility of individual i is graphed with respect to individual j’s income holding income of individual i constant at pi and income of any others constant as well. Clearly if individual i is self-interested (Fig. 1) utility does not change with individual j’s income. However, if individual i is an inequity averter (Fig. 2), utility increases as j’s income increases until j’s income is equal to i’s income and then utility declines with further increases in j’s income. The utility of a social surplus maximizer (Fig. 3) rises with increases in j’s income regardless of the size of j’s income but efﬁciency maximizers’ utility is linear with respect to j’s income, whereas compassionate social surplus maximizers’ utility has a curvature since the increase in utility with a one unit increase in j’s income falls with higher levels of j’s income.

Predicting Charitable Behavior Given these utility functions, we determine under what conditions (values of parameters) individuals with different social preferences will give to a

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Ui(πj |πi)

Self-Interested

A

B πi = πj

C

πj

Utility for Self-Interested.

Fig. 1.

Ui(πj |πi)

Inequity Averter

A

Fig. 2.

B π i = πj

C

πj

Utility for Inequity Averters.

charity and, if possible, the amount of the gift. This analysis can also help us generate hypotheses to test with the experimental data. People who are purely self-interested do not give up money to beneﬁt others and, therefore, are not willing to give to charity regardless of mission or subsidy level. Inequity averters prefer more equitable income allocations to less equitable ones. Therefore, they will be most attracted to charities that redistribute income from the wealthy to the needy. Finally, because social surplus maximizers’ utility increases as the total allocation increases, they prefer charities that promote increased production or economic surplus over

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Ui(πj |πi)

Compassionate SWM Efficiency Maximizer

A

Fig. 3.

B π i = πj

C

πj

Utility for Social Surplus Maximizers.

those that reduce inequality. Therefore, we can identify the following two predictions: 1. Self-interested individuals will give nothing to charity, regardless of mission or subsidy level. 2. Inequity averters will prefer charities that reduce income disparities while social surplus maximizers will be drawn to charities that increase production or productivity. In the case of two participants, similar to a donor and a charity (where the charity is a composite of other economics actors), inequity averters will only consider giving up some of their own income, Dpi , to increase the income to the charity, Dpj , if the charity is giving to those who are worse off than the donor. More speciﬁcally, the inequality averter will only give if bi/(1 bi)Z Dpi/Dpj (where Dpi/Dpj, the loss to self divided by the gain to the charity, is the price of giving, P). If the price of giving is one (no subsidy to giving), the condition for giving is: biZ0.5 and individuals with these b’s will give until pj ¼ pi. Individuals with b less than 0.5 will not give at all.7,8 Social surplus maximizer i will give to charity j if Dpi =ð1 þ lii Þ

lij Dpj or ½lij =ð1 þ lii Þ ðDpi =Dpj Þ or ½lij =ð1 þ lii Þ P. In the absence of subsidies, when Dpi ¼ Dpj, social surplus maximizers will give if ½lij =ð1 þ lii Þ 1. Therefore, efﬁciency maximizers will give nothing unless they are indifferent between income to self and others (lij ¼ 1 for all i6¼j and lii ¼ 0). In this special case, the amount of the gift

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is indeterminate. However, if the efﬁciency maximizer believes that the gift will be used to generate more income, gifts may be positive. Compassionate social surplus maximizers, on the contrary, will give to recipients whose incomes are low enough so that lij exceeds 1 þ lii. Here the level of giving will be the amount that when added to pj (initial income of charity j), results in a decreases of lij to 1 þ lii. This amount will vary across individuals depending on their degree of compassion (elasticity of lij with respect to pj). These arguments contribute to the third prediction: 3. With a unitary price of giving, some inequity averters and compassionate social surplus maximizers will give to charity because they are concerned about those worse-off while efﬁciency maximizers will give only if they think the charity has a positive effect on social output. Matching or rebate subsidies effectively reduce the price of giving. Under a matching subsidy, where m is the matching rate (the proportion of each dollar donated that is matched by a third-party donor), the price of giving is 1/(1 þ m). In the case of rebates where r is the rebate rate (the proportion of each dollar donated that is returned to the donor), the price of giving is (1 r). These conditions are equivalent because the ratios of net gift to the amount the charity receives (or the price of giving) across the two types of subsidies are equal when m ¼ r/(1 r). As a result we can compare giving in matching and rebate programs with the same price of giving. This condition leads us to the fourth prediction: 4. Rational individuals, regardless of social preference type, should give the same amount under a matching and rebate program when the price of giving is the same across the two programs. As the price of giving falls, inequity averters and social surplus maximizers respond differently. In the case of matching programs inequity averters will give to those worse off if b/(1 b)Z1/(1 þ m) or bZ1/(m þ 2), whereas the condition for giving with rebates is b/(1 b)Z(1 r) or bZ(1 r)/(2 r). More generally, in terms of the price of giving, inequity averters will give when bZP/(1 þ P). Therefore, under both matching and rebate subsidies, some inequity averters who do not give in the absence of a subsidy (since bo0.5) may begin to give as the price of giving declines, so that the number of inequity averters donating will increase with increased subsidization. On the other hand, giving by individual inequity averters, who seek to achieve perfect equity, is (pi–pj)[P/(1 þ P)], which is increasing in P. Giving by

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individuals will decrease as the subsidy rate increases because a smaller donation can achieve the same amount of equality. Therefore, the overall effect on giving by inequity averters as subsidization increases is indeterminate. As P falls below one with subsidization, a greater number of efﬁciency maximizers and compassionate social surplus maximizers will give to charity since giving will increase utility if P falls below ½lij =ð1 þ lii Þ. Those efﬁciency maximizers who were indifferent to giving at a unitary price (since lij ¼ 1 for all i6¼j and lii ¼ 0) will be motivated to give all of own income to charity because total payoffs will increase, implying a large within-person response to price changes. Similarly, as P declines, compassionate social surplus maximizers, who gave in the no subsidy scenario, will give more since the level of giving will be the amount which now when added to pj decreases lij so that ½lij =ð1 þ lii Þ ¼ P. In contrast to inequity averters, for both groups of surplus maximizers, there will be unambiguous increases in charitable giving with a decreased price in giving as more individuals donate and individual donations become larger. Therefore, our ﬁfth and ﬁnal prediction: 5. As the price of giving declines due to matching or rebate subsidies, the number of social surplus maximizers and inequity averters making charitable contributions will increase, but the individual donations of social surplus maximizers will be much more responsive to price changes than those of inequity averters.

CHARITABLE GIVING UNDER REBATES AND MATCHING SUBSIDIES In principle, as noted by prediction 4, matching and rebate subsidies that imply an equivalent price of giving should elicit the same donation to the charity. For example, under a 100% matching grant, if a person gives up $1, the charity receives $2. This is equivalent to a 50% rebate in which the individual, by donating $2 and being refunded $1, would be giving up $1 while the charity receives $2. As indicated earlier, matching and rebates are equivalent when m ¼ r/(1 r). However, in a series of papers, Eckel and Grossman (2003, 2006a, 2006b, 2007) have found that in both laboratory experiments and ﬁeld studies, matching subsidies elicit far larger receipts for the charities than do equivalent rebates.9 Eckel and Grossman postulate that the larger giving

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under matching may be due to the framing of giving as a ‘‘cooperative’’ action, where others (those offering the subsidy) give along with the donor. It is also possible that there is ‘‘rebate aversion’’ resulting from previous bad experiences from commercial rebate programs spilling over into the laboratory. Undesirable aspects of rebates include the costs and hassles associated with obtaining rebates, having to wait for the money, and the uncertainty of receiving the refund. When Eckel and Grossman (2006a) offered the participants a choice between the two types of subsidies, slightly more chose rebates than matching but the difference was not signiﬁcant. However, they ﬁnd some evidence of rebate aversion in their ﬁeld study, as the percentage of donors accepting the matching grants far exceeded those willing to take the rebate subsidy. Davis, Miller, and Reilly (2005) and Davis and Miller (2005) hypothesize that the differences found between matching and rebates may be the result of people utilizing a ‘‘constant contribution rule’’ wherein participants pass the same proportion of the endowment under both type of subsidies leading to larger receipts to the charity under matching. They ﬁnd evidence in favor of their hypothesis. Davis and Miller (2005) also ﬁnd there is rebate aversion, with four times as many choosing matching over rebates. Davis (2006) shows that by changing subjects’ focal point (‘‘isolation effects’’) away from the amount passed to the maximum possible receipt by the charity, the differences between matching and rebate are eliminated. Confusion as to how much donors are giving up and how much the charity receives may contribute to larger giving under matching subsidies. In experiments that ask participants how much of a given endowment they would like to ‘‘pass’’ (donate) to a charity people may ﬁnd it difﬁcult to compare the amount given up relative to what the charity receives or overestimate the price of giving under rebates. Davis et al. (2005) include a treatment in their experiments where the participants are provided a table that gives details on the amount held for oneself, the amount passed to the charity, the amount taken home, and the amount sent to the charity. Although the percentage of optimal decisions increases, charity receipts remain higher under matching grants. In the laboratory experiments in which subjects pass or donate portions of an endowment, there is a higher maximum possible receipt to the charity under matching than rebates: with the full endowment donated, the charity receives the endowment plus the matching gift in a matching program but only the endowment under rebates. This higher upper-bound could partly explain higher charity receipts under matching. Davis (2006) eliminates this difference between the two types of subsidies by providing the same

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maximum charity contribution for matching and rebates. This may partially explain the ﬁnding of no difference in charity receipts between matching and rebate subsidies in his study. In summary, the ﬁndings of greater charity receipts under matching than rebate subsidies may be the result of greater giving under cooperative framing, rebate aversion, participants’ use of a rule of thumb donation, confusion as to how much will be given up relative to what the charity receives, isolation effects leading people to focus on what they donate rather than what they give up, or a higher upper-bound on giving under matching. In our charitable giving experiments, we try to rule out two of these reasons for giving more under matching than rebate subsidies. First, in an attempt to minimize error or misunderstanding, we provide the participants with complete tables identifying the donated amount, the matching donation or rebated amount, the amount given up by the individual, the amount the individual keeps, and the amount the charity receives for each donation choice. Second, we specify the donation exercises so that the upper-bounds of receipts to the charities are the same under equivalent matching and rebate subsidies for each price of giving.

EXPERIMENT DESIGN Students were paid $10 for participating in the study. There are two parts to the experiment, with the order of the two parts reversed for approximately half the sample. In one part, the students are asked how they would choose to allocate money among themselves and two other participants in the room. These 10 questions serve to classify the students’ social preference types, as described later in text. At the end of the experiment, one of the 10 allocation choices was randomly chosen to be paid out to the students. The other part of the experiment asks students whether they would like to donate some, all, or none of the money they are paid for participating in the experiment to a charity under various match and rebate rates. At the end of the session, one of these exercises was randomly chosen to be implemented. Social preferences of the subjects are categorized based on a set of ten allocation questions, where there are three choices in how money is to be divided among the dictator and two other anonymous participants. Examples of the questions are provided in Table 1 (the full set of 10 allocations is provided in Table A1 of the appendix). The participants in the experiments were provided the ﬁrst ﬁve columns; the rest of the information is given here for expositional purposes. In the top allocation (Q7) in the

7

8

B

C

10

7

6

A

B

C

Q4

6

X

II

A

Q7

I

6

6

6

7

7

10

YOU

6

6

4

8

7

6

Z

IV

Distribution

III

V

18

19

20

23

21

22

VII

0

1

4

1

0

4

0

0

2

1

0

4

Difference Difference self self to X to Z

VI

A,B,C

A

Selfinterested

1

VIII

C

A,B

Inequity averse (IA)

2

IX

A

A,C

3A. Efﬁciency maximizer

X

A,B

A,C

3B. Compassionate SSM

3

XI

Category

XII

IA

Compassionate SSM

Efﬁciency Max, SSM

SSM

IA

Self-interested, IA, SSM

Sample Allocation Exercise and Associated Preference Classiﬁcations.

Total Payoff

Table 1.

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table, because all preference types value income to self, they all might choose allocation (A), which gives the dictator the highest payoff. However, the inequity averse may prefer option (B), which equalizes the distribution, whereas a social surplus maximizer may choose (C), which provides the highest sum of payoffs. There are ﬁve questions where a self-interested choice is possible. Those who choose the highest payoff for themselves in all ﬁve questions are classiﬁed as self-interested because they never take the opportunity to give up own payoff to reduce inequality or increase surplus. However, it may be that people who appear to be self-interested in some situations may act in an other-directed manner in other situations. For example, when confronted with deciding on payoffs between themselves and others who are in a similar socio-economic situation (such as in our allocation experiments among students) the person might behave selﬁshly. Yet, when the recipient of their potential largess is a charity representing low income individuals, this same person may act in a compassionate manner. Therefore, these people identiﬁed as self-interested in classroom allocation exercises could be inequity averters or social surplus maximizers when giving to a charity; their coefﬁcients on income to others in their utility functions are relatively small when the recipient is a fellow student but much larger when the recipient is a charity.10 The remaining respondents are classiﬁed as inequity averters if they choose either the self-interested choice or the inequity averse choice in all ten allocation decisions and as social surplus maximizers if they choose the selfinterested allocation or the social surplus maximizing allocation in all ten questions. Those whose choices are not always consistent with one of the preference types are placed in the unable to classify category. These people may have preferences for both equality and total surplus (positive d and r), which compete in their decision making. The second allocation decision (Q4) in Table 1 shows how we distinguish between efﬁciency maximizers and compassionate social surplus maximizers. Inequity averters would choose (C), which equalizes payoffs, while efﬁciency maximizers would choose (A) since it provides the highest sum of payoffs. However, a compassionate social surplus maximizer may be willing to reduce the total surplus from $20 to $19 to raise the income of the worstoff person, so that person Z receives $6 rather than only $4 (taking $3 from person X to give $2 to person Z). Therefore, those who chose (B) would be classiﬁed as compassionate social surplus maximizers. This question also illustrates the difference between inequity averters and compassionate social surplus maximizers. Although both prefer to increase incomes of those

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earning less than themselves, the inequity averter would choose C while the compassionate social surplus maximizer would choose B, which increases payoff to person X and social surplus without reducing payoff to anyone else. In the other part of the experiment, the participants are asked whether they would like to donate some, none, or all of the $10 they are paid for participating in the experiment to either America’s Second Harvest or ACCION USA, and they are allowed to choose between the two charities. The charities provide different types of services: America’s Second Harvest provides food to low-income people so that it works to decrease income inequality, whereas ACCION USA provides small loans to low-income entrepreneurs implying an increase in production or productivity. These charities were chosen because they appeal to different motivations for giving, as speciﬁed in our second prediction. There are seven questions in this part of the experiment with different rates of subsidies. The ﬁrst question asks how much, if any, the individual will donate when there is no subsidy to giving; for every dollar donated the charity receives a dollar, implying the price of giving is 1. Three questions ask how much, if any, they would like to donate when the experimenters match their donation at 25%, 50%, or 100% (implying prices of giving of 0.8, 0.67, or 0.5, respectively). Another three questions ask how much, if any, they want to donate when they will receive a rebate of 20%, 33%, or 50% of the original donation (again implying prices of giving of 0.8, 0.67, or 0.5, respectively). The order of the matching and rebate questions is reversed for half the sample. To avoid participant confusion about how much they donate, how much they give up and keep, and how much the charity receives, we provide a detailed table listing these variables (Table 2). Similarly, to avoid potential bias in perceptions, we have made the maximum amount that the charities can receive and the minimum amount kept equal under the two subsidy schemes, as illustrated in Table 2.

RESULTS The experiments were held in classrooms in numerous disciplines to provide a balanced sample of major, gender, and class rank. The sample size is 210 (103 men and 107 women; 60 business majors and 150 other majors). The experiments were designed to ensure complete anonymity. Students chose their own code word to use for all the experiment treatments and the demographic information sheet. The payoffs were made after all parts of the

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Table 2.

Sample Matching and Rebate Questions. Matching Question (Price of giving is 0.8)

You will be paid $10 for your participation in this experiment. If you choose, you may donate some, none, or all of this to the charity you previously chose. This donation will be treated like a situation where another donor matches your donation: for each $1 you donate, the experimenters will add $0.25 to your donation. (1) (2) (3) (4) (5) Donation Matching donation Amount you give up Amount you keep Charity receives _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

$0.00 $1.00 $2.00 $3.00 $4.00 $5.00 $6.00 $7.00 $8.00 $9.00 $10.00

$0.00 $0.25 $0.50 $0.75 $1.00 $1.25 $1.50 $1.75 $2.00 $2.25 $2.50

$0.00 $1.00 $2.00 $3.00 $4.00 $5.00 $6.00 $7.00 $8.00 $9.00 $10.00

$10.00 $9.00 $8.00 $7.00 $6.00 $5.00 $4.00 $3.00 $2.00 $1.00 $0.00

$0.00 $1.25 $2.50 $3.75 $5.00 $6.75 $7.50 $8.75 $10.00 $11.25 $12.50

Rebate Question (Price of giving is 0.8) You will be paid $10 for your participation in this experiment. If you choose, you may donate some, none, or all of this to the charity you previously chose. This donation will be treated like a situation where you receive a tax deduction for donating: for each $1 you agree to donate, your taxes decline by $0.20 so that you will be rebated $0.20.

_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

(1) Donation

(2) Your tax rebate

$0.00 $1.00 $2.00 $3.00 $4.00 $5.00 $6.00 $7.00 $8.00 $9.00 $10.00 $11.00 $12.00 $12.50

$0.00 $0.20 $0.40 $0.60 $0.80 $1.00 $1.20 $1.40 $1.60 $1.80 $2.00 $2.20 $2.40 $2.50

(3) (4) (5) Amount you give up Amount you keep Charity receives $0.00 $0.80 $1.60 $2.40 $3.20 $4.00 $4.80 $5.60 $6.40 $7.20 $8.00 $8.80 $9.60 $10.00

$10.00 $9.20 $8.40 $7.60 $6.80 $6.00 $5.20 $4.40 $3.60 $2.80 $2.00 $1.20 $0.40 $0.00

$0.00 $1.00 $2.00 $3.00 $4.00 $5.00 $6.00 $7.00 $8.00 $9.00 $10.00 $11.00 $12.00 $12.50

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experiment were completed and one person put the money in the envelopes while another handed the envelopes to the participants. The sessions took approximately 45 minutes and students received an average $32.07. The amount sent to America’s Second Harvest was $1,280.50 and to ACCION USA was $319.

Classiﬁcation of Social Preferences The classiﬁcations of the participants into social preference categories based on their answers to the ten allocation exercises for the full sample, separated by gender and by major, are presented in Table 3. The distribution of participants by social preference category is similar to the distribution in previous research (Kamas & Preston, 2009). We ﬁnd about two-thirds of the participants answer all 10 questions consistent with one of the preference types, with 10% self-interested, 24% inequity averse, and 32% social surplus maximizers.11 Within the social surplus category, 19% are pure efﬁciency maximizers and 14% are compassionate social surplus maximizers.12 Men are far more likely to be social surplus maximizers (42% compared to 23% of women), whereas women are more likely to be inequity averters (29% compared to 19% of men). Within the category of social surplus maximizers, men are more often found to be efﬁciency maximizers than compassionate social surplus maximizers (25% compared to 17%), whereas women are more evenly split between the two categories (12% and 11%, respectively). Table 3.

Distribution of Participants across Social Preference Categories, by Gender and Major.

Percentage of the sample who are

1. Self-interested 2. Inequity Averter (IA) 3. Social surplus maximizer (SSM) 3a. Efﬁciency maximizer 3b. Compassionate SSM 4. Unclassiﬁed a

All

Male

Female

Business

Other

(1)

(2)

(3)

(4)

(5)

10.0 23.8 32.4 18.6 13.8 33.8

8.7 18.5a 41.8a 25.2a 16.6 31.5

11.2 28.9 23.4 12.2 11.2 36.5

16.7b 6.7b 31.7 26.7b 5.0b 44.9b

7.3 30.7 32.7 15.3 17.4 29.3

The percentage in the male sample is signiﬁcantly different than the percentage in the female sample at the 0.05 level. b The percentage in the sample of business majors is signiﬁcantly different than the percentage in the sample of other majors at the 0.05 level.

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Business majors are more often classiﬁed as self-interested than other majors (17% compared to 7%) and are far less likely to be inequity averters (7% of business majors and 31% of other majors). Although the percentages of social surplus maximizers are similar across majors, business majors are far more likely to be efﬁciency maximizers than other majors (27% compared to 15%) and far less likely to be compassionate social surplus maximizers (5% compared to 17%). A large fraction of business majors (45%) make inconsistent decisions and, therefore, are not classiﬁed. Choice of Charity According to prediction 2, if social preferences were the sole force behind donation decisions, inequity averters would give to charities that reduce inequality and social surplus maximizers would give to charities that encourage self-reliance and productivity. In the context of our experiments inequity averters will be more likely to donate to America’s Second Harvest because by providing food to the poor it reduces inequality, and social surplus maximizers will prefer ACCION USA because it promotes production. Although inequity averters may also see the merits of ACCION USA in that the ﬁnancing is directed toward lower income entrepreneurs, in a two way comparison the redistribution effects of America’s Second harvest are more direct. The charities chosen by the various social preference categories are presented in Table 4. All social preference types Table 4. Percentage Choosing Each Charity by Social Preference Category. America’s Second Harvest

ACCION USA

(1)

(2)

Total

79.0

21.0

Social preference category: 1. Self-interested 2. Inequity Averter (IA) 3. Social surplus maximizer (SSM) 3a. Efﬁciency maximizer 3b. Compassionate SSM 4. Unclassiﬁed

85.7 89.4 72.1 69.2 75.9 77.5

14.3b 10.6a 27.9a 30.8a 24.1 22.5

a

Mean value of variable for starred sub-sample is signiﬁcantly different than mean value for the remainder of the sample at the 0.01 level. b Mean value of variable for starred sub-sample is signiﬁcantly different than mean value for the remainder of the sample at the 0.05 level.

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choose America’s Second Harvest the most often, however, there are signiﬁcant differences among social preference types in choosing ACCION USA. Social surplus maximizers (28%) are signiﬁcantly more likely to give to ACCION USA than are individuals in the other categories of social preferences (14% of the self-interested and 11% of inequity averse). Efﬁciency maximizers choose ACCION USA (31%) more than any other group. In a head to head comparison, social surplus maximizers as a group and efﬁciency maximizers and compassionate social surplus maximizers as sub-groups are each signiﬁcantly more likely than inequity averters to choose ACCION USA at a p value of 0.00. These choices are consistent with the prediction that social surplus maximizers are more likely than inequity averters to favor charities that support increased production. Amount of Gift Table 5 provides the percent of individuals giving to charity and the average gift for the total sample and by social preference classiﬁcation when no subsidy is provided (price of giving is one). According to prediction 1, the self-interested should give nothing to charity. Prediction 3 states that efﬁciency maximizers will give only if they believe the charity will increase production but inequity averters, whose weight on equity is relatively large Table 5.

Mean Giving with No Subsidy. Percent Giving (1)

Mean Gift (2)a

Total

78.0

$4.52

1. Self-interested

52.6

2. Inequity averter (IA)

91.5

3. Social surplus maximizer (SSM)

70.1

$3.11 (0.10) $5.38 (0.08) $4.24 (0.47) $3.31 (0.03) $5.54 (0.14) $4.59 (0.84)

3a. Efﬁciency maximizer

64.5

3b. Compassionate SSM

78.6

4. Unclassiﬁed a

82.9

p-values are presented in parentheses identifying the signiﬁcance level at which we can reject the null hypothesis that the category mean is equal to the mean from all other categories.

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(above 0.5), and compassionate social surplus maximizers, who place a large weight on gifts to low income individuals, will give a positive amount to charity. Therefore, if social preferences are the only motivator, inequity averters are most likely to give, followed by compassionate social surplus maximizers, efﬁciency maximizers and the self-oriented. The size of the gift of the social surplus maximizers and the inequity averters depends on their weights on payoffs to low income individuals or inequity, respectively. Column 1 gives the percent of each group giving, and consistent with the predictions, the highest rate of giving, as displayed in column 2, is among the inequity averters of whom almost 92% give to charity. Furthermore, 78.6% of the compassionate social surplus maximizers, 64.5% of the efﬁciency maximizers, and 52.6% of the self-interested give to charity when the price of giving is one. Although the percent giving for both the efﬁciency maximizers and the self-interested is surprisingly high, the ordering conforms to predictions. In addition, the differences in the neighboring percentages in this ordering are signiﬁcant at the 0.1 level except between the efﬁciency maximizers and the self-interested. The average amount donated by the total sample (column 2) is $4.52. Consistent with the predictions, we ﬁnd inequity averters and compassionate social surplus maximizers give the most, with mean giving of $5.38 by inequity averters and $5.54 by compassionate SSMs compared to $3.11 by ‘‘self-interested’’ and $3.31 by efﬁciency maximizers. Pairwise comparisons reveal that amounts given by inequity averters and compassionate SSMs are not signiﬁcantly different from one another, nor is giving by efﬁciency maximizers compared to the self-interested. However, giving by both inequity averters and compassionate SSMs is signiﬁcantly higher at the 0.01 level than giving by both the self-interested and the efﬁciency maximizers. Again, the non-zero gifts are surprising for both the efﬁciency maximizers and the self-interested. Efﬁciency maximizers are not expected to give a positive amount to charity since giving does not increase the total surplus or payout. However, although those efﬁciency maximizers for whom income to self and others are perfect substitutes are simply indifferent between keeping and donating income and may give an indeterminate amount, one would not expect almost two-thirds (64.5%) of efﬁciency maximizers to be characterized in this manner. Possibly, when the recipient is the beneﬁciary of a charity, some of those who were classiﬁed as efﬁciency maximizers in the allocation exercises act as compassionate social surplus maximizers (or lij =ð1 þ lii Þ 41 for these individuals when the recipient is a beneﬁciary of a charity). Alternatively, some efﬁciency maximizers may interpret giving to ACCION USA as increasing surplus even at a price of one because the recipients engage in productive activities.

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What Can Social Preferences Tell Us About Charitable Giving?

In the case of the self-interested, while mean giving is less than giving from other categories, still 52.6% give something to the charity when the price is one. Furthermore, only 5 of the 21 people classiﬁed as self-interested never give anything to anyone in the various treatments of the experiment. These results clearly violate prediction 1. However, many of those classiﬁed as ‘‘selfinterested’’ may be other-directed when the recipient is a charity or their weights in their utility functions (b or l) are larger for charities than fellow students.13 Table 6 presents the results of estimating two-limit tobits, with the dependent variable equal to the natural logarithm of the amount given up (net gift) plus 0.1 (since some gave zero).14 Because this equation includes all the giving scenarios, we include the natural logarithm of price as well as social preference categories and demographic variables as explanatory variables.15 Column 1 reveals that price has a negative signiﬁcant impact on giving and the elasticity is very close to one. Results from column 2 support the prediction that controlling for prices, individuals with different social preference types donate signiﬁcantly different amounts. In comparison to the Table 6.

1. ln (price)

Determinants of Charitable Giving. (1)

(2)

1.068

1.071

(0.310)

(0.303) 1.417 (0.257) 0.385 (0.190) 0.625 (0.174)

2. Self-interested 3. Inequity averter 4. Social surplus maximizer 4a. Efﬁciency maximizer 4b. Compassionate SSM

(3)

(4)

(5)

1.071 (0.567) 1.411 (0.255) 0.383 (0.188)

1.063

1.063 (0.298) 1.402 (0.254) 0.293 (0.193)

1.115 (0.203) 0.055 (0.226)

0.963 (0.203) 0.159 (0.226) 0.685 (0.143)

0.0179

0.0223

5. Female

(0.298) 1.418 (0.253) 0.343 þ (0.187)

6. Business major 7. Pseudo R2

0.0023

0.014

0.958 (0.203) 0.111 (0.230) 0.677 (0.143) 0.166 (0.164) 0.0225

Notes: A two-level tobit was estimated with the dependent variable equal to the natural logarithm of the amount given up plus 0.1. The upper level used was 2.3 and the lower level was 2.3. Standard errors are in parentheses. Coefﬁcient is signiﬁcantly different from zero at the 0.01 level. Coefﬁcient is signiﬁcantly different from zero at the 0.05 level. þ Coefﬁcient is signiﬁcantly different from zero at the 0.10 level.

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omitted group, unclassiﬁed, the inequity averters give 48% more (coefﬁcient ¼ 0.39) to charity and the self-interested and social surplus maximizers give 65% (coefﬁcient ¼ –1.42) and 47% (coefﬁcient ¼ –0.63) less respectively.16 Column 3 reveals that the lower giving by social surplus maximizers is due to 67% lower giving by efﬁciency maximizers (coefﬁcient ¼ –1.12); compassionate social surplus maximizers’ giving is not signiﬁcantly different from giving by the unclassiﬁed group. These results hold for the most part after inclusion of the sex and major variables, columns 4 and 5, which reveal that women give 99% more than men (coefﬁcient ¼ 0.69) in addition to giving more because they are more often inequity averters, and business majors give 49% less than other majors (coefﬁcient ¼ –0.67), in addition to giving less because they are more often efﬁciency maximizers.

Price Responsiveness The mean amounts given up (net gift) and percentage of participants donating at various prices of giving for the total sample and by each preference category are provided in Table 7. According to prediction 5, the Table 7.

Mean Gift and Percentage Making a Gift at Different Prices. P¼1

P ¼ 0.8

P ¼ 0.67

P ¼ 0.5

Mean gift

% giving

Mean gift

% giving

Mean gift

% giving

Mean gift

% giving

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

4.52 (3.91)

78.0

4.66 (3.86)

80.6

4.84 (3.87)

83.5

5.14 (3.82)

88.8

3.10 (4.08) 2. Inequity averter 5.38 (3.81) 3. Social surplus 4.24 maximizer (4.07) 3a. Efﬁciency maximizer 3.31 (3.90) 3b. Compassionate SSM 5.54 (4.01) 4. Unclassiﬁed 4.60 (3.71)

52.6

3.59 (3.96) 5.44 (3.69) 4.19 (4.0) 3.52 (3.92) 5.09 (3.97) 4.88 (3.72)

64.3

3.65 (3.91) 5.42 (3.69) 4.44 (3.98) 3.69 (3.81) 5.45 (4.02) 5.18 (3.79)

66.7

4.18 (3.93) 5.90 (3.70) 4.87 (3.82) 4.00 (3.66) 6.03 (3.74) 5.16 (3.82)

73.8

Total 1. Self-interested

91.5 70.1 64.1 78.6 83.6

91.0 71.1 66.2 77.6 87.2

Note: Standard deviations of giving are in parentheses.

91.0 76.5 73.1 81.0 90.1

95.0 85.3 82.1 89.7 92.1

What Can Social Preferences Tell Us About Charitable Giving?

185

number of both social surplus maximizers and inequity averters giving to charity should increase as the price of giving falls, but the amount of the gift should be much more sensitive to price for social surplus maximizers than for inequity averters. For all groups including the self-interested, the number of givers increases as the price falls. For inequity averters, of whom 91.5% give when the price of giving is one, the increase is modest. However, the percent giving increases by 21 percentage points for the self-interested, 18 percentage points for the efﬁciency maximizers, and 11 percentage points for the compassionate social surplus maximizers. For the total sample, with no subsidy, the mean amount given is $4.52. As the price of giving declines, this increases to $4.66 at a price of 0.8, $4.84 at price of 0.67, and $5.14 at the lowest price of 0.50. The responses by social preference types differ; among the self-interested and efﬁciency maximizers, mean gifts consistently increase. However, compassionate social surplus maximizers and inequity averters only display appreciable increases in the mean gift and the percentage giving when comparing giving where price equals one and price equals 0.5. They do not seem to respond to the intermediate price reductions of 0.8 and 0.67. At low subsidy rates, giving by inequity averters and compassionate social surplus maximizers is in some cases being ‘‘crowded-out’’ by the subsidy in that the amount given up declines (but, the charities still receive more due to the addition of the subsidy). This crowding-out was predicted for inequity averters but not for compassionate social surplus maximizers. Table 8 presents estimates of two-level tobits that estimate the price elasticity of demand for the total sample (column 1) and then for the different social preference categories. We include individual ﬁxed effects to control for participant heterogeneity so the estimates give us within-person responses to changes in the price of giving. The price elasticity of demand for the full sample is –1.07. However, there are signiﬁcant differences in price elasticity among the social preference types: social surplus maximizers respond more to the price of giving than the unclassiﬁed [signiﬁcant coefﬁcient of 0.79 with similar size effects for efﬁciency maximizers ( 0.83) and compassionate social surplus maximizers ( 0.72)]; inequity averters do not respond more to the price of giving (insigniﬁcant coefﬁcient of 0.42); and ‘‘self-interested’’ respond the most to the price of giving ( 1.04 less than the unclassiﬁed). These results support the prediction that social surplus maximizers will be more price responsive than inequity averters. Hypothesis testing reveals that the coefﬁcient on the social surplus maximizers is signiﬁcantly lower at the 0.01 level than the coefﬁcient on inequity averters for the whole group of social surplus maximizers and for the compassionate social surplus

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Table 8.

Effects of Price on Charitable Giving – Fixed Effects. (1)

(2)

(3)

1.067 0.825 0.825 (0.129) (0.208) (0.209) 2. ln (price) self-interested 1.041 1.041 (0.479) (0.479) 3. ln (price) inequity averter 0.424 0.424 (0.339) (0.339) 4. ln (price) social surplus maximizer 0.785 (0.310) 4a. ln (price) efﬁciency maximizer 0.825 (0.362) 4b. ln (price) compassionate social surplus maximizer 0.724 þ (0.428) 0.4831 0.4863 0.4863 5. Pseudo R2

1. ln (price)

Note: A two-level tobit was estimated with the dependent variable equal to the natural logarithm of the amount given up plus 0.1. The upper level used was 2.3 and the lower level was 2.3. Standard errors are in parentheses. Coefﬁcient is signiﬁcantly different from zero at the 0.01 level. Coefﬁcient is signiﬁcantly different from zero at the 0.05 level. þ Coefﬁcient is signiﬁcantly different from zero at the 0.10 level.

maximizers and efﬁciency maximizers separately. The high price responsiveness of the ‘‘self-interested’’ contradicts our hypotheses about selfinterested individuals, but may be the result of our inability to identify truly self-interested individuals. Some of those classiﬁed as self-interested in the allocation exercises with other students may care about others, but the weights on income to others are low so that they do not give. When the recipient is a charity aiding very low income people however, the relative weights may differ. If some of these individuals give when the price is one, even more will give in the presence of a subsidy since giving conditions are relaxed [biZP/(1 þ P) for inequity averters or ½lij =1 þ lii P for social surplus maximizers].17 Table 7 supports this interpretation as the percentage of the self-interested who give increases from 52.6% with no subsidy to 73.8% with a 50% subsidy.

Matching vs. Rebates Mean giving under matching and rebate subsidies at the various prices of giving are provided in Table 9. Contrary to prediction 4, we ﬁnd that

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What Can Social Preferences Tell Us About Charitable Giving?

Table 9. Mean Amount Given Up to Charity under Matching and Rebate Subsidies at Various Prices of Giving. No Subsidy

Matching Subsidy

Rebate Subsidy

Price ¼ 0.8

Price ¼ 0.67

Price ¼ 0.5

Price ¼ 0.8

Price ¼ 0.67

Price ¼ 0.5

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Total

4.52

4.84

5.13

5.58

4.49

4.55

4.70

1. Self-interested 2. Inequity averter (IA) 3. Social surplus maximizer (SSM) 3a. Efﬁciency maximizer 3b. Compassionate SSM 4. Unclassiﬁed

3.11 5.38 4.24 3.31 5.54 4.59

3.90 5.72 4.22 3.52 5.10 5.09

4.10 5.86 4.66 3.82 5.79 5.38

5.14 6.40 5.29 4.38 6.52 5.41

3.28 5.17 4.16 3.49 5.08 4.68

3.21 4.97 4.22 3.56 5.10 4.97

3.21 5.39 4.44 3.62 5.55 4.91

matching subsidies generate greater giving than rebates at every price for all social preference types and these differences increase with the rate of subsidy. The percentage differences between mean giving under matching and rebate subsidies for the total sample are: 7.8%, 12.7%, and 18.7% for prices of giving of 0.8, 0.67, and 0.5, respectively. Although this ﬁnding is consistent with the earlier studies (Eckel & Grossman, 2005, 2006a, 2006b; Davis et al., 2005), these differences are smaller than those found in the previous studies. This may be due to the greater clarity provided by our tables and the equal upper-bound on giving for matching and rebate subsidies. Table 9 also reveals that price responsiveness is much larger under matching than rebates. The crowding-out of giving at low subsidy rates discussed in the previous section occurs almost entirely under rebates; the only case of crowding-out found under matching subsidies is for compassionate social surplus maximizers at a price of 0.8. Inequity averters and compassionate social surplus maximizers give less under low rebate subsidies than with no subsidy, and at the highest rebate rate of 50%, they give virtually the same amount as with no rebate at all. This suggests that, with respect to these groups, the resources provided by third-party donors would be better given directly to the charities. On the contrary, efﬁciency maximizers unambiguously increase giving as rebate rates rise, and the difference between giving under no subsidy and the highest rebate is substantial. The self-interested give the most under the 20% rebate and the unclassiﬁed give the most with the 25% rebate, with the latter group giving a much larger amount compared to the no subsidy case.

188

Table 10.

LINDA KAMAS AND ANNE PRESTON

Differences between Matching and Rebate Amount Given Up to Charity. Price ¼ 0.80

Price ¼ 0.67

Price ¼ 0.50

25% match 20% rebate (1)

50% match 33% rebate (2)

100% match 50% rebate (3)

Total

0.36 (1.60)

0.56 (2.09)

0.84 (2.38)

1. Self-interested

0.63 (1.97) 0.55 (1.95) 0.15 (1.26) 0.24 (1.10) 0.03 (1.45) 0.35 þ (1.48)

0.89 (1.93) 0.89 (2.37) 0.45 þ (1.96) 0.26 (1.47) 0.69 (2.49) 0.34 (2.03)

1.93 (2.93) 1.01 (2.97) 0.85 (2.04) 0.77 (1.83) 0.97 (2.32) 0.38 þ (1.92)

2. Inequity averter (IA) 3. Social surplus maximizer (SSM) 3a. Efﬁciency maximizer 3b. Compassionate SSM 4. Unclassiﬁed

Note: If people respond to matching and rebates as equivalent subsidies, the difference would be zero, implying they give up/the charity receives the same amount under both types of subsidies. Standard deviations are included in parentheses. Mean is signiﬁcantly different from 0 at the 0.01 level. Mean is signiﬁcantly different from 0 at the 0.05 level. þ Mean is signiﬁcantly different from 0 at the 0.10 level.

Dollar differences in net giving under matching and rebates at comparable prices are provided in Table 10. If the participants are acting as hypothesized, the differences should not be signiﬁcantly different from zero. The total sample gives signiﬁcantly more under a matching subsidy than rebate subsidy at all prices of giving, and the difference rises from $0.36 to $0.56 to $0.84 as the subsidy rate increases. In addition, we ﬁnd differences among the social preference types. Inequity averters give signiﬁcantly more under matching than rebates at all subsidy levels. However, social surplus maximizers and self-interested do not give signiﬁcantly more with matching under the two lower subsidies but do give more under the highest subsidy rate. All preference groups give more to matching when there is a 100% matching as opposed to a 50% rebate. In Table 11, we rerun the two-limit tobits allowing price responsiveness to vary according to whether the price reductions occur through matched giving or rebates. Again we include ﬁxed effects so we are comparing

What Can Social Preferences Tell Us About Charitable Giving?

Table 11.

189

Price Elasticities of Charitable Giving by Social Preferences for Matching and Rebate Subsidies – Fixed Effects. (1)

Matching 1. ln (price)

1.459 (0.146)

2. ln (price) self-interested 3. ln (price) inequity averter 4. ln (price) social surplus maximizer

(2)

(3)

2.779 (0.479) 0.837 (0.296) 2.087 (0.258)

2.779 (0.502) 0.837 (0.296)

4a. ln (price) efﬁciency maximizer 4b. ln (price) compassionate SSM 0.921 (0.240)

5. ln (price) unclassiﬁed Rebate 6. ln (price)

0.699 (0.142)

7. ln (price) self-interested 8. ln (price) inequity averter 9. ln (price) social surplus maximizer

1.14 (0.470) 0.015 (0.276) 1.150 (0.253)

9a. ln (price) efﬁciency maximizer 9b. ln (price) compassionate SSM 10. ln (price) unclassiﬁed 11. Pseudo R2

0.4831

0.617 (0.236) 0.4935

1.982 (0.332) 2.243 (0.408) 0.921 (0.240)

1.143 (0.470) 0.015 (0.276) 1.325 (0.327) 0.889 (0.400) 0.617 (0.236) 0.4939

Note: A two-level tobit was estimated with the dependent variable equal to the natural logarithm of the amount given up plus 0.1. The upper level used was 2.3 and the lower level was 2.3. Standard errors of the coefﬁcients are in parentheses. Coefﬁcient is signiﬁcantly different from 0 at the 0.01 level. Coefﬁcient is signiﬁcantly different from 0 at the 0.05 level.

within-person responses to changes in price and changes in subsidy. Similar to results from previous studies, for the total sample individuals are roughly twice as responsive to matching subsidies as rebate subsidies (column 1). When we explore these differences in responsiveness across preference categories, we ﬁnd some interesting differences. The self-interested, who are

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LINDA KAMAS AND ANNE PRESTON

the most responsive to matching subsidies, have a price elasticity for matching gifts that is almost 2.5 times as great as their elasticity for rebates. Inequity averters do not respond to rebates at all but have an elasticity of 0.8 for matching subsidies. Both types of social surplus maximizers respond more to matching gifts than to rebates but the difference for efﬁciency maximizers is much less than for compassionate social surplus maximizers whose elasticity, similar to the self-interested, increases two and a half times when moving from a rebate to a matching program.18 The unclassiﬁed are the group that has the smallest differences in elasticities across the two programs. The difference in price sensitivity to the two types of subsidies is signiﬁcant at the 0.01 level for inequity averters, both types of social surplus maximizers, and ‘‘self-interested,’’ but only signiﬁcant at the 0.17 level for the unclassiﬁed.19 The difference in giving across the rebate and matching subsidies calls for an examination of previous explanations. We begin by considering the constant contribution rule or rule-of-thumb explanation that the amount passed or donated will be the same proportion of endowment for both subsidy types (Davis et al., 2005; Davis & Miller, 2005). If the amount passed/donated does not respond to the type of subsidy, the same amount passed/donated will imply larger receipts to the charity under matching than under rebates, potentially explaining why charities receive more under matching than rebate subsidies. To test the constant contribution explanation we run a ﬁxed effects two-level tobit with the amount passed (rather than the amount given up as in the previous tables) as the dependent variable. The results are presented in Table 12. In column 1, the coefﬁcient Table 12. Responses of Amount Passed to Price and Type of Subsidy (Fixed Effect Regression with Dollar Amount Passed as Dependent Variable).

1. Price 2. Rebate subsidy 3. Matching subsidy

Total Sample

Total Sample

P ¼ 0.8

P ¼ 0.67

P ¼ 0.5

(1)

(2)

(3)

(4)

(5)

6.22

7.61

–

–

–

(0.42) –

(0.54) 0.14 (0.27) 1.98 (0.27)

0.76 (0.14) –

1.71 (0.22) –

3.88 (0.34) –

–

Note: Standard errors of the coefﬁcients are in parentheses.

Coefﬁcient is signiﬁcantly different from 0 at the 0.01 level.

What Can Social Preferences Tell Us About Charitable Giving?

191

on price, the only independent variable, is negative and signiﬁcant, suggesting that individuals do not pass the same amount regardless of the subsidy rate. A one-half unit change in price (reducing price from 1 to 0.5) increases the amount passed by approximately 3 dollars. In column 2 we add dummies for the rebate and the matching subsidy. The alternative is no subsidy, and we ﬁnd that, controlling for price, matching subsidies reduce the amount passed signiﬁcantly; that is, under matching subsidies, the subjects respond by passing less (yet the charity still receives more) while under rebates subjects pass more (since some of what they pass is returned to them leaving less for the charity). In columns 3–5, we limit the sample to observations where the price of giving is 0.8, 0.67, and 0.5, respectively. In each of these samples we regress the amount passed on the dummy for a rebate subsidy. The omitted group is the matching subsidy since the no-subsidy treatment is not part of any of the samples. In each of these sub-samples, the coefﬁcient on rebate is positive and signiﬁcant, and its magnitude increases with the size of the subsidy. This implies that at each subsidy rate, the amount passed under rebates is more than passed under matching, so that the subjects are indeed adjusting the amount passed in response to the type of subsidy rather than donating the same amount. This suggests that the greater amount received by charities under matching compared to rebates is not explained by a constant contribution rule. An alternative explanation for the difference between matching and rebate donations is there is ‘‘rebate aversion,’’ spillovers from past rebate experiences involving costs, hassles, or wait times. We asked the participants which type of subsidy they preferred (Table 13), and the answers were only slightly in favor of matching (54%) over rebates (45%).20 However, the inequity averse (62%) and compassionate social surplus maximizers (69%) had much stronger preferences for matching than efﬁciency maximizers (46%) and the self-interested (52%). The two people who said there was no difference between matching and rebates were efﬁciency maximizers. Table 13.

Preferred Type of Subsidy. Matching

Rebate

Same

Total

53.8

45.2

1.0

1. Self-interested 2. Inequity averter (IA) 3. Social surplus maximizer (SSM) 3a. Efﬁciency maximizer 3b. Compassionate SSM 4. Unclassiﬁed

52.4 62.0 55.9 46.2 69.0 46.5

47.6 38.0 41.2 48.7 31.0 54.5

0 0 2.9 5.1 0 0

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LINDA KAMAS AND ANNE PRESTON

Table 14.

Stated Reason for Preference of Matching or Rebate Subsidies. Prefer

1. 2. 3. 4. 5. 6. 7.

Matching (%)

Rebate (%)

32.9 4.3 4.3 2.9

18.6

Charity receives more money/self gives up less money Like to see others donate along with oneself Want to help others/don’t want money back Matching is simpler to ﬁgure out Rebate gives money back – self-interest Rebate means government gets less money Other reasons

8. Total

7

9 6 10

54

45

Note: 2 people (1%) said matching and rebates were equivalent.

We also asked the students to explain why they preferred one type of subsidy (Table 14). The answers suggest that many people do not understand the equivalence of matching and rebates at the same price of giving: ‘‘Charity gets more money/I give up less’’ was cited by 52% of the participants to explain their choice of matching or rebates. Only 2 of 210 people (1%) said matching and rebates are equivalent. Four percent said they like matching because someone else gives along with them, providing only minimal support for the Eckel–Grossman hypothesis of cooperative giving. In addition, 4% say they want to give, not to get money back, and 3% say matching is easier to ﬁgure out. Those who prefer rebates like the idea of getting money back for self-interested reasons (9%), whereas 6% support tax deductions/rebates because the ‘‘government’’ gets less money. In addition, although 54% prefer to give under matching, 69% think others would prefer rebates, mostly because they say other people are selﬁsh. Taking all the responses together, there is the widespread misconception that matching programs provide a more generous (or less selﬁsh) way to give to charities than rebate programs. Our data and results seem to further imply that the promise of a 100% matching program is too good to pass up.

CONCLUSIONS This chapter investigates the effects of social preferences on charitable giving under alternative prices of giving and types of subsidies. We compare

What Can Social Preferences Tell Us About Charitable Giving?

193

within-person decision-making in alternative contexts to determine whether there is consistent carryover in behavior from one economic situation to another. We utilize a set of ten allocation decisions to classify participants in one of the following social preference types: inequity averters, social surplus maximizers (efﬁciency maximizers or compassionate social surplus maximizers), or self-interested. The participants in the study are offered the opportunity to make donations to one of two charities (America’s Second Harvest, which provides food to low-income people, and ACCION USA, which makes micro loans to small entrepreneurs) under a series of different prices and subsidization schemes. We then evaluate whether these charitable giving decisions are consistent with predictions based on the characteristics of their social preference types. The evidence strongly supports the predictions. We ﬁnd that social surplus maximizers are more likely to give to a charity that increases production/productivity like ACCION USA than are the other preference types. Both inequity averters and compassionate social surplus maximizers give more to charity than do efﬁciency maximizers or the ‘‘self-interested.’’ We ﬁnd a signiﬁcant price response of giving under subsidies, with social surplus maximizers and self-interested more responsive to the price of giving than are inequity averters. All categories give more under matching than rebates and the difference increases as the subsidy rate rises, that is, price responsiveness is greater under matching than subsidies for all preference types. Rebates at the lowest subsidy rates crowd-out private giving of inequity averters and compassionate social surplus maximizers as these groups give up less than before the subsidy was offered. The difference in giving between matching and rebate subsidies is not explained by a ‘‘constant contribution’’ rule-of-thumb, cooperative giving, or rebate aversion. We conclude that participants are confused about the effects of matching and rebates and generally believe that matching programs provide a more generous (less selﬁsh) means to give to charity than rebate programs. In conclusion, social preferences have quite a lot to tell us about charitable giving. Social preferences inﬂuence charitable giving in predictable ways in the type of charity chosen, the size of donations, and the response to matching and rebate subsidies. This information may be of use in designing fundraising programs: matching subsidies generate more net giving while the return on rebate subsidies may be low enough to crowd-out some individuals’ giving; people respond to the price of giving and increase their donations with larger subsidy rates; individuals who behave as social surplus maximizers (e.g., more likely men and those in business) respond

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more to subsidies than do inequity averters (e.g., more likely women and those in other occupations) implying that charitable solicitations to the former groups may generate more giving with subsidy incentives, whereas the latter groups may give more if inequality or the disadvantaged situation of the recipients of the charity are stressed. These ﬁndings suggest the need for further research in how heterogeneous social preferences should be take into account in explaining or promoting other-directed behaviors such as charitable giving.

NOTES 1. For recent studies on social preferences see Bolton and Ockenfels (2000, 2006), Charness and Rabin (2002), Cox and Sadiraj (2006), Engelmann and Strobel (2004, 2005, 2006, 2007), Fehr and Schmidt (1999), Fehr, Naef, and Schmidt (2006), and Kamas and Preston (2009). Erlei (2008) shows that heterogeneous social preferences can explain economic behavior in various games. 2. It is possible, even likely, that inequity aversion is non-linear, so that a and b increase with inequality. 3. We term those who prefer advantageous inequality to disadvantageous inequality (aiWbi) competitive inequity averters and those who dislike advantageous inequality more than disadvantageous inequality (aiobi) compassionate inequity averters. See Table A1 in the Appendix. For a more detailed explanation, see Kamas and Preston (2009). 4. Strictly speaking, since these people care about their own return as much or more than efﬁciency, they might be called ‘‘egocentric efﬁciency maximizers’’ as is done by Cox and Sadiraj (2006). 5. Andreoni and Vesterlund (2001) present evidence that some individuals treat giving to self and others as perfect substitutes. 6. Essentially for these individuals @lij/qpjo0. This condition is similar to Cox and Sadiraj’s (2006) egocentric altruism and Engelmann and Strobel’s (2005, 2007) generalized quasi-maximin preferences. 7. In the case of larger n, the condition will change, so that giving will only occur if bZ(n 1)/n. Although such a condition implies that giving will fall as n increases, an individual’s weight on equality, either a or b, may rise with n since the potential for more inequality rises with more individuals. 8. Because inequity averters will not give to those better off than themselves, we ignore the other term in the utility function. 9. Field experiments that focus exclusively on matching grants (Karlan & List, 2007; Meier, 2007) ﬁnd that subsidies increase giving. 10. This, in fact, does occur. As a preview of our results, we ﬁnd that two-thirds of those who are always self-interested in the allocation exercises with fellow students

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are willing to give money to charity. Only 5 of 210 participants (2%) never give any money away in any of the treatments. 11. These proportions are similar to those in our previous study (Kamas & Preston, 2009) where we found 14% self-interested, 27% inequity averse and 25% social surplus maximizers. The larger percentage of social surplus maximizers in this study may be due to a larger number of engineering majors (who are more often social surplus maximizers) here. This illustrates how important the composition of the sample can be in identifying social preferences if people hold heterogeneous preferences that differ by demographic characteristics. 12. These people may act as efﬁciency maximizers in a subset of the questions, but act as compassionate social surplus maximizers in at least one of the questions. 13. Within the context of the 10 allocation exercises, there are several questions where the price of giving is less than 0.5 and those who were classiﬁed as selfinterested were unwilling to give money away. Therefore, these participants’ bs or ls are higher for a charity than for fellow students since they are willing to give money to a charity at a price of 0.5 or above. 14. Dummy variables representing the four different possible orders of the components of the experiment were included in the speciﬁcations and the results are not appreciably different from those presented. However, the groups for whom the charitable giving preceded the allocation exercise tended to give less to charity and to be classiﬁed more often as selﬁsh. However, these groupings showed no correlation with any of the other explanatory variables. 15. The regressions were run with both a log-log speciﬁcation and a log-linear speciﬁcation. The results are very similar in terms of signiﬁcance and meaning of coefﬁcients. We present the log-log speciﬁcation because elasticities are easily inferred and pseudo R2 is higher than in the log-linear speciﬁcation. 16. The percentages are derived by noting that a one unit change in the preference category dummy variable causes giving to change by ½ebx 1100% where bx is the coefﬁcient on the preference category dummy. 17. Of the 21 self-interested participants, 7 have secondary preferences consistent with inequity aversion and 10 have secondary preferences consistent with social surplus maximization. Of the secondary preferences consistent with social surplus maximization half are efﬁciency maximizers. 18. Hypothesis tests on the coefﬁcients presented in Table 11 also conﬁrm prediction 5. Regardless of the type of subsidy, efﬁciency maximizers and social surplus maximizers are more sensitive to price changes than inequity averters. For matching programs the price coefﬁcients on inequity averters are signiﬁcantly lower than those for both types of social surplus maximizers at the 0.01 level. For rebate programs the price coefﬁcients on inequity averters are signiﬁcantly lower than those for efﬁciency maximizes at the 0.01 level and than those of compassionate social surplus maximizers at the 0.10 level. 19. Because order does not change within subject, the ﬁxed effects cannot include order effects. Separating the analysis by order provides some differences in coefﬁcients but the general results hold. 20. This is similar to Eckel and Grossman (2006a), who ﬁnd that there was no signiﬁcant difference in students’ choice between matching and rebate subsidies.

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ACKNOWLEDGMENT We gratefully acknowledge grants supporting this research from the Breetwor FellowshipFund and Leavey School of Business at Santa Clara University and from Haverford College.

REFERENCES Andreoni, J., & Vesterlund, L. (2001). Which is the fair sex? Gender differences in Altruism. The Quarterly Journal of Economics, 116(1), 293–312. Bolton, G. E., & Ockenfels, A. (2000). ERC: A theory of equity, reciprocity, and competition. American Economic Review, 90(1), 166–193. Bolton, G. E., & Ockenfels, A. (2006). Inequality aversion, efﬁciency, and maximin preferences in simple distribution experiments: Comment. American Economic Review, 96(5), 1906–1911. Charness, G., & Rabin, M. (2002). Understanding social preferences with simple tests. Quarterly Journal of Economics, 117(3), 817–869. Cox, J. C., & Sadiraj, V. (2006). Direct tests of models of social preferences and a new model. Working paper, Experimental Economics Center, Georgia State University. Davis, D. D. (2006). Rebate subsidies, matching subsidies, and isolation effects. Judgment and Decision Making, 1(1), 13–22. Davis, D., & Miller, E. L. (2005). Rebates, matches, and consumer behavior. Southern Economic Journal, 72(2), 410–421. Davis, D., Miller, E. L., & Reilly, R. J. (2005). Subsidy schemes and charitable contributions: A closer look. Experimental Economics, 8(1), 85–106. Eckel, C. C., & Grossman, P. J. (2003). Rebate versus matching: Does how we subsidize charitable Contributions matter? Journal of Public Economics, 87(4), 681–701. Eckel, C. C., & Grossman, P. J. (2006a). Do donors care about subsidy type? An experimental study. In: R. M. Isaac & D. D. Davis (Eds), Experiments investigating fundraising and charitable contributors, research in experimental economics (Vol. 11, pp. 157–175). Amsterdam: Elsevier Press. Eckel, C. C., & Grossman, P. J. (2006b). Subsidizing charitable giving with rebates or matching: Further laboratory evidence. Southern Economic Journal, 72(4), 794–807. Eckel, C. C., & Grossman, P. J. (2007). Encouraging giving: Subsidies in the ﬁeld. ASSA meetings, January 2007, Boston, MA. Engelmann, D., & Strobel, M. (2004). Inequity aversion, efﬁciency, and maximin preferences in simple distribution experiments. American Economic Review, 94(4), 857–869. Engelmann, D., & Strobel, M. (2005). Fairness on the internet – The role of distributional concerns in dictator games with high social distance. Mimeo. Engelmann, D., & Strobel, M. (2006). Inequality aversion, efﬁciency, and maximin preferences in simple distribution experiments: Reply. American Economic Review, 96(5), 1918–1923. Engelmann, D., & Strobel, M. (2007). Preferences over income distributions, experimental evidence. Public Finance Review, 35(2), 285–310. Erlei, M. (2008). Heterogeneous social preferences. Journal of economic behavior and organization, 65(3), 436–457.

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Fehr, E., Naef, M., & Schmidt, K. M. (2006). Inequality aversion, efﬁciency, and maximin preferences in simple distribution experiments: Comment. American Economic Review, 96(5), 1912–1917. Fehr, E., & Schmidt, K. M. (1999). A theory of fairness, competition, and cooperation. The Quarterly Journal of Economics, 114(3), 817–868. Kamas, L., & Preston, A. (2009). On measuring compassion in social preferences: Do gender, price of giving, or inequality matter? Manuscript. Karlan, D., & List, J. A. (2007). Does price matter in charitable giving? Evidence from a largescale natural ﬁeld experiment. Manuscript. Meier, S. (2007). Do subsidies increase charitable giving in the long run? Matching donations in a ﬁeld experiment. Working paper, Federal Reserve Bank of Boston.

4

3

2

1

4

C

III

10

7

6

C

5

C

B

8

B

A

10

A

6

8

9

B

C

6

6

6

6

6

6

6

7

8

6

6

YOU

Distribution

4

A

6

8

B

X

II

A

I

6

6

4

5

6

5

6

5

4

4

8

5

Z

IV

V

18

19

20

16

20

21

21

19

15

16

22

17

Total payoff

VI

0

1

4

1

2

4

3

2

3

4

2

0

Diff. self to X

0

0

2

1

0

1

0

1

3

4

2

1

Diff. self to Z

VII

A,B,C

A,B,C

A

C

X

C

C

A,B

A,C

C

B

A,C

A,B,C

(2B) Compassionate IA

(2A)

Inequity averse (IA)

2

Competitive IA

IX

(3A)

A,C

B,C

Efﬁciency max

A

A

3

XII

A,B

A,B

A,C

B,C

Compassionate SSM

(3B)

Social surplus max (SSM)

XI

Ten Allocation Exercises and Classiﬁcations.

Self-interested

1

VIII

Table A1.

APPENDIX

IA

IA

Compass SSM

SSM

Competitive IA

Compass SSM, compass IA

SSM

SSM, compass IA

Competitive IA

Selﬁsh, IA, SSM

Selﬁsh, IA, SSM

SSM, compass IA

Categorya

XIII

7

11

B

C

8

B

C

5

15

10

B

C

4

A

5

13

B

C

9

B

C

7

6

6

8

5

3

5

3

5

4

4

5

8

7

6

4

7

1

2

1

3

23

17

13

20

23

15

13

22

20

23

21

22

16

21

15

20

15

19

3

0

4

5

10

0

1

8

5

1

0

4

0

2

2

4

0

2

2

1

4

0

2

0

1

1

0

1

0

4

2

1

7

5

6

4

A

A,B,C

A,B,C

A

A

A,B,C

A,B

A

C

A,B

A,C

B

A,B,C

A

A,C

A,B

A,B,C

A

A,C

B

B

A,C

A,B

C

A,C

B,C

A,B

A,C

A,B

A,C

SSM, compass IA

IA

Selﬁsh, IA, SSM

Compass SSM

SSM

IA

IA

SSM

Compass SSM, Compass IA

SSM

IA

Selﬁsh, IA, SSM

IA

SSM, Compass IA

Selﬁsh, IA, SSM

SSM

Competitive IA

Compass SSM, Compass IA

a

IA refers to both competitive (ai W bi), and compassionate (aiobi) inequity averters and SSM refers to both efﬁciency (lij ¼ lik for all j,k) and compassionate (lijWlik for pjopk) social surplus maximizers. See Kamas and Preston (2009) for further details.

3

6

A

5

5

5

5

5

7

7

10

10

A

6

7

A

6

8

6

B

C

6

8

7

7

7

6

A

9

A

10

9

8

7

6

5

CHARITY AUCTIONS IN THE EXPERIMENTAL LAB Jeffrey Carpenter, Jessica Holmes and Peter Hans Matthews ABSTRACT To transform donations ‘‘in kind’’ into cash, charities of all sizes use auctions and rafﬂes. Despite this, neither the theory nor the practice of efﬁcient fund-raising – and, in particular, charity auctions – has received sufﬁcient attention from economists, especially the fact that participation in fund-raisers is endogenous. We describe, in detail, the design and implementation of an experiment to examine 15 charity auction mechanisms. While some of the mechanisms have already received attention from both theorists and empiricists, ours is the ﬁrst comprehensive examination of all existing mechanisms and the ﬁrst to explore the potential of a few new formats. Our analysis focuses on participation differences among the formats and how theory and supplemental survey data can help explain some of these differences.

1. INTRODUCTION Nonproﬁt organizations employ more than 15% of all service sector workers in the United States (Benz, 2005) and depend on charitable Charity with Choice Research in Experimental Economics, Volume 13, 201–249 Copyright r 2010 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0193-2306/doi:10.1108/S0193-2306(2010)0000013010

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donations to provide more than 20% of all cash revenue (Andreoni, 2006). In 2004, these revenues amounted to $250 billion (Giving-USA, 2005) or a little more than 2% of GDP. Both the size of the nonproﬁt sector and its reliance on donations are more pronounced than in other industrialized economies. In much of Western Europe, for example, the size of the nonproﬁt sector and their reliance on donations are much closer to 10% (Benz, 2005; Andreoni, 2006). In more concrete terms, American cultural, educational, and religious institutions count on private philanthropic support more than their counterparts elsewhere. However, this support does not come cheap. In 2001, for example, 200 major charities spent almost $2.5 billion on their efforts to raise funds. Despite this, neither the theory nor the practice of efﬁcient fund-raising has received as much attention from economists as they should. Charities frequently use fund-raisers to transform ‘‘in-kind’’ donations into cash. The scale of these fund-raisers ranges from local church rafﬂes that produce a few hundred dollars to the annual Napa Valley Wine Auction, which raises almost $10 million (Engers & McManus, 2006) or the Robin Hood Foundation auction that raised $71 million on one night in 2007. A brief examination of eBay’s special site for charity auctions, Giving Works that by itself has raised more than $80 million since 2000, reveals wide variation in both the items sold and the nearly 7,000 nonproﬁts who beneﬁt from their sale. There is much less variation, however, in the mechanisms charities use to auction these items. The familiar oral ascending or English, silent and ﬁrst-price sealed-bid auctions dominate the landscape. The motivation for the analysis we present here is very speciﬁc: the reliance of the current literature on ‘‘ﬁxed N’’ analyses of charity auctions. With one exception (Carpenter, Holmes, & Matthews, 2007) in the small theoretical literature and another in the empirical literature (Carpenter, Holmes, & Matthews, 2008), existing studies of charity auctions focus entirely on situations in which all bidders participate. This is obviously problematic when one realizes that both bidding behavior and the number of bidders are likely to affect auction revenues. Furthermore, to the extent that sellers may desire greater participation for other reasons (e.g., better advertising for the businesses that donate in-kind goods, greater prestige for the bidders who desire public recognition, and more publicity for the charitable works of the organization), a better understanding of mechanismspeciﬁc entry preferences is also important. The potential signiﬁcance of endogenous entry is highlighted in the left panel of Fig. 1, which illustrates the relationship between participation rates and revenues raised in our ﬁeld study of 80 auctions conducted 20 at a time

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400 300 0

100

200

Revenue (in EMUs)

1.5 1 .5 0

Revenue (Fraction of Retail Value)

2

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Charity Auctions in the Experimental Lab

0

5

10

15

20

25

Number of Active Bidders Fitted

FPAP

SPWP

0

2

4

6

8

10

Number of Active Bidders FPWP

Fitted

FPAP

SPWP

FPWP

Fig. 1. Revenue versus the Number of Active Bidders in the Field (left) and in the Lab (right) by Mechanism (FPAP is First-Price All-Pay, SPWP is Second-Price Winner-Pay, and FPWP is First-Price Winner-Pay).

at four local preschools (Carpenter et al., 2008). As the ﬁgure clearly shows, there are both quantiﬁable differences in entry across mechanisms and a strong positive relationship between participation and revenue: Each additional bidder is associated with a 4.4% increase in the fraction of an item’s retail value raised in the auction. The ﬁrst-price sealed-bid auction had both higher participation rates and higher revenue than either secondprice sealed-bid or all-pay auctions. Especially conspicuous is the low participation in the all-pay format and the resulting large variance in revenue. Because revenue in the ﬁeld seemed to depend as much on participation as on bidding behavior, we decided to focus our attention on mechanism-speciﬁc entry decisions in a new experimental design. The present chapter describes a large set of laboratory experiments that examine the participation rates and revenue generating properties of three broad categories of fund-raising mechanisms. The ﬁrst set are those that have received some attention in the empirical literature, in particular, rafﬂes, ﬁrst-price sealed-bid winner-pay and ﬁrst-price sealed-bid all-pay auctions. The second set are motivated by the growing theoretical literature on

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auctions but have received little or no attention in the lab or ﬁeld, for example, second-price sealed-bid winner-pay, kth price sealed-bid all-pay, English, Dutch, and silent auctions. The ﬁnal set are new mechanisms developed as a result of our experience conducting charity auctions in the ﬁeld. We ﬁnd that participation differences exist between mechanisms and that these differences persist even when we control for one’s private value and a proxy for cognitive ability. We then use a bit of existing theory and our extensive survey data to better understand why some mechanisms are more popular than others. We begin, in Section 2, by reviewing the literature on charity auctions and endogenous entry. In Section 3, we describe each of the 15 mechanisms under investigation. In Section 4, we describe the details of our experimental design. In Section 5, we discuss summary statistics describing our participants from the post-experiment survey and test for randomization into treatment in Section 6. In Sections 7 and 8, we analyze the participation choices of the potential bidders and in Section 9 offer a few ﬁnal thoughts. Three sets of instructions and the full survey appear in the Appendixes A and B.

2. PREVIOUS WORK ON CHARITY AUCTIONS The theoretical literature on auctions is extensive (see Klemperer, 2004, for an overview) and numerous experimental studies have tested the theoretical predictions either in the lab (e.g., Isaac, Salmon, & Zillante, 2005; Kagel, 1995) or in the ﬁeld (e.g., Hossain & Morgan, 2003; Isaac, Salmon, & Zillante, 2007; List & Lucking-Reiley, 2000, 2002; Lange, Price, & List, 2004; Lucking-Reiley, 1999). The literature on charitable fund-raising is also well developed (e.g., Andreoni, 1989, 1998; List & Lucking-Reiley, 2002). The intersection of these two literatures, charity auctions, has only recently gained signiﬁcant attention by economists (e.g., Carpenter et al., 2008; Carpenter, Holmes, & Matthews, 2009; Davis, Razzolini, Reilly, & Wilson, 2006; Engers & McManus, 2006; Goeree, Maasland, Onderstal, & Turner, 2005; Schram & Onderstal, 2009). The distinction between charity and noncharity auctions is an important one because the externality that all participants can expect to receive from the winning bid in a charity auction substantially alters standard predictions about optimal bids and expected revenues. The ﬁrst puzzle we examine is the disjunction between what is observed in the ﬁeld where lotteries and winner-pay auctions dominate and recent theoretical models of charity auctions which predict that these mechanisms

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should be ‘‘revenue dominated’’ by others; more speciﬁcally, Engers and McManus (2006) and Goeree et al. (2005) predict that charities would do better with all-pay auctions, in which all bidders forfeit their bids, than any of the winner-pay mechanisms now in use. The basic intuition for this result is not difﬁcult. To paraphrase Goeree et al. (2005), if all bidders derive some beneﬁt from the revenues that accrue to the nonproﬁt, winner-pay formats compel bidders to sacriﬁce positive externalities when they outbid their competitors, and this results in lower revenues. Davis et al. (2006) ﬁnd support for this prediction in the lab. Speciﬁcally, they ﬁnd that lotteries – which could be viewed as inefﬁcient all-pay auctions in the sense that all ‘‘bidders’’ forfeit their bids but the bidder who has purchased the most tickets is only the most likely, rather than the certain, winner – generate more revenues than ascending auctions. Furthermore, Davis et al. (2006) show that this outcome is robust with respect to the distribution of bidder values, the attachment of bidders to the charity, and repeated play. Morgan (2000) and Morgan and Sefton (2000) also focus on lotteries as fund-raising mechanisms and ﬁnd (both theoretically and experimentally) that when rafﬂe proceeds are used to fund charitable organizations, the revenues raised are higher than with fund-raising through voluntary contributions; here, the chance of winning the rafﬂed item alleviates the free-rider problem commonly associated with the standard voluntary contributions mechanism. Schram and Onderstal’s (2009) experiment, in which altruistic private values are induced in the lab, provides even more direct evidence: The allpay mechanism was observed to revenue dominate the lottery that in turn revenue dominated the ﬁrst-price sealed-bid mechanism. In Orzen (2008), which Schram and Onderstal (2009) cite, lotteries and two variations of the all-pay are compared, but, in this experiment, values were common, not private. Lastly, Isaac and Schneir (2005) use both the lab and the ﬁeld to testbed features of the silent charity auction; in particular, they focus on the impact of minimum bid increments on efﬁciency, revenue, and the presence of jump-bidding. The vast majority of work in auction theory has assumed a ﬁxed number of bidders. A subset of studies (both theoretical and empirical) has attempted to endogenize the entry decision (e.g., Bajari & Hortacsu, 2003; Chakraborty & Kosmopoulou, 2001; Samuelson, 1985; Engelbrecht-Wiggans, 1993; McAfee & McMillan, 1987; Levin & Smith, 1994; Menezes & Monteiro, 2000; Palfrey & Pevnitskaya, 2008; Pevnitskaya, 2004; Reiley, 2004; Smith & Levin, 1996, 2001) with the primary points of departure being the amount and timing of information and the risk tolerance of the participant pool.

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Although these studies have provided a ﬁrm scaffolding on which to model endogenous entry, the majority of this research has focused on social welfare, efﬁciency, and the optimality of entry fees and reserve prices rather than the impact of mechanism choice on bidder participation. However, there are a few exceptions. In a theoretical piece, Smith and Levin (1996) show that when entry is treated endogenously and bidders exhibit decreasing absolute risk aversion, the second-price auction may generate more revenue than the ﬁrst-price auction. Work by Pevnitskaya (2004) and Palfrey and Pevnitskaya (2008) suggests that bidding will be less aggressive with endogenous entry because only risk-tolerant bidders will self-select into the auction. IvanovaStenzel and Sonsino (2004) conduct an experiment in which subjects are allowed to choose between a standard ﬁrst-price sealed-bid auction and a modiﬁed two-bid auction in which the subjects submit a high bid and a low bid such that the winner pays her low bid if it was higher than all other bids; they ﬁnd strong subject preferences for the two-bid format. Lastly, in a series of studies, Ivanova-Stenzel and Salmon (2004, 2008a, 2008b, 2009) examine bidder preferences for sealed-bid and ascending auctions and show that subjects strongly prefer the ascending format. Furthermore, these preferences cannot be explained by loss aversion or ‘‘clock aversion’’ (i.e., impatience or distaste for the dynamic nature of the ascending mechanism), but more likely result from risk aversion (Ivanova-Stenzel & Salmon, 2008b) or differences in bidder value; high value bidders prefer ascending auctions while low value bidders seek out ﬁrst-price sealed-bid auctions (Ivanova-Stenzel & Salmon, 2009). The authors ﬁnd that while participation is higher in the ascending format than the ﬁrst-price sealed-bid framework, revenue raised and efﬁciency are statistically indistinguishable across mechanisms, although bidder surplus is slightly higher in the ascending framework (Ivanova-Stenzel & Salmon, 2008a; Ivanova-Stenzel & Salmon, 2009). Notable however is that none of the above-mentioned studies explore endogenous entry in the charity auction setting. As mentioned above, the potential effects of endogenous entry on mechanism design in charity auctions are highlighted in Carpenter et al. (2008), the ﬁrst ﬁeld study to test the proposition that the all-pay auction revenue dominates other winner-pay formats. In 80 auctions conducted 20 at a time at four local preschools, we found that ﬁrst-price sealed-bid auctions raised more revenue and were more efﬁcient than either secondprice sealed-bid or all-pay auctions. The unusual circumstances and design features of the experiment, which allowed us to collect data from active and inactive bidders, lead to a tentative explanation for the differences in outcomes in the lab and ﬁeld: participation in charity auctions is endogenous

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and mechanism-speciﬁc. In particular, the ratio of active to potential bidders was much smaller in the all-pay auctions, and this was sufﬁcient to drive revenues below the revenues produced in the ﬁrst-price sealed-bid auctions. In a companion paper (Carpenter et al., 2007), we construct a hybrid model, based on Engers and McManus (2006) and the work of Menezes and Monteiro (2000), of endogenous participation that provides a theoretical framework for our ﬁeld results. While our ﬁeld work highlighted endogenous participation as an important component of mechanism design, we were unable to fully explain the reason(s) for the differences in ﬁeld participation. There are at least two explanations for participation differentials, each with its own implications for charities or, for that matter, mechanism design. The ﬁrst is that some formats are less familiar or harder to ‘‘solve’’ than others. In our experience, for example, even professional microeconomists ﬁnd it difﬁcult to derive optimal all-pay bids on the spur of the moment if they are unfamiliar with auction theory. If this is the reason for the differential, however, charities that switch from winner-pay to all-pay mechanisms could eventually extract more revenue, as bidders become more comfortable. Our panel design in both the lab and the ﬁeld allows us to explore this possibility. The second explanation is that the participation differential is a consequence of bidder preferences or norms. The potential bidder in our ﬁeld experiment who told us that he resented the ‘‘forced contribution’’ under the rules of the all-pay – an objection that did not extend to the rafﬂe that the preschool itself held on the same day – seemed to be motivated by a contextspeciﬁc and perhaps idiosyncratic norm: He seemed to feel that the rafﬂe, in which everyone has a chance to win, was more fair. A bidder with loss averse preferences, on the contrary, will be more wary of bid forfeiture in the all-pay for another reason. In these cases, however, the participation and consequent revenue differentials will be more persistent, because the problem is not familiarity. Our exit surveys help us to explore these potential explanations.

3. AUCTION MECHANISMS We extend the current empirical literature in several directions, each of which we describe in more detail below. First, whereas previous studies have been limited to small (and often different) sets of mechanisms – so that some comparisons are indirect, and assume that results are transitive across experiments – we consider the broadest possible set of 15 formats, one that includes almost all of those tested in the past and some that have never been

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tested in the lab. Second, and as a consequence of what we have learned in the ﬁeld, our choice of design is intended to introduce endogenous participation in the lab. As a result, we will be able to provide a richer characterization of sample selection than we did in Carpenter et al. (2008). In each treatment, all bidders, whether they subsequently decide to participate or not, received a private value vi, determined as the realization of a random variable with uniform distribution over the interval [0,100]. The other common feature is that each bidder received a beneﬁt b for each experimental monetary unit (EMU) she contributes to the ‘‘charity,’’ and a beneﬁt arb for each EMU that another bidder contributes where, following Engers and McManus (2006), the difference g ¼ ba is ‘‘warm glow.’’ Our implementation employed a ¼ 0.10 and g ¼ 0.05. To streamline the descriptions of each mechanism, suppose that there are MoN active bidders and that their bids are ordered b1ob2oyobM, where it is at least possible that some bi are zero. The values of these bids may differ across formats. The ﬁrst three mechanisms that we examine are those that have received the most attention in the literature: First-price sealed-bid winner-pay: Each active bidder submits a sealed bid. The prize is awarded to bidder M, who pays the value of her bid bM, for a pay-off of vM(1g)bM þ abM. No other active bidder pays anything, so that the pay-offs for all other bidders, active and nonactive, is abM Auction revenues are bM. First-price sealed-bid all-pay: Each active bidder submits a sealed bid. The prize is awarded to bidder M, who pays the value of her bid bM, but all other active bidders must pay the values of their P own bids, too. Bidder M’s pay-off is therefore vM Pð1 gÞbM þ a M j¼1 bj . Each of the other M þ a b , and each nonactive bidder receives active bidders receives b i j j¼1 PM P b . Revenues are b . a M j j j¼1 j¼1 Rafﬂe: Each active bidder spends bi on ‘‘tickets’’ that cost r each, and one ticket is drawn at random to determine the winner. If the winner is bidder k, where k and PM M need not be the same, she receives gÞb þ a vk ð1 k j¼1 bj . Each of the other active bidders iak receives P P bi þ a M b , and each of the nonactive bidders receives a M j j¼1 P j¼1 bj . b . Revenues are M j j¼1 The next four have appeared in the theoretical literature but have been tested less often. Some have never been tested in the charity context: Second-price sealed-bid winner-pay: Each active bidder submits a sealed bid. The prize is awarded to bidder M but she pays only bM1, the value

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of the second highest bid. Bidder M’s pay-off is therefore vM bM1 þ ða þ gÞbM1 . All other bidders, active and nonactive, receive abM1 Revenues are bM1. First-price ascending oral (English button): A computer screen ‘‘clock’’ starts at some very low value and becomes the bid of the ﬁrst active bidder to ‘‘claim’’ it. The clock then ticks upward a small amount (0.10), and the new value can be claimed by some (other) bidder. If no one claims a value within some preannounced interval, the prize is awarded to the bidder who claimed the previous value, bM. The winner’s pay-off is vM ð1 gÞbM þ abM . All other bidders, active and nonactive, receive abM. Revenues are bM. All-pay button: This mechanism proceeds just as the English ‘‘button’’ auction except that allPbidders pay their bids. The winner’s pay-off is vM P ð1 gÞbM þ a M All other Pactive bidders receive j¼1 bj . M þ a b , nonactive bidders receive a M b j¼1 j j¼1 bj , and revenues are PMi b . j¼1 j Oral descending (Dutch): A computer screen ‘‘clock’’ starts at some very high bid value and ticks downward. The ﬁrst bidder to stop the clock wins the auction and pays the listed price, bM, for a pay-off of vM ð1 gÞbM þ abM . All other bidders, active and nonactive, receive abM. Revenues are bM. Silent auction(s): Bidders submit increasing bids until a predetermined ending point and each active bidder sees the entire bid history evolve in real time. The winner is the bidder who has submitted the highest bid bM, and she receives vM ð1 gÞbM þ abM . All other bidders, active and nonactive, receive abM. Revenues are bM. There are also two variants of the basic silent format. In the ﬁrst, the ‘‘no-sniping’’ variation, the auction ends 30 seconds after the last bid. In the second, the bidders are given heterogeneous times to be active in the auction. Elsewhere (Carpenter et al., 2009), we examine whether this is an explanation of ‘‘jump’’ bidding.

The next, which to our knowledge has never been tested in either the charity or the noncharity context, ﬁnds its inspiration in the work of Goeree et al. (2005) on ‘‘kth price all-pay’’ charity auctions that should, in theory, do even better than the k–1st price all-pay: Last-price sealed-bid all-pay: Each bidder submits a sealed bid. The prize is awarded to bidder M, who pays the value of the lowest bid submitted b1, as do all of the other active bidders. Bidder M’s pay-off is vM ð1 gÞb1 þ aMb1 . Each of the other active bidders receives b1 þ aMb1 , and each of the nonactive bidders receives aMb1. Revenues are Mb1.

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To maximize the beneﬁts of our research to nonproﬁts, however, it will be important to see whether what we have learned in either the ﬁeld or the lab can be used to develop new, perhaps hybrid, mechanisms that perform even better. Based on our initial experience in the ﬁeld and standard results in behavioral economics, the ﬁnal two mechanisms are as follows: First-price/lottery hybrid: To become active bidders, participants must ﬁrst submit an entry fee r, but those who do so are simultaneously entered in an ‘‘s–lottery.’’ The winner of the lottery receives srM, for some preannounced s between 0 and 1, and the charity receives (1s)rM. If s ¼ 1/2, as in our implementation, this is the familiar ‘‘50–50 lottery.’’ At the same time, active bidders submit bids under the rules of the ﬁrst-price sealed-bid mechanism. If bidder M wins both the auction and the lottery, she receives ðvM þ srMÞ ð1 gÞðbM þ rÞ þ aðbM þ ð1 sÞrMÞ. If she wins the auction but not the lottery, she receives vM ð1 gÞðbM þ rÞ þ aðbM þ ð1 sÞrMÞ. An active bidder who wins the lottery but not the auction receives srM ð1 gÞr þ að1 sÞrM. Last, an active bidder who wins neither receives ð1 gÞr þ að1 sÞrM. Auction revenues are bM þ ð1 sÞrM. ‘‘Bucket’’ auction(s): A computer ‘‘bucket’’ circulates in predetermined order. Subjects ‘‘bid’’ by adding a small ﬁxed increment to the bucket and the auction is over when M–1 of the other participants drop out, and so, the winner is the last person to have contributed to the bucket. If bidder L is the last contributor PM and her total contribution is bL, her pay-off is gÞb þ a active bidders receives vL ð1 L j¼1 bj . Each of the other P PM M b þ a b , each nonactive bidder receives a i j j¼1 j¼1 bj and revenues are PM j¼1 bj . There are also two bucket variations. Instead of the prize going to the last person to bid, in the ﬁrst variant, it goes to the person who contributed the most. In the second variant (the poker bucket), the bidding proceeds according to the ‘‘seeing’’ and ‘‘raising’’ protocol of poker.

4. EXPERIMENTAL DESIGN Based on the work by Kagel (1995) which reports auction sizes of between 3 and 10 bidders, we decided that 10 potential bidders would be needed for each 1.5-hour session. The number of active bidders averaged 4.8, which is in the middle of this range. We calibrated the ﬁnal expected earnings to be $25 per participant including a $10 show-up fee (the actual average was $25.15). To run the experiment, we used zTree by Fischbacher (2007). To recruit participants, we used the Orsee recruitment program and advertised

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Fig. 2.

211

Experimental Session Log (Shading Indicates Sessions Run at UMassAmherst).

mainly via email. Because of the number of participants needed, we ran approximately half of the sessions at Middlebury College and the other half at the University of Massachusetts-Amherst. Fig. 2 details the sessions and their locations. Subjects were provided with a comprehensive set of instructions and ample time to read and ask clarifying questions about the protocol (see Appendix A for a sample of the instructions1). At the beginning of the ﬁrst round, subjects were asked to take a quiz designed to test their basic numeracy and comprehension skills. They were asked four multiple choice questions about how their pay-offs were calculated that required some multiplication and addition. After they took the quiz, they were shown the answers in an effort to eliminate any lingering confusion. Because the questions were mostly a test of numeracy, the number of correct answers will be used as a proxy for our subjects’ cognitive ability.

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0

.05

.1

Fraction .15

.2

.25

A two-stage design allowed us to partially attenuate earned income effects (i.e., ‘‘playing with house money’’) and to endogenize participation. At the start of the experiment, each subject was asked to solve a number of ‘‘word scrambles’’ or anagrams in a predetermined period (12 minutes), similar in spirit to Gneezy, Niederle, and Rustichini (2003) or Hoff and Pandey (2006). Subjects were paid a piece rate of 10 EMUs per correct response and the scramble difﬁculty; the rate and the time limit were chosen so that mean earnings would be about $15 with little variance. While we wanted subjects to earn their endowments for the auctions, we did not want there to be a lot of variation in the endowments that might cause income effects. Indeed, it turned out to be relatively easy to get 10 scrambles right, but it was hard to get more than 16 right. Fig. 3 illustrates the distribution of endowments earned in the ﬁrst stage of the experiment. The mean is 14.00 correct responses and the standard deviation is 1.81. Although the majority of participants ended up in our targeted range, two people did extremely poorly (0 correct and 2 correct) because of confusion.

0

Fig. 3.

1

2

3

4

5

6

7 8 9 10 11 12 13 14 15 16 17 18 19 20 Correct Responses

The Distribution of Earned Endowments in the First Stage (Each Correct Response was Worth 10 EMUs).

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After the 12-minute endowment stage, the auctions (or rafﬂes) began. At the beginning of each of the 10 trials in a session, subjects chose to either participate in the auction whose rules were again explained in detail, and in which all bids were paid from the cash accumulated in the ﬁrst stage or do another word scramble. So that participants did not condition their choice of whether to participate or not on the observed choices of the others, participation choices were conveyed privately and those participants who chose not to participate in the auction remained in the computer lab and solved a word scramble for a ﬁxed piece rate of 15 EMUs per correct response. The opportunity cost of participating was the same for each mechanism. Subjects learned their private values before the participation decision, but they did not know how many other participants selected into the auction. This was done because we expected that there might be an interesting interaction between auction mechanism and private value that justiﬁed complicating the design. Furthermore, theory suggests that participation will depend on one’s value. Along with their private values, participants were also told how hard (on a scale of 1–5) the alternative word scramble would be for the round. The difﬁculty measure allows us to identify selection separately from bidding behavior (i.e., there is no reason to believe that the difﬁculty of the scramble will affect one’s bid amount). We initially selected a sequence of difﬁculty levels randomly and then used this sequence of difﬁculty levels for every session. This allowed us to separate the effect on participation of scramble difﬁculty from the mechanism effect. Subjects were then asked how many bidders they expected to enter the auction and what they thought that their (subjective) chances were to get the puzzle (of stated difﬁculty) correct. As we noted earlier, our interest in the possible effects of learning on both participation and, conditional on this, the decisions of active bidders prompted us to run 10 trials during each session. Between auction trials, participants received feedback that might have facilitated learning (e.g., the winning bid and the share of active bidders). However, to prevent as much as possible one trial from spilling over to affect the results of others (e.g., trying to make up losses in earlier trials), each participant was re-endowed at the beginning of each auction with the amount they earned in the ﬁrst stage of the experiment and only one trial, choosen randomly, was paid. Before leaving, we conducted a survey of the sociodemographic characteristics of our participants and got their reactions to the experiment (see Appendix B).

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5. PARTICIPANT CHARACTERISTICS We ran 75 sessions (ﬁve sessions per treatment). This translates into 745 participants.2 We actively recruited nonstudents to increase the variation in our demographics. Table 1, which provides an overall summary and summaries by location, reports the characteristics of our participants. The mean age of our participants was a little more than 24 years and exactly half of our participants were female. However, our Middlebury participants were signiﬁcantly older (po0.01) and more female (po0.10) than at UMass. We were able to recruit just a few townspeople (1%) and faculty (6%), but these numbers were statistically the same at each location. We were more successful in attracting staff members at Middlebury (po0.01), and as a result students make up a signiﬁcantly larger share of the UMass participants (po0.01). Unfortunately, we were unable to get much racial diversity. Overall, 75% of the participants were Caucasian and 81% were born in the United States, and the distributions do not vary signiﬁcantly by location. There were some signiﬁcant differences in the educational achievements by location. More of the UMass participants were either still in college or had only partially completed their bachelor’s degree (po0.05), but there were more participants with graduate degrees in Amherst (po0.10). Finally, as one might expect given UMass is a large state school and Middlebury is a small liberal arts school, there were more participants from households that earn less than $25,000 at UMass (po0.01) and more participants from households that earn more than $150,000 per year in Middlebury (po0.01). We asked three questions about previous experience in experiments and auctions. The overall mean number of previous experiments (not necessarily economic experiments) was 0.52 (72% of the participants had never participated in an experiment before), but the number was signiﬁcantly higher in Middlebury, which makes sense because the pool of potential subjects is smaller and ours was one of the ﬁrst large-scale experiments conducted in the new Resource Economics experimental lab at UMass. The Middlebury participants also had more experience in both charity (po0.01) and noncharity (po0.01) auctions. Indeed, very few (8%) of the UMass participants had ever participated in a real charity auction. Consistent with the format used by Dohmen et al. (forthcoming), we asked relatively straightforward questions about our participants’ attitudes toward risk, loss, and competitiveness. For example, we asked, ‘‘In general, do you see yourself as someone who is willing, even eager, to take risks, or as someone who avoids risks whenever possible?’’. The mean response was

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Table 1. Summary Statistics (Overall and by Location).

Age Female (fraction) Subject pool (fraction) Townsperson Faculty Staff Student Race (fraction) African-American Asian-American/Asian Latino/Hispanic White/Caucasian Other/mixed Born in the United States (fraction) Schooling (fraction) High school degree Some college College degree Graduate degree Household income (fraction) Less than $25,000 $25,001–$50,000 $50,001–$75,000 $75,001–$100,000 $100,001–$125,000 $125,001–$150,000 More than $150,000 Previous experiment participation (no.) Past participation in a charity auction (fraction) Past participation in a noncharity auction (fraction) General risk taker (1 ¼ low, 10 ¼ high) Financial risk taker (1 ¼ low, 10 ¼ high) General loss averter (1 ¼ low, 10 ¼ high) Financial loss averter (1 ¼ low, 10 ¼ high)

Overall (N ¼ 745)

Middlebury (N ¼ 365)

Umass (N ¼ 380)

24.20 (9.96) 0.50 (0.50)

26.32 (12.45) 0.53 (0.50)

22.16 (6.09) 0.46 (0.50)

F-stat| p-Value 1.48|0.11 0.83|0.63

0.01 0.06 0.14 0.79

(0.11) (0.23) (0.35) (0.41)

0.01 0.04 0.21 0.73

(0.12) (0.21) (0.41) (0.45)

0.01 0.07 0.07 0.85

(0.10) (0.25) (0.25) (0.35)

1.17|0.29 1.36|0.17 1.44|0.13 1.08|0.37

0.03 0.13 0.03 0.75 0.06 0.81

(0.16) (0.34) (0.17) (0.43) (0.23) (0.39)

0.02 0.14 0.02 0.76 0.05 0.79

(0.15) (0.35) (0.15) (0.43) (0.23) (0.41)

0.03 0.12 0.04 0.74 0.06 0.83

(0.18) (0.33) (0.19) (0.44) (0.24) (0.38)

0.72|0.75 0.55|0.91 1.04|0.41 0.72|0.75 1.21|0.26 1.06|0.39

0.07 0.68 0.14 0.11

(0.25) (0.47) (0.35) (0.31)

0.08 0.63 0.19 0.09

(0.38) (0.48) (0.40) (0.29)

0.06 0.72 0.09 0.13

(0.23) (0.45) (0.29) (0.34)

0.78|0.69 1.41|0.14 1.15|0.31 1.52|0.10

0.24 0.13 0.15 0.16 0.11 0.07 0.14 0.52

(0.43) (0.34) (0.36) (0.37) (0.31) (0.25) (0.35) (1.14)

0.15 0.14 0.18 0.16 0.12 0.07 0.19 0.73

(0.35) (0.34) (0.38) (0.37) (0.32) (0.26) (0.39) (1.41)

0.34 0.12 0.13 0.16 0.10 0.06 0.09 0.33

(0.47) (0.33) (0.33) (0.37) (0.30) (0.24) (0.29) (0.76)

3.31|o0.01 1.13|0.33 1.04|0.41 1.46|0.12 1.01|0.44 1.07|0.38 1.71|0.05 1.77|0.04

0.16 (0.37)

0.24 (0.43)

0.08 (0.27)

1.94|0.02

0.43 (0.49)

0.50 (0.50)

0.36 (0.48)

0.95|0.50

5.18 (2.58)

5.15 (2.50)

5.21 (2.67)

0.94|0.52

3.48 (2.42)

3.33 (2.26)

3.63 (2.56)

0.73|0.74

3.87 (2.38)

3.97 (2.35)

3.78 (2.41)

1.69|0.05

3.01 (2.28)

3.01 (2.24)

3.01 (2.31)

1.31|0.20

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Table 1. (Continued ) Overall (N ¼ 745) General competitiveness 6.10 (1 ¼ low, 10 ¼ high) Sports competitiveness 6.14 (1 ¼ low, 10 ¼ high) Sunk cost sensitivity (fraction): Commit fallacy one 0.34 Commit fallacy two 0.55 Commit fallacy three 0.24

Middlebury (N ¼ 365)

Umass (N ¼ 380)

(2.83)

6.13 (2.70)

6.06 (2.95)

1.55|0.09

(3.12)

5.96 (3.09)

6.31 (3.14)

0.87|0.59

(0.47) (0.50) (0.43)

0.29 (0.45) 0.50 (0.50) 0.24 (0.42)

0.39 (0.49) 0.59 (0.49) 0.24 (0.43)

1.33|0.18 0.54|0.91 0.85|0.61

F-stat| p-Value

Note: Means and (standard deviation). The F-statistic and p-value in the last column are from the linear regression of each characteristic on treatment indicators. A signiﬁcant difference (t-test) between locations at the 10% level. A signiﬁcant difference (t-test) between locations at the 5% level. A signiﬁcant difference (t-test) between locations at the 1% level.

5.18, which is directly in the middle of the 1 (low) to 10 (high) scale, and neither the responses to this or any of the other similar questions varied signiﬁcantly by location.3 What is interesting, however, is that in the broader population of participants, people demonstrated some of the common trends seen in similar experiments. For example, people are signiﬁcantly more averse to losses in both the general and the ﬁnancial domains (po0.01 for both). Lastly, we asked three vignette questions to determine the extent to which people are sensitive to sunk costs. In the ﬁrst vignette, the participant has to decide whether or not she would buy another movie ticket after losing the ﬁrst one. Overall, 34% of the participants said that they would not buy another ticket and the percentage was 10% higher at UMass (po0.01). There was also a signiﬁcant difference in the rate of committing the sunk cost fallacy in the second vignette. Here, participants were told that they had made reservations, and paid a deposit to a hotel in Montreal, but then decided that they could have more fun by going somewhere else. In this case, 55% of the people said that they would still go to Montreal and, again, the response rate differed by almost 10% (po0.01). The last vignette was a little more complicated in that responders could choose among ﬁve responses. In this scenario, the participant had bought wine for $20 a bottle in the past but could now sell it on eBay for $75 a bottle. When asked how much it cost to drink one of the bottles, only 24% of the people said $20. The rate of responding with $20 did not vary signiﬁcantly by location.

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6. RANDOMIZATION TO TREATMENT The obvious test of whether we achieved randomization to treatment in our experiment is to regress each of the characteristics in Table 1 on treatment indicators and test whether any of the point estimates are signiﬁcantly different from another. For the sake of brevity, we employ a slightly cruder method. In the last column of Table 1, we report just the F-statistics and p-values from these regressions. Our test is whether the treatment indicators are jointly signiﬁcant or not.4 It appears that, based on four-ﬁfths of the characteristics, our randomization worked well. In 28 of the 35 characteristics, the F-statistic is relatively low and insigniﬁcant at the conventional 10% level. However, the other ﬁfth of the characteristics show more of a pattern. For example, it appears that having a gaduate degree and mechanism are related. This is likely due to the fact that more of the last-price all-pay and ﬁrst-price rafﬂe hybrids occurred at UMass where there were more graduate students. Similarly, there appears to also be a relationship between income and format, but, again, this is not much of a surprise because there were more students from households earning less than $25,000 at UMass and more from families earning more than $150,000 at Middlebury. In particular, the fact that most of the silent auctions and (again) last-price all-pay suctions were run at UMass accounts for this result. Differential participation of UMass participants, who had signiﬁcantly less experience in experiments and auctions, in the silent, Dutch, and English auctions explains the signiﬁcant F-statistics on previous experiment and charity auction experience. Both of the last two cases are less obvious but apparently due to the fact that more of the silent and (nonbasic) bucket auctions were run at UMass. While not perfect, our randomization worked pretty well and our full set of survey responses allows us to correct for any biases that might result from differential selection into one treatment or another.

7. ENDOGENOUS PARTICIPATION DIFFERENCES Our main focus here is on endogenous participation. With 745 subjects eligible to participate in 10 separate auctions, we have 7,450 observations of the participation decision. Table 2, a summary of the mean levels of participation by mechanism, supports the notion that substantial differences exist between formats. For example, the ﬁrst-price lottery hybrid and the basic silent auction garnered nearly 60% participation while the ﬁrst-price all-pay,

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Table 2. Format First-price winner-pay First-price lottery hybrid Second-price winner-pay First-price all-pay Last-price all-pay All-pay button English Dutch Rafﬂe Silent (basic) Silent (no sniping) Silent (heterogeneous times) Bucket (basic) Bucket (highest contributor) Bucket (poker)

Participation, by Format. Participation Rate

Standard Deviation

0.462 0.586 0.464 0.424 0.456 0.424 0.522 0.478 0.480 0.559 0.526 0.502 0.486 0.418 0.454

0.499 0.493 0.499 0.495 0.498 0.495 0.500 0.500 0.500 0.497 0.500 0.500 0.500 0.494 0.498

the all-pay button, and the bucket (most) generated participation rates closer to 40%. Table 3 presents the results of a random effects probit analysis of the individual’s decision to enter an auction. Column (1) includes only the mechanism dummies in the estimation and we use the basic silent auction as the omitted category because it is clearly one of the most commonly used charity formats (Wall Street Journal, May 8, 2002, p. D2). The evidence is again clear; there exist signiﬁcant (in both economic and statistical senses) mechanism-speciﬁc differences in one’s willingness to participate. Relative to the basic silent auction, subjects are signiﬁcantly less likely to enter the ﬁrst-price winner-pay, second-price winner-pay, ﬁrst-price all-pay, last-price all-pay, all-pay button, Dutch, rafﬂe, and all three varieties of the bucket auction. There appear to be no signiﬁcant differences among the silent mechanisms or between the basic silent and either the English button or the ﬁrst-price lottery hybrid. Pairwise comparisons of the probit coefﬁcients highlight some interesting relationships among the formats (we omit the presentation of these results for brevity). If high participation is the seller’s goal, then the ﬁrst-price lottery hybrid is the clear winner; subjects are signiﬁcantly more likely to enter a ﬁrstprice lottery auction than almost any other format (the only exception is the silent basic in which participation rates in the two mechanisms are statistically indistinguishable). The direct comparison between the ﬁrst-price lottery

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Table 3.

Testing for Participation Differences. (1)

First-price winner-pay (I) First-price lottery hybrid (I) Second-price winner-pay (I) First-price all-pay (I) Last-price all-pay (I) All-pay button (I) English (I) Dutch (I) Rafﬂe (I) Silent (no sniping) (I) Silent (heterogeneous times) (I) Bucket (basic) (I) Bucket (highest contributor) (I) Bucket (poker) (I) Male (I) Age Private value Endowment Puzzle difﬁculty Numeracy Experienced bidder (I) Relatively risk averse (I) Relatively loss averse (I) Sunk cost sensitive (I) Competitive (I) Mechanism is unfair (I) Mechanism is complex (I) Observations

0.104 0.030 0.100 0.146 0.110 0.143 0.040 0.087 0.084 0.036 0.062 0.079 0.149 0.111

7,450

(2) (0.044) (0.046) (0.045) (0.043) (0.044) (0.043) (0.045) (0.045) (0.045) (0.046) (0.045) (0.045) (0.043) (0.044)

0.145 0.005 0.116 0.177 0.141 0.206 0.062 0.124 0.131 0.054 0.064 0.099 0.173 0.133 0.007 0.002 0.007 0.002 0.198 0.020 0.066 0.064 0.046 0.012 0.019 0.032 0.031

(0.052) (0.056) (0.054) (0.050) (0.052) (0.049) (0.055) (0.053) (0.053) (0.055) (0.055) (0.054) (0.051) (0.052) (0.022) (0.001) (0.000) (0.001) (0.006) (0.013) (0.041) (0.025) (0.023) (0.026) (0.023) (0.027) (0.036)

7,450

Notes: Marginal effects from probit estimates; (standard errors). Estimates include individual random effects. po0.10. po0.05. po0.01.

hybrid and the standard ﬁrst-price winner-pay may provide some intuition for the relative success of the hybrid. While the auction winner is determined in exactly the same way in both formats, recall that the ﬁrst-price lottery hybrid requires an additional (ﬁxed) entry fee with 50% of the entry revenue awarded to one randomly chosen participant (who may or not be the winner of the auction). The signiﬁcantly greater willingness to participate in the ﬁrst-price lottery hybrid than in the standard ﬁrst-price winner-pay (the coefﬁcient

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difference is 0.34, po.01) suggests that subjects ﬁnd the possibility of winning by pure luck appealing, appealing enough to outweigh the additional participation cost imposed by the entry fee. Comparisons among the most commonly discussed formats in the literature – ﬁrst-price winner-pay, second-price winner-pay, ﬁrst-price all-pay, all-pay button, English, and Dutch – suggest minimal differences in participation rates. The two exceptions are between the ﬁrst-price all-pay and the English (po.05) and the all-pay button and the English (po.05); subjects ﬁnd the two all-pay formats much less attractive to enter than the standard winner-pay English auction. It is likely that the all-pay component has a depressing effect on participation. Despite our deliberate attempt to randomize into treatment, one might wonder if the results are driven by demographic differences between sessions. Column (2) of Table 3 adds auction-speciﬁc and demographic controls to the analysis. Notable is that the marginal effects of the mechanisms become larger (not smaller) in magnitude. Furthermore, although not shown, the pairwise comparisons remain virtually unchanged with the addition of the controls. This suggests that even after controlling for demographic characteristics of the subject pool, participation is endogenous; auction formats are still signiﬁcant predictors of one’s willingness to enter an auction. In terms of the additional covariates in Column (2), we ﬁnd that older subjects are more likely to participate, as are subjects with higher values and those who have participated in more than 10 auctions outside the experiment. Not surprisingly, an increase in the puzzle difﬁculty leads to greater auction participation as the expected value of the puzzle payout decreases. Subjects with higher endowments are less likely to enter an auction, most likely a reﬂection of their greater aptitude for puzzles. Risk averse subjects are 6% less likely to participate while loss averse subjects are 5% less likely to enter an auction. Gender, sunk cost sensitivity, and competiveness played no signiﬁcant role in the decision to participate.5 Neither, to our surprise, did the perceived fairness or complexity of the format.6

8. RETURNING TO EARLIER WORK: A STRUCTURAL APPROACH For a subset of our mechanisms, we can test whether the participants entered the auctions as basic theory might predict. Motivated by the large

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participation differences found in the ﬁeld between the ﬁrst-price winnerpay, the second-price winner-pay, and the ﬁrst-price all-pay mechanisms (Carpenter et al., 2008), we developed a model of participation thresholds (Carpenter et al., 2007), expressed in terms of minimum private values, which, in principle, can be estimated with our lab data. The underlying question is whether the modeled structure of participation choices is present in our lab data where all the important parameters have been induced and, therefore, controlled. Using the notation introduced in Section 3 (e.g., a is the common return and g is warm glow), we begin by describing the theoretical thresholds (drawn from Carpenter et al., 2007) that bidders should have used to decide when to enter auctions and when to stay out. In that model, we consider the case of NZ2 potential risk neutral bidders whose private values, v, are drawn independently from some distribution over the unit interval and who know these values before they must decide whether to participate. Following Samuelson (1985) and Menezes and Monteiro (2000), we assume that potential bidders confront some cost of participation that may simply reﬂect the resources needed to formulate a bid or may even be partially determined by innate bidder preferences. The cost, 0rcjo1, where j ¼ f(irst price), s(econd price), a(ll pay), may therefore vary from one mechanism to the next. Within this framework, symmetric Bayes–Nash equilibria are identiﬁed for bid functions sj (vi) that are assumed to be differentiable above some participation threshold 0 v o1. With all of the details available in Carpenter et al. (2007), we do no more than restate a few main results here. In the case of the ﬁrst-price winner-pay format, for example, the threshold bidder is someone for whom Fðv ÞN1 v ¼ c f This condition deﬁnes an implicit function in which the participation threshold v depends on the costs of participation cf, the number of potential bidders N, and, implicitly, the shape of the distribution function F(v). Furthermore, the underlying intuition for the condition is straightforward: At the threshold, a bidder is indifferent between bidding zero for a good worth v to her and paying the participation cost cf. The expected beneﬁt of this bidding strategy is just v times the probability of winning, that is, the probability that everyone else has a lower bid, which is equal to Fðv ÞN1 . In the special case of a uniform distribution over the unit interval, the threshold is simple to derive: FðvÞ ¼ v and, after simpliﬁcation, the

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condition can be rewritten as follows: 1

v ¼ ðc f ÞN Notice that the comparative statics are intuitive: The threshold rises and participation rates fall either when potential bidders have better outside options or when there are more potential bidders. Unfortunately, the threshold for the second-price winner-pay format is somewhat more complicated: Fðv ÞN1 v þaðN 1ÞFðv ÞN2 ð1 FðvÞÞss ðvÞ ¼ c s where ss ðvÞa0 is the optimal threshold bid in the second-price auction, as further described in Carpenter et al. (2007). There are at least two properties of this threshold that call for attention. First, unlike its ﬁrst-price and allpay equivalents, the second-price threshold is sensitive to the common rate of return a. Second, when participation costs are the same, the second-price threshold is lower, and it should draw more bidders. The explanation is found in a comparison of the threshold conditions, the difference in which is the term aðN 1ÞFðv ÞN2 ð1 FðvÞÞss ðvÞ, which is the beneﬁt that accrues to the threshold bidder in the second-price auction when there is just one other bidder and, as a result, she determines both what the winner pays and the common return. The threshold condition for the all-pay is the same as that for the ﬁrstprice winner-pay, which implies that when participation costs are the same, so are participation rates. We provide a more detailed discussion in Carpenter et al. (2007), but the intuition is that because the optimal threshold bid under both the ﬁrst-price and the all-pay formats is zero, the difference between the beneﬁts of participation and nonparticipation for a bidder on the threshold is just Fðv ÞN1 v. As the cost of participation is ca, the threshold bidder will just be indifferent when Fðv ÞN1 v ¼ ca which, in the uniform case, implies v ¼ ðca Þð1=NÞ . The crisp predictions of the model could, in principle, be put to direct test. Given the complicated form of the second-price threshold and the fact that bidders do not have the same option value, structural estimation is difﬁcult. Instead, we estimate a model that we believe allows for inferences about the structure of participation decisions.

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Speciﬁcally, we start by imputing thresholds for each participant and each period. To do this, we ﬁrst need some sense of the participation costs that individual bidders face before each auction. To do this, we use the endowment stage data to calculate what fraction pi,k of the word scrambles of level k individual i solved correctly. As the scrambles before each auction paid 15 EMUs – or, scaled down to the unit interval, 0.15 – when solved, the expected value of the outside option is therefore ci;k ¼ 0:15pi;k for a level k puzzle. We then calculated the ﬁrst-price and all-pay thresholds directly, as ð1=10Þ v ¼ ci;k , where N ¼ 10 is the session size, and used numerical methods to solve jointly for the threshold and threshold bid in the less tractable secondprice format. To illustrate, consider a subject who solved two-thirds of the level 3 puzzles correctly in the endowment stage and who must now decide whether to enter an auction whose private value is 75 EMUs or do another level 3 scramble. We estimate the expected costs of participation to be 0:10 ¼ 0:15 ð2=3Þ and the threshold for either a ﬁrst-price or all-pay auction to be 0:7943 ¼ ð0:10Þð1=10Þ or, scaling up to the [0,100] lab interval, 79.43 EMUs. As the threshold exceeds her private value, our model predicts that she should not enter the auction. More generally, we deﬁne an indicator for each indvidual and period, ‘‘Value W Threshold,’’ or VGT for short, to be 1 whenever a potential bidder’s randomly assigned value exceeds her imputed threshold and 0 otherwise. Combined, the participation and VGT indicators allow the sample to be divided into four categories: entered when should have, did not enter when should not have, entered when should not have, and last, did not enter when should have. Within the framework of our model, the last two can be counted as ‘‘errors.’’ The overall error rate for our sample is 32%, but the two sorts of errors are not equally likely: entering when one should not is three times more common than not entering when one should. To understand the data better, consider Fig. 4, which includes frequencyweighted scatter plots for each of the three mechanisms of the number of bidders who entered a particular auction and the number of those for whom VGT ¼ 1, that is, the number who, within the framework of our structural model, should have entered. We also plot, in each diagram, a 45-degree line and a simple best ﬁt (least squares) line. Several properties are common to all three mechanisms. First, under the parameters of our experiment, it was seldom the case that ﬁve or more should have entered and, consistent with the internal logic of our model, this happened more often under the secondprice rules because its threshold is lower, ceteris paribus, than the common

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The Numbers who Enter versus Numbers who Should Enter by Mechanism (Bubble Size Depends on the Number Of Identical Observations).

ﬁrst-price and all-pay thresholds. Second, the number who do enter is positively correlated with the number who should but inasmuch as the scatter is not clustered around the 45-degree line, it does not seem that the two are equal. Third, it appears that ‘‘overexuberance’’ – a characteristic of auctions above the 45-degree line, in which the number who enter exceeds the number who should – explains much of this difference. There are some important differences across formats, too. In particular, there are two features of the second-price mechanism that merit attention. First, the correlation between ‘‘should enter’’ and ‘‘did enter’’ is closer to one for the second-price than either the ﬁrst-price or the all-pay auctions: in visual terms, the best ﬁt line is closer to the 45-degree line. Second, there is also less variation around the best ﬁt line under the second-price format. In short, participation in second-price auctions appears both more consistent with our structural model and more predictable. Last, we note that there are more extreme cases of ‘‘overexuberance’’ under the ﬁrst-price mechanism.

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In more formal terms, we consider a test of the structural participation model based on the random effects probit: Participateni;t ¼ b0 þ b1 VGTi;t þ b2 SPWP þ b3 FPAP þ b4 VGTi;t SPWP þ b5 VGTi;t FPAP þ b6 NUMi þ b7 NUMi SPWP þ b8 NUMi FPAP þ b9 LOSSi þ b10 LOSSi SPWP þ b11 LOSSi FPAP þ b12 COMPi þ b13 COMPi SPWP þ b14 COMPi FPAP þ ai þ ui;t ( Participatei;t ¼

1 if Participateni;t 40 0 if Participateni;t 0

where i indexes individuals, t indexes periods, ui;t iid N(0,1), ai Nð0; s2a Þ and is independent of ui,t, SPWP and FPAP are the basic treatment indicators, VGTi,t is the ‘‘should enter’’ indicator deﬁned above, NUMi is the measure of the ith bidder’s numeracy, and LOSSi and COMPi are indicators that are equal to 1 when the bidder is, respectively, relatively loss averse and competitive. Some features of this speciﬁcation call for comment. First, VGT and private value are correlated but not identical, and the relevant coefﬁcients are more than ‘‘value effects.’’ Some bidders with high values will also have high participation costs, for example, and the latter affects their participation threshold and, therefore, the value at which VGT ﬂips from 0 to 1. The value of VGT is also mechanism-speciﬁc: a private value that should induce participation in a second-price auction will sometimes not be sufﬁcient to induce it in a ﬁrst-price or all-pay auction. This said, the relevant test of our structural model is not the joint hypothesis b2 ¼ b3 ¼ . . . b14 ¼ 0 and Fðb0 þ b1 Þ Fðb0 Þ40 but rather b2 ¼ b3 ¼ . . . b14 ¼ 0 and Fðb0 þ b1 Þ Fðb0 Þ ¼ 1: in other words, someone who should enter does so for sure, independent of treatment because all of the relevant structure is embodied in the thresholds, and individual characteristics other than value and threshold. We already know, of course, that 32% of all participation decisions are ‘‘mistaken.’’ The question here is whether or not these mistakes are random or not. The indicators and interaction terms complicate both the calculation and the presentation of marginal effects, and what we present in Table 4 is

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Table 4.

Estimated Participation Marginal Effects, by Format. FPWP

Value W threshold (I) Numeracy Relatively loss averse (I) Competitive (I)

0.374 0.008 0.132 0.134

SPWP (0.045) (0.044) (0.066) (0.075)

0.539 0.013 0.030 0.000

FPAP (0.044) (0.038) (0.063) (0.066)

0.251 0.091 0.077 0.153

(0.059) (0.047) (0.070) (0.070)

Notes: Estimates include individual random effects; (standard errors). po0.10. po0.05. po0.01.

intended to summarize our main results. Consider, for example, perhaps the most basic question, whether or not bidders who should enter do so. Recall that the construction of the VGT variable allows for mechanism-speciﬁc threshold differences but that our econometric model allows for additional, ‘‘nonstructural’’ treatment effects. Under the second-price mechanism, for example, we estimate the effect to be as follows: b þb b1 þ b b2 þ b b4 þ ðb b6 þ b b7 Þ NUM þ ðb b9 þ b b10 ÞLOSS þ ðb b12 þ b b13 ÞCOMP F b 0 F b b0 þ b b2 þ ðb b6 þ b b7 Þ NUM þ ðb b9 þ b b10 ÞLOSS þ ðb b12 þ b b13 ÞCOMP and report both the result (0.539) and the standard error (0.044) in the ﬁrst row (VGT) and second column (SPWP) of Table 4. In broader terms, Table 4 reports the marginal effects of VGT, numeracy, loss aversion, and competitiveness (rows) by format (columns). The ﬁrst row of Table 4 has two important implications. First, the VGT indicator is statistically and economically signiﬁcant under all three formats: even if this reﬂects, at least in part, the positive correlation between private value and ‘‘should enter,’’ those who should enter are more likely to do so. Second, however, chi-square tests (in each case, w2 4100 and po0.01) also reveal that the effect is, in a statistical sense, smaller than one. If our structural model were correct, however, the effect would equal one: those who should enter would enter, and vice versa. The difference between ‘‘should’’ and ‘‘do’’ is most apparent in the all-pay auction, in which our estimates suggest that those who should enter are only 25% more likely to do so. There is, in short, limited support for the participation logic outlined in Carpenter et al. (2007), but as the other rows in Table 4 hint, there is evidence that other inﬂuences are (also) at work.

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Consider the effects of bidder competitiveness on participation. Whatever its conditional (on participation) effect on bids – intuition suggests that competitive bidders will be more aggressive than standard models predict – our data suggests that such bidders are also much more likely (0.153, po0.01) to enter an all-pay auction, but much less likely (0.134, po0.10) to enter a ﬁrst-price auction. Given the small differences in overall participation rates, it seems reasonable to conclude that there are more low (i.e., below threshold) value but competitive bidders in all-pay auctions. The practical implications for auctioneers are immediate: The choice of auction format affects not just the number of active bidders but their nature, both of which have revenue consequences. However, the explanation for the differential effects of competitiveness is not obvious. All three mechanisms are, in effect, normal form games without much ‘‘thrill of the chase.’’ It is possible, however, that competitive individuals were drawn to the all-pay format because it requires all bidders ‘‘to have some skin in the game.’’ To the extent that the all-pay mechanism is differentially attractive to ‘‘hot blooded’’ and therefore, perhaps, unpredictable bidders, it is reasonable to suppose that more numerate bidders will be more reluctant to enter than our structural model predicts. The second row of Table 4 conﬁrms that this is indeed the case: a numerate bidder is 9.1% (po0.10) less likely to enter an all-pay auction. On the contrary, such a bidder is no more or less likely to enter a ﬁrst- or second-price winner-pay auction. This is another result with practical consequences: Auctioneers expend considerable effort creating the ‘‘right atmosphere’’ for a particular choice of format, but should also consider the indirect relationship between format and bidder types and, therefore, atmosphere. In this case, the all-pay mechanism does not just attract ‘‘hot’’ bidders but repels ‘‘cold’’ ones. We had a strong prior that loss averse bidders would also be more reluctant to participate in all-pay auctions, but while the marginal effect (0.07) is plausible, it is statistically insigniﬁcant. The real surprise is found in the ﬁrst column where our results indicate that loss averse bidders will be 13.2% less likely to participate in ﬁrst-price winner-pay auctions than bidders who are not, and the difference is statistically signiﬁcant at better than the 5% level.

9. CONCLUDING REMARKS Despite the importance of fund-raising for the vast number of philanthropic organizations that exist, very little attention has been given to endogenous

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participation, either in the ﬁeld or in the lab. In fact, only Carpenter et al. (2008) has explored the possibility that format choice can affect participation (and thus revenue generation) in charity auctions. This study ﬁlls that void in its detailed description of a large-scale laboratory experiment in which the participation decision is closely examined for 15 different fundraising formats. From Fig. 1, we can see that our new lab results support the ﬁeld work of Carpenter et al. (2008); there are mechanism-speciﬁc participation differences that researchers must account for in their analysis of mechanism design. While the participation results are more subtle in the lab (right panel), the ﬁrst-price all-pay mechanism continues to yield lower participation (Tables 2 and 3), and most imortantly, overall auction revenue continues to depend critically on the number of participants. In addition, we ﬁnd that these participation differences are robust to the inclusion of demographic controls. If maximizing participation is a goal of the charity, the ﬁrst-price lottery hybrid or the basic silent auction appear to be the best choices. The formats in which everyone must forfeit his or her bid (e.g., the all-pays and the buckets) seem to reduce participation.

NOTES 1. We chose to append only a few versions of the instructions because the full set for all the 15 mechanisms ﬁlls about 75 pages. Any of the omitted instructions are available upon request. 2. Despite running 71 sessions with 10 participants, we were forced, because of no-shows, to run three nine-person sessions (one basic bucket, one basic silent, and one all-pay button) and one second-price winner-pay that had only eight participants. 3. Except the fact that there are slightly more ﬁnancial risk takers at UMass (po0.10). 4. We use linear probability models in the case of dichotomous characteristics. 5. An individual was deemed to be sunk cost sensitive if he or she answered ‘‘no’’ to the movie ticket question and ‘‘yes’’ to the Montreal hotel question on the last page of the questionnaire. An individual was considered ‘‘competitive’’ if he or she perceived his or her own competitiveness to be greater than 7 on a scale of 1–10, both generally and in sports. 6. The mechanism is considered ‘‘unfair’’ if the individual answered 0–2 (out of 10) when asked ‘‘Do you think that participants in this fundraising mechanism are treated fairly?’’. The mechanism is ‘‘complex’’ if the individual answered 4 or greater (out of 5) when asked, ‘‘How difﬁcult was it to understand the rules of this experiment?’’.

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ACKNOWLEDGMENTS We thank Stella Nordhagen for research assistance and Carolyn Craven, Steve Holmes, and Corinna Noelke for valuable comments. We also acknowledge the ﬁnancial support of Middlebury College and the National Science Foundation (SES 0617778).

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APPENDIX A. SAMPLE INSTRUCTIONS A.1. First-price winner-pay A.1.1. Introduction Today you are participating in a decision-making experiment. You will earn $10 just for showing up. The instructions are straightforward, and if you follow them, you may be able to make a considerable amount of money. During the experiment, all decisions will be framed in terms of EMUs. At the conclusion of the experiment, all the EMUs that you have accumulated will be converted into real dollars at the rate of 10 EMUs per real dollar (i.e., we will divide your EMUs by 10). You will be paid in cash at the end of the experiment. Please read these instructions carefully, as understanding the rules is essential for doing well. You may refer to these instructions at any time during the experiment. If you have any questions while these instructions are being read, please raise your hand and we will attempt to answer them. You are not allowed to communicate with other participants during the experiment, even to clarify instructions; doing so may be grounds for dismissal from the experiment, forfeiture of earnings, and being banned from future experiments. The same is true of opening other computer programs or modifying the computer set-up during the experiment. The experiment consists of three phases, all conducted using the computer: In the ﬁrst, you will earn an amount of money, your ‘‘endowment,’’; in the second, you will be able to use those earnings to take part in an auction, if you so choose; and in the last phase, you will

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complete a brief survey. Your ﬁnal pay-off will depend on your performance in the ﬁrst phase and your own actions as well as the actions of the other participants in the second phase. A.1.2. Experiment Phase One: Endowment During the ﬁrst part of the experiment, the ‘‘endowment phase,’’ you will be asked to solve a series of word scrambles – puzzles in which the letters of a word are mixed up. It is your task to unscramble them. On your computer screen, you will see one scrambled word at a time, with a blank below each given letter. In each blank, enter the letter that you think belongs in that space in the correct, unscrambled word – see the example below for clariﬁcation. In each blank, please enter only one letter, with no spaces, and use only the letters given in the original scramble. Failure to do so will result in an error message, which you will have to correct before moving on. Note that you can use the tab key to quickly move from one cell to the next. You will have a total of 12 minutes to correctly solve as many scrambles as you can, and for each that you solve correctly, you will earn an additional 10 EMUs. The puzzles increase in difﬁculty as you progress, and you will have only one chance to solve each puzzle. You may leave a puzzle blank, but once you click the ‘‘Submit and Continue to Next Puzzle’’ button, you will not be able to return to that puzzle. There are a total of 25 scrambles. You will not know how many you have solved correctly until the phase is over. Once you have reached the end of the puzzles, please sit quietly and wait for other participants to ﬁnish. At the end of the phase, the number of puzzles you solved correctly and the total EMUs you earned will be shown to you. This amount of EMUs constitutes your endowment and will be used to participate in the second phase of the experiment. A.1.3. Experiment Phase Two: Auction A.1.3.1. Motivation. In the second phase of the experiment, we simulate a charity auction. Charity auctions are different from regular, for-proﬁt, auctions because everyone associated with the charity beneﬁts from the money that is raised. In noncharity auctions, only winners beneﬁt. To simulate this difference, participants in these charity auction simulations will earn beneﬁts from three sources: they earn beneﬁts from winning the auction, they earn beneﬁts from the total amount of money raised by the auction, and they earn beneﬁts from their own contributions. The second source of beneﬁts represents the fact that everyone beneﬁts when money is

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contributed to charity, and the third source represents the fact that people often feel good about themselves for giving money. A.1.4. Deciding whether to Participate and Bidding In the second phase of the experiment, there will be 10 periods. At the beginning of each period, you will decide whether you want to participate in an auction or try to solve another word scramble. In the auction, you will have the opportunity to bid on a single unit of a ﬁctitious good. Although the good is ﬁctitious, it will have some real ‘‘value’’ to you – you can think of this as being the amount of money that the experimenter would pay you for the item if you obtained it in the auction. Each participant will learn his or her value for the item at the beginning of each period, but will not know any of the other participants’ values. Other participants will have different values. Your value for the good will change each period, and how this value is determined is described in detail below. If you choose to participate in the auction, you will submit a bid for the ﬁctitious commodity. The computer will show you your value for the period and will prompt you to enter a bid. You will make one bid per auction and you will not know the bids of the other participants when you choose your own bid. The person who bids the most will win the auction. If you win the auction, you will have to pay your bid out of your endowment, and so, your bid must be greater than or equal to zero but less than your endowment. Bids and values will both be denominated in EMUs. When you make a bid, you will not know how many others are participating in the auction – in each auction, there could be as few as 0 or as many as 10 total bidders, depending on the decisions of the other participants. How auction gains are determined is described in the next section. As indicated above, participation in the auction is a choice. Before you decide to enter a bid or solve a scramble, you will be shown the value you will have for the ﬁctitious good in the auction and the difﬁculty of the scramble you will have to solve. If you choose not to participate in the auction, you will have 2 minutes to solve the word scramble. If you solve it within the time limit, you will earn 15 EMUs; if you do not, you will earn 0 EMUs. The difﬁculty of the puzzle will change randomly at the beginning of each period, but the difﬁculty is the same for all scramble solvers within a period. A.1.5. Auction Rules and Determining Proﬁts The highest bidder wins the auction. The revenue generated by the auction is the amount paid by the auction winner. As mentioned in Section A.1.3.1,

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this revenue has value for all participants, regardless of whether they participate in the auction or try the scramble: each person earns 0.10 times the total auction revenue – the second source of beneﬁts referred to above. The amount the winning bidder contributes to the auction revenue has an additional value for him or her, so that the winner earns an additional 0.05 times the amount (s)he pays. This is the third source of beneﬁts mentioned in Section A.1.3.1. We can work through an example to illustrate the pay-offs. Suppose that six people have entered the auction – let’s call them Arthur, Barbara, Charles, Diane, Ethan, and Frances – and that four others have attempted the scramble. Suppose, too, that Diane bids the most and therefore has won the auction. To calculate how much Diane gains or loses from this win, we need to know how much she values the object and how much she bid. Suppose, for the sake of argument, that the object is worth 75 EMUs to her, she bid 50. Diane’s direct gain, the difference between what the object is worth and what she paid for it, is 75–50 or 25. Because the winning bid is 50, all 10 participants, will receive an additional beneﬁt worth 0.10 50 or 5 EMUs because the charity raised 50 EMUs of revenue from the auction. And last but not least, Diane’s good feeling is worth 0.05 of her contribution or 0.05 50 ¼ 2.5 EMUs to her. Altogether, Diane’s direct and additional gains are therefore equal to 25 þ 5 þ 2.5 ¼ 32.5 EMUs. If she started the auction with an endowment of, say, 120 EMUs, she would leave it with 120 þ 32.5 ¼ 152.5 EMUs. What about someone like Arthur, who did not win the auction? Let’s suppose that Arthur’s endowment was 110 EMUs, that the object was worth 40 EMUs to him, and that he bid 15 EMUs. Arthur’s direct gain is 0 EMUs (i.e, he gains nothing) because he bids 15 EMUs but does not win the object. The ﬁrst of his two additional gains is the same as Diane’s, or 0.10 50 ¼ 5 EMUs, while the second is 0.05 0 ¼ 0 EMUs because he did not win, and therefore, his bid does not determine the auction revenue. Altogther, Arthur’s net gain is 0 þ 5 þ 0 or 5 EMUs. As he entered the auction with an endowment of 110 EMUs, he leaves with 115 EMUs. Finally, what about those who attempted the word scrambles? Let’s consider the hypothetical cases of Gerry, who does not solve his scramble, and Hannah, who does solve her scramble. Gerry does not earn the 15 EMUs for solving the scramble, but he does receive the 0.10 50 ¼ 5 EMUs that each of the bidders and nonbidders

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received in this auction. If he started with the auction with an endowment of 120 EMUs, he ends it with 125 EMUs. Hannah earns 15 EMUs for her scramble and the 0.10 50 ¼ 5 EMUs that all participants receive, and so, her combined gain is 20 EMUs. If she started the auction with an endowment of 130 EMUs, for example, she ends it with 150 EMUs. In algebraic terms, the earnings of any participant can be summarized as follows: Winning bidder earnings ¼ ½Endowment þ ðValue BidÞ þ ð0:10 BidÞ þ ð0:05 BidÞ The total earnings for an auction participant who does not win are as follows: Earnings of other bidders ¼ Endowment þ ð0:10 Winning bidÞ The earnings of people who choose to try the scramble instead of participating in the auction are as follows: if you get it right: Earning of scrambler ¼ ðEndowment þ 15Þ þ ð0:10 Winning bidÞ if you get it wrong: Earning of srambler ¼ Endowment þ ð0:10 Winning bidÞ

A.1.6. Determination of Final Dollar Pay-offs After 10 rounds of the auction have been played, the computer will randomly pick one round to count toward your ﬁnal earnings from the experiment. Because the computer will pick one round randomly, each auction period is completely independent of the others (i.e., you do not accumulate gains or losses from one period to the next). However, if you make losses in the auction phase, they will be deducted from the money you earn in the ﬁrst, endowment phase. The computer will report to you the randomly chosen round and your ﬁnal pay-off in EMUs. After the questionnaire stage is complete, the computer will report your earnings in dollars. All data collected in the experiment will be anonymous and used only for academic research. You will be paid privately, and no other participant will be told what you earned in the experiment.

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A.1.7. Auction Details A.1.7.1. How are the Values Generated? Values are chosen randomly from the interval 0 to 100 EMUs. Your value is independent of the values of all other experiment participants and of your value from other rounds: Knowing your value in a given round tells you nothing about the values of other experiment participants, and knowing your values in previous rounds tells you nothing about your value in the current round. All values between 0 and 100 are equally likely. A.1.7.2. Tie-Breakers. In the event of a tie – when two or more people make the highest bid – the computer randomly determines a winner from among the group of high bidders. Each high bidder has the same chance of winning as the others. A.2. English Button A.2.1. Introduction Today you are participating in a decision-making experiment. You will earn $10 just for showing up. The instructions are straightforward, and if you follow them, you may be able to make a considerable amount of money. During the experiment, all decisions will be framed in terms of EMUs. At the conclusion of the experiment, all the EMUs that you have accumulated will be converted into real dollars at the rate of 10 EMUs per real dollar (i.e., we will divide your EMUs by 10). You will be paid in cash at the end of the experiment. Please read these instructions carefully, as understanding the rules is essential for doing well. You may refer to these instructions at any time during the experiment. If you have any questions while these instructions are being read, please raise your hand and we will attempt to answer them. You are not allowed to communicate with other participants during the experiment, even to clarify instructions; doing so may be grounds for dismissal from the experiment, forfeiture of earnings, and being banned from future experiments. The same is true of opening other computer programs or modifying the computer set-up during the experiment. The experiment consists of three phases, all conducted using the computer: In the ﬁrst, you will earn an amount of money, your ‘‘endowment,’’; in the second, you will be able to use those earnings to take part in an auction, if you so choose; and in the last phase, you will complete a brief survey. Your ﬁnal pay-off will depend on your performance in the ﬁrst phase and your own actions as well as the actions of the other participants in the second phase.

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A.2.2. Experiment Phase One: Endowment During the ﬁrst part of the experiment, the ‘‘endowment phase,’’ you will be asked to solve a series of word scrambles – puzzles in which the letters of a word are mixed up. It is your task to unscramble them. On your computer screen, you will see one scrambled word at a time, with a blank below each given letter. In each blank, enter the letter that you think belongs in that space in the correct, unscrambled word – see the example below for clariﬁcation. In each blank, please enter only one letter, with no spaces, and use only the letters given in the original scramble. Failure to do so will result in an error message, which you will have to correct before moving on. Note that you can use the tab key to quickly move from one cell to the next. You will have a total of 12 minutes to correctly solve as many scrambles as you can, and for each that you solve correctly, you will earn an additional 10 EMUs. The puzzles increase in difﬁculty as you progress, and you will have only one chance to solve each puzzle. You may leave a puzzle blank, but once you click the ‘‘Submit and Continue to Next Puzzle’’ button, you will not be able to return to that puzzle. There are a total of 25 scrambles. You will not know how many you have solved correctly until the phase is over. Once you have reached the end of the puzzles, please sit quietly and wait for other participants to ﬁnish. At the end of the phase, the number of puzzles you solved correctly and the total EMUs you earned will be shown to you. This amount of EMUs constitutes your endowment and will be used to participate in the second phase of the experiment. A.2.3. Experiment Phase Two: Auction A.2.3.1. Motivation. In the second phase of the experiment, we simulate a charity auction. Charity auctions are different from regular, for-proﬁt, auctions because everyone associated with the charity beneﬁts from the money that is raised. In noncharity auctions, only winners beneﬁt. To simulate this difference, participants in these charity auction simulations will earn beneﬁts from three sources: they earn beneﬁts from winning the auction, they earn beneﬁts from the total amount of money raised by the auction, and they earn beneﬁts from their own contributions. The second source of beneﬁts represents the fact that everyone beneﬁts when money is contributed to charity, and the third source represents the fact that people often feel good about themselves for giving money. A.2.3.2. Deciding whether to Participate and Bidding. In the second phase of the experiment, there will be 10 periods. At the beginning of each period,

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you will decide whether you want to participate in an auction or try to solve another word scramble. In the auction, you will have the opportunity to bid on a single unit of a ﬁctitious good. Although the good is ﬁctitious, it will have some real ‘‘value’’ to you – you can think of this as being the amount of money that the experimenter would pay you for the item if you obtained it in the auction. Each participant will learn his or her value for the item at the beginning of each period, but will not know any of the other participants’ values. Other participants will have different values. Your value for the good will change each period, and how this value is determined is described in detail below. If you choose to participate in the auction, you will submit a bid for the ﬁctitious commodity. The computer will show you your value for the period and will prompt you to enter a bid. Bidding in the auction will be done through a ‘‘price clock,’’ the counts upwards from 0 EMUs. You will actively be bidding in the auction and commit to pay the displayed price until you click the ‘‘Drop Out’’ button. In other words, your bid will be equal to the displayed price at which you click the ‘‘Drop Out’’ button. The auction ends automatically when only one bidder is left. This bidder wins the ﬁctitious good and pays the price at which the second highest bidder dropped out. You will have to pay your bid out of your endowment, and so, your bid must be greater than or equal to zero but less than your endowment. Bids and values will both be denominated in EMUs. When you make a bid, you will not know how many others are participating in the auction – in each auction, there could be as few as 0 or as many as 10 total bidders, depending on the decisions of the other participants. How auction gains are determined is described in the next section. As indicated above, participation in the auction is a choice. Before you decide to enter a bid or solve a scramble, you will be shown the value you will have for the ﬁctitious good in the auction and the difﬁculty of the scramble you will have to solve. If you choose not to participate in the auction, you will have 2 minutes to solve the word scramble. If you solve it within the time limit, you will earn 15 EMUs; if you do not, you will earn 0 EMUs. The difﬁculty of the puzzle will change randomly at the beginning of each period, but the difﬁculty is the same for all scramble solvers within a period. A.2.3.3. Auction Rules and Determining Proﬁts. The highest bidder (i.e., the last person to drop out) wins the auction. The revenue generated by the auction is the amount paid by the auction winner. As mentioned in Section A.2.3.1, this revenue has value for all participants, regardless of whether

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they participate in the auction or try the scramble: each person earns 0.10 times the total auction revenue – the second source of beneﬁts referred to above. The amount the winning bidder contributes to the auction revenue has an additional value for him or her, so that the winner earns an additional 0.05 times the amount (s)he pays. This is the third source of beneﬁts mentioned in Section A.2.3.1. We can work through an example to illustrate the pay-offs. Suppose that six people have entered the auction – let’s call them Arthur, Barbara, Charles, Diane, Ethan, and Frances – and that four others have attempted the scramble. Suppose, too, that Diane bids the most and therefore has won the auction. To calculate how much Diane gains or loses from this win, we need to know how much she values the object and how much she bid and the amount of the second highest bid. Suppose, for the sake of argument, that the object is worth 75 EMUs to her, she dropped out at 55, and that the second highest bidder dropped out at 50. Diane will therefore have to pay 50 EMUs. Diane’s direct gain, the difference between what the object is worth and what she paid for it, is 7550 or 25. Because the revenue generated is 50, all 10 participants, will receive an additional beneﬁt worth 0.10 50 or 5 EMUs because the charity raised 50 EMUs of revenue from the auction. And last but not least, Diane’s good feeling is worth 0.05 of her contribution or 0.05 50 ¼ 2.5 EMUs to her. Altogether, Diane’s direct and additional gains are therefore equal to 25 þ 5 þ 2.5 ¼ 32.5 EMUs. If she started the auction with an endowment of, say, 120 EMUs, she would leave it with 120 þ 32.5 ¼ 152.5 EMUs. What about someone like Arthur, who did not win the auction? Let’s suppose that Arthur’s endowment was 110 EMUs, that the object was worth 40 EMUs to him, and that he bid 15 EMUs. Arthur’s direct gain is 0 EMUs (i.e., he gains nothing) because he bids 15 EMUs but does not win the object. The ﬁrst of his two additional gains is the same as Diane’s, or 0.10 50 ¼ 5 EMUs, while the second is 0.05 0 ¼ 0 EMUs because he did not win, and therefore, his bid does not determine the auction revenue. Altogether, Arthur’s net gain is 0 þ 5 þ 0 or 5 EMUs. As he entered the auction with an endowment of 110 EMUs, he leaves with 115 EMUs. Finally, what about those who attempted the word scrambles? Let’s consider the hypothetical cases of Gerry, who does not solve his scramble, and Hannah, who does solve her scramble. Gerry does not earn the 15 EMUs for solving the scramble, but he does receive the 0.10 50 ¼ 5 EMUs that each of the bidders and nonbidders

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received in this auction. If he started with the auction with an endowment of 120 EMUs, he ends it with 125 EMUs. Hannah earns 15 EMUs for her scramble and the 0.10 50 ¼ 5 EMUs that all participants receive, and so, her combined gain is 20 EMUs. If she started the auction with an endowment of 130 EMUs, for example, she ends it with 150 EMUs. In algebraic terms, the earnings of any participant can be summarized as follows: Wining bidder earnings ¼ ½Endowment þ ðValue Second highest bid þ ð0:10 Second highest bidÞ þ ð0:05 Second highest bidÞ The total earnings for an auction participant who does not win are as follows: Earnings of other bidders ¼ Endowment þ ð0:10 Second highest bidÞ The earnings of people who choose to try the scramble instead of participating in the auction are as follows, if you get it right: Earnings of scrambler ¼ ðEndowment þ 15Þ þ ð0:10 Second highest bidÞ if you get it wrong: Earnings of scrambler ¼ Endowment þ ð0:10 Second highest bidÞ

A.2.3.4. Determination of Final Dollar Pay-offs. After 10 rounds of the auction have been played, the computer will randomly pick one round to count toward your ﬁnal earnings from the experiment. Because the computer will pick one round randomly, each auction period is completely independent of the others (i.e., you do not accumulate gains or losses from one period to the next). However, if you make losses in the auction phase, they will be deducted from the money you earn in the ﬁrst, endowment phase. The computer will report to you the randomly chosen round and your ﬁnal pay-off in EMUs. After the questionnaire stage is complete, the computer will report your earnings in dollars. All data collected in the experiment will be anonymous and used only for academic research. You will be paid privately, and no other participant will be told what you earned in the experiment.

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A.2.4. Auction Details A.2.4.1. How are the Values Generated? Values are chosen randomly from the interval 0 to 100 EMUs. Your value is independent of the values of all other experiment participants and of your value from other rounds: Knowing your value in a given round tells you nothing about the values of other experiment participants, and knowing your values in previous rounds tells you nothing about your value in the current round. All values between 0 and 100 are equally likely. A.2.4.2. Tie-Breakers. In the event of a tie – when two or more people make the highest bid – the computer randomly determines a winner from among the group of high bidders. Each high bidder has the same chance of winning as the others.

A.3. Basic Bucket A.3.1. Introduction Today you are participating in a decision-making experiment. You will earn $10 just for showing up. The instructions are straightforward, and if you follow them, you may be able to make a considerable amount of money. During the experiment, all decisions will be framed in terms of EMUs. At the conclusion of the experiment, all the EMUs that you have accumulated will be converted into real dollars at the rate of 10 EMUs per real dollar (i.e., we will divide your EMUs by 10). You will be paid in cash at the end of the experiment. Please read these instructions carefully, as understanding the rules is essential for doing well. You may refer to these instructions at any time during the experiment. If you have any questions while these instructions are being read, please raise your hand and we will attempt to answer them. You are not allowed to communicate with other participants during the experiment, even to clarify instructions; doing so may be grounds for dismissal from the experiment, forfeiture of earnings, and being banned from future experiments. The same is true of opening other computer programs or modifying the computer set-up during the experiment. The experiment consists of three phases, all conducted using the computer: In the ﬁrst, you will earn an amount of money, your ‘‘endowment,’’; in the second, you will be able to use those earnings to take part in an auction, if you so choose; and in the last phase, you will complete a brief survey. Your ﬁnal pay-off will depend on your performance in the ﬁrst phase and your

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own actions as well as the actions of the other participants in the second phase. A.3.2. Experiment Phase One: Endowment During the ﬁrst part of the experiment, the ‘‘endowment phase,’’ you will be asked to solve a series of word scrambles – puzzles in which the letters of a word are mixed up. It is your task to unscramble them. On your computer screen, you will see one scrambled word at a time, with a blank below each given letter. In each blank, enter the letter that you think belongs in that space in the correct, unscrambled word – see the example below for clariﬁcation. In each blank, please enter only one letter, with no spaces, and use only the letters given in the original scramble. Failure to do so will result in an error message, which you will have to correct before moving on. Note that you can use the tab key to quickly move from one cell to the next. You will have a total of 12 minutes to correctly solve as many scrambles as you can, and for each that you solve correctly, you will earn an additional 10 EMUs. The puzzles increase in difﬁculty as you progress, and you will have only one chance to solve each puzzle. You may leave a puzzle blank, but once you click the ‘‘Submit and Continue to Next Puzzle’’ button, you will not be able to return to that puzzle. There are a total of 25 scrambles. You will not know how many you have solved correctly until the phase is over. Once you have reached the end of the puzzles, please sit quietly and wait for other participants to ﬁnish. At the end of the phase, the number of puzzles you solved correctly and the total EMUs you earned will be shown to you. This amount of EMUs constitutes your endowment and will be used to participate in the second phase of the experiment. A.3.3. Experiment Phase Two: Auction A.3.3.1. Motivation. In the second phase of the experiment we simulate a charity auction. Charity auctions are different from regular, for-proﬁt, auctions because everyone associated with the charity beneﬁts from the money that is raised. In noncharity auctions, only winners beneﬁt. To simulate this difference, participants in these charity auction simulations will earn beneﬁts from three sources: they earn beneﬁts from winning the auction, they earn beneﬁts from the total amount of money raised by the auction, and they earn beneﬁts from their own contributions. The second source of beneﬁts represents the fact that everyone beneﬁts when money is contributed to charity, and the third source represents the fact that people often feel good about themselves for giving money.

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A.3.3.2. Deciding whether to Participate and Bidding. In the second phase of the experiment, there will be 10 periods. At the beginning of each period, you will decide whether you want to participate in an auction or try to solve another word scramble. In the auction, you will have the opportunity to bid on a single unit of a ﬁctitious good. Although the good is ﬁctitious, it will have some real ‘‘value’’ to you – you can think of this as being the amount of money that the experimenter would pay you for the item if you obtained it in the auction. Each participant will learn his or her value for the item at the beginning of each period, but will not know any of the other participants’ values. Other participants will have different values. Your value for the good will change each period, and how this value is determined is described in detail below. If you choose to participate in the auction, you will submit bids for the ﬁctitious commodity. This will be done by adding money to a ‘‘bucket’’ that holds all the bids. Each participant will be able to bid by paying money, at least 5 EMUs at a time, into the bucket. The bucket will be passed from one participant to another in an order that is randomly set at the beginning of the period. Once you have placed money in the bucket, it cannot be taken back and must be paid out of your endowment, and so, you cannot put more than your endowment into the bucket. At any time during the auction when it is your turn to add money to the bucket, you can ‘‘pass,’’ which means you pass the bucket to the next participant without adding anything. Once you pass you will be removed from the bidding for the period. The auction will end when there are two people left in the auction and one passes. The winner of the auction will be the person who last put money into the bucket, even if that person has not added the most in total. Bids and values will both be denominated in EMUs. How auction gains are determined is described in the next section. As indicated above, participation in the auction is a choice. Before you decide to enter a bid or solve a scramble, you will be shown the value you will have for the ﬁctitious good in the auction and the difﬁculty of the scramble you will have to solve. If you choose not to participate in the auction, you will have 2 minutes to solve the word scramble. If you solve it within the time limit, you will earn 15 EMUs; if you do not, you will earn 0 EMUs. The difﬁculty of the puzzle will change randomly at the beginning of each period, but the difﬁculty is the same for all scramble solvers within a period. A.3.3.3. Auction Rules and Determining Proﬁts. After all but one of the bidders have passed, the auction will end and the last person to add to the

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bucket will win. The revenue generated by the auction is the total amount in the bucket – the amount paid by all participants. As mentioned in Section A.3.3.1, this revenue has value for all participants, regardless of whether they participate in the auction or try the scramble: each person earns 0.10 times the total auction revenue – the second source of beneﬁts referred to above. The amount each bidder contributes to the bucket has an additional value for them, so that each bidder earns an additional 0.05 times the amount (s)he placed in the bucket. This is the third source of beneﬁts mentioned in Section A.3.3.1. We can work through an example to illustrate the pay-offs. Suppose that six people have entered the auction – let’s call them Arthur, Barbara, Charles, Diane, Ethan, and Frances – and that four others have attempted the scramble. Suppose, too, that after Diane added some EMUs to the bucket, Ethan, Francis, Arthur, Barbara, and Charles all passed, so that Diane has won the auction. To calculate how much Diane gains or loses from this win, we need to know how much she values the object, how much she contributed to the bucket, and how much all of the others contributed. Suppose, for the sake of argument, that the object is worth 50 EMUs to her, she contributed 10, and that the ﬁve other bidders put a total of 90 EMUs in the bucket. Diane’s direct gain, the difference between what the object is worth and what she paid for it, is 5010, or 40. Because 100 EMUs have been contributed to the bucket – the 10 that Diane contributed and the 90 that Arthur, Barbara, Charles, Ethan, and Frances combined contributed – each of them, and each of the four nonbidders, will receive an additional beneﬁt worth 0.10 100 or 10 EMUs because the charity raised 100 EMUs of revenue from the auction. And last but not least, Diane’s good feeling is worth 0.05 of her contribution or 0.05 10 ¼ 0.5 EMUs to her. Altogether, Diane’s direct and additional gains are therefore equal to 40 þ 10 þ 0.5 ¼ 50.5 EMUs. If she started the auction with an endowment of, say, 120 EMUs, she would leave it with 120 þ 50.5 ¼ 170.5 EMUs. What about someone like Arthur, who did not win the auction? Let’s suppose that Arthur’s endowment was 110 EMUs, that the object was worth 40 EMUs to him, and that he added 30 EMUs to the bucket. (Even if Arthur contributes more than Diane, he does not win the auction if he is not the last one to add to the bucket.) Arthur’s direct gain is 30 EMUs (i.e., he suffers a direct loss) because he bids 30 EMUs but does not win the object. The ﬁrst of his two additional gains is the same as Diane’s, or 0.10 100 ¼ 10 EMUs, while the second is 0.05 30 ¼ 1.5 EMUs because he put 30 EMUs in the bucket.

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Altogether, Arthur’s net gain is 30 þ 10 þ 1.5 or 18.5 EMUs. As he entered the auction with an endowment of 110 EMUs, he leaves with 91.5 EMUs. Finally, what about those who attempted the word scrambles? Let’s consider the hypothetical cases of Gerry, who does not solve his scramble, and Hannah, who does solve her scramble. Gerry does not earn the 15 EMUs for solving the scramble, but he does receive the 0.10 100 ¼ 10 EMUs that each of the bidders and nonbidders received in this auction. If he started with the auction with an endowment of 120 EMUs, he ends it with 130 EMUs. Hannah earns 15 EMUs for her scramble and the 0.10 100 ¼ 10 EMUs that all participants receive, and so, her combined gain is 25 EMUs. If she started the auction with an endowment of 130 EMUs, for example, she ends it with 155 EMUs. In algebraic terms, the earnings of any participant can be summarized as follows: Winning bidder earnings ¼ ½Endowment þ ðValue Amount placed in bucketÞ þ 0:10 ðTotal amount in bucketÞ þ 0:05 ðAmount placed in bucketÞ where ‘‘Amount placed in bucket’’ is the amount added by just this bidder, and ‘‘Total amount in bucket’’ is the amount added by all bidders combined. The total earnings for an auction participant who is not the last one to add to the bucket are as follows: Earnings of other bidders ¼ ½Endowment Amount placed in bucketÞ þ 0:10 ðTotal amount in bucketÞ þ 0:05 ðAmount placed in bucketÞ The earnings of people who choose to try the scramble instead of participating in the auction are as follows: if you get it right: Earnings of scrambler ¼ ðEndowment þ 15Þ þ 0:10 ðTotal amount in bucketÞ if you get it wrong: Earnings of scrambler ¼ Endowment þ 0:10 ðTotal amount in bucketÞ

A.3.3.4. Determination of Final Dollar Pay-offs. After 10 rounds of the auction have been played, the computer will randomly pick one round to

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count toward your ﬁnal earnings from the experiment. Because the computer will pick one round randomly, each auction period is completely independent of the others (i.e., you do not accumulate gains or losses from one period to the next). However, if you make losses in the auction phase, they will be deducted from the money you earn in the ﬁrst, endowment phase. The computer will report to you the randomly chosen round and your ﬁnal pay-off in EMUs. After the questionnaire stage is complete, the computer will report your earnings in dollars. All data collected in the experiment will be anonymous and used only for academic research. You will be paid privately, and no other participant will be told what you earned in the experiment. A.3.4. Auction Details A.3.4.1. How are the Values Generated? Values are chosen randomly from the interval 0 to 100 EMUs. Your value is independent of the values of all other experiment participants and of your value from other rounds: Knowing your value in a given round tells you nothing about the values of other experiment participants, and knowing your values in previous rounds tells you nothing about your value in the current round. All values between 0 and 100 are equally likely. A.3.4.2. How Much and How Little Can I Add to the Bucket? You can add as little as 5 EMU, and as much as you like as long as the total amount you have placed in the bucket does not exceed your endowment. The bucket will start out empty. If all active bidders pass the bucket before anyone adds money to it, the auction ends, there is no winner, and auction revenues and all auction participants’ gains are zero. If this is the randomly chosen round for payment, all the auction participants will just earn their phase one endowments.

APPENDIX B. THE SURVEY B.1. Experiment Summary and Concluding Questionnaire While we determine how much we owe you, please complete a short questionnaire to be used in our analysis of the experimental data. The questionnaire should take less than 10 minutes to complete. All responses will be kept conﬁdential and will not be stored with any

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personally identiﬁable information. By completing this survey, you consent to having the anonymous information used solely for purposes of academic research. 1. How old are you? [years] 2. What is your sex? [female, male] 3. From which group were you recruited? [student, staff, faculty, not directly afﬁliated with the College] 4. Which of these racial/ethnic groups describes you best? [white/ Caucasian, African-American, Asian-American/Asian, Latino/Hispanic, other/mixed] 5. Were you born in the United States? [yes, no] 6. If you were not born in the U.S., how many years have you lived here? [years] 7. What is the zip code of your permanent residence? [5 digits] 8. What is your occupation? [text input] 9. How much schooling have you had? [less than high school, high school degree, some college, college degree, graduate degree] 10. What is your annual household income? [less than $25k, $25k-$50k, $50k-$75k, $75k-$100k, $100k-$125k, $125k-$150k, more than $150k] 11. In how many economic experiments (besides this one) have you participated? [number] 12. Have you ever participated in the charity auction? [yes, no] 13. Have you ever participated in a noncharity auction? [yes, no] 14. Approximately how many auctions have you participated in over the past 2 years (including online auctions like eBay)? [none, 1–10, more than 10] 15. How difﬁcult was it to understand the rules of this experiment [5 point likert] 16. Brieﬂy, how did you decide whether or not to participate in a given round? [text input] 17. Brieﬂy, how did you decide what to bid in the auction (or how much money to spend on tickets in the rafﬂe)? [text input] 18. In the ﬁrst round in which you bid or bought rafﬂe tickets, how difﬁcult was it to decide how much money to spend? [5 point likert] 19. In the last round in which you bid or bought rafﬂe tickets, how difﬁcult was it to decide how much money to spend? [5 point likert] 20. In your opinion, how many rounds (between 1 and 10) would it take the typical person to fully understand this fund-raising mechanism? [number between 1 and 10]

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21. Do you think that participants in this fund-raising mechanism are treated fairly? [10 point likert] 22. We are interested in your opinion as to the ability of different mechanisms to raise money for charity. Please consider some other mechanisms that you might not have participated in today. In each case we will describe the mechanism and then ask you how well you think it will perform based on three criteria: revenue for the charity, fairness to participants, and complexity. (Move the slider bar to the left or right to indicate your ranking.) 23. The standard auction in which an auctioneer calls out prices and the highest bidder wins and pays his or her bid. [revenue rank, fairness rank, complexity rank] 24. The all-pay auction in which the highest bidder wins but all participants have to pay their bids whether they win or lose. [revenue rank, fairness rank, complexity rank] 25. The silent auction in which participants write bids on a sheet of paper and the highest bidder wins and pays his or her bid. [revenue rank, fairness rank, complexity rank] 26. The rafﬂe in which participants buy tickets and the winning ticket is drawn at random. [revenue rank, fairness rank, complexity rank] 27. The mechanism you participated in today if it is not listed above. [revenue rank, fairness rank, complexity rank] 28. We would also like to ask you a few questions about your personal preferences and attitudes. 29. In general, do you see yourself as someone who is willing , even eager, to take risks, or as someone who avoids risks whenever possible? [10 point likert] 30. Concerning just personal ﬁnance decisions, do you see yourself as someone who is willing, even eager, to take risks, or as someone who avoids risks whenever possible? [10 point likert] 31. In general, do you see yourself as someone who, when faced with an uncertain situation, worries a lot about possible losses, or someone who seldom worries about them? [10 point likert] 32. Concerning just personal ﬁnance decisions, are you someone who, when faced with an uncertain situation, worries a lot about possible losses, or someone who seldom worries about them? [10 point likert] 33. In general, how competitive do you think that you are? [10 point likert] 34. Concerning just sports and leisure activities, how competitive do you think that you are? [10 point likert]

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35. Lastly, we would also like to ask you to predict how you would behave in a few hypothetical situations. 36. Imagine that you’ve decided to see a movie in town and have purchased a $10 ticket. As you’re waiting outside to theatre for a friend to join you, you discover that you’ve lost the ticket. The seats are not marked and the ticket cannot be recovered because the person who sold it doesn’t remember you. Would you buy another $10 ticket? [yes, no] 37. Imagine that a month ago, you and a friend made a nonrefundable $100 deposit on a hotel room in Montreal for the coming weekend. Since the reservation was made, however, the two of you have been invited to spend the same weekend at another friend’s cottage in Vermont. You’d both prefer to spend the weekend at the cottage but if you don’t go to Montreal, the $100 deposit will be lost. Would you still go to Montreal? [yes, no] 38. Finally, imagine that some time during the summer of 2009 you purchased several bottles of the same wine at a price of $20 each, in anticipation of some later celebration. The celebration never happened, however, and, until now, the bottles were forgotten. You ﬁnd out, however, that the wine can now be sold for $75 per bottle. You nevertheless decide to drink one of the bottles. Which of the following best captures your own feeling of the cost, to you, of drinking the bottle? [$55, $0, $20, more than $20 but less than $75, $75]