Incentives and Prosocial Behavior

By ROLAND BE´NABOU AND JEAN TIROLE*

We develop a theory of prosocial behavior that combines heterogeneity in individual altruism and greed with concerns for social reputation or self-respect. Rewards or punishments (whether material or image-related) create doubt about the true motive for which good deeds are performed, and this “overjustification effect” can induce a partial or even net crowding out of prosocial behavior by extrinsic incentives. We also identify the settings that are conducive to multiple social norms and, more generally, those that make individual actions complements or substitutes, which we show depends on whether stigma or honor is (endogenously) the dominant reputa- tional concern. Finally, we analyze the socially optimal level of incentives and how monopolistic or competitive sponsors depart from it. Sponsor competition is shown to potentially reduce social welfare. (JEL D11, D64, D82, Z13)

People commonly engage in activities that are times has a perverse effect, reducing the total costly to themselves and that primarily benefit contribution provided by agents. Such a crowding others. They volunteer, help strangers, vote, give out of “intrinsic motivation” by extrinsic incen- to political or charitable organizations, donate tives has been observed in a broad variety of social blood, join rescue squads, or even sacrifice their interactions (see Bruno S. Frey, 1997, and Frey life for strangers. In experiments, many subjects and Reto Jegen, 2001, for surveys). Studying also display altruistic or reciprocal behaviors. At schoolchildren collecting donations for a charita- the same time, a number of important phenomena ble organization, Uri Gneezy and Aldo Rustichini and puzzles cannot be explained by the sole pres- (2000b) thus found that they collected less money ence of individuals with other-regarding prefer- when given performance incentives (see also Frey ences. What is, therefore, the broader set of and Lorenz Go¨tte, 1999, on volunteer work sup- motives that shape people’s social conduct, and ply). These findings are in line with the ideas in how do these motives interact with each other and Richard Titmuss (1970), who argued that paying the economic environment? blood donors could actually reduce supply. On the A first puzzle is that providing rewards and punishment side, George A. Akerlof and William punishments to foster prosocial behavior some- T. Dickens (1982) suggested that imposing stiffer penalties could sometimes undermine individuals’ “internal justification” for obeying the law. Frey *Be´nabou: Department of Economics and Woodrow Wil- (1997) provided some evidence to that effect with son School, Princeton University, Princeton, NJ 08544, Cana- respect to tax compliance, and Gneezy and Rus- dian Institute for Advanced Research, Centre for Economic tichini (2000a) found that fining parents for pick- Policy Research, Institute for the Study of Labor, and National Bureau for Economic Research (e-mail: rbenabou@princeton. ing up their children late from day-care centers edu); Tirole: Institut d’Economie Industrielle, 21 Alle´es de resulted in more late arrivals. In experiments on Brienne, 31000 Toulouse, France, Groupe de Recherche en labor contracting, subjects provided less effort E´conomic Mathe´matique et Quantitative, Centre d’Enseigne- when the contract specified fines for inadequate ment et de Recherche en Analyse Socioe´conomique, and Mas- performance than when it did not (Fehr et al., sachusetts Institute of Technology (e-mail: [email protected]). We thank George Akerlof, Samuel Bowles, Armin Falk, Roland 2001; Fehr and Ga¨chter, 2001) and they behaved Fryer, Timur Kuran, Bentley MacLeod, Eric Rasmusen, Tom much less generously when the principal had sim- Romer, participants at various seminars and conferences, and ply removed from their choice set the most selfish three anonymous referees for useful comments. We are espe- options (Armin Falk and Michael Kosfeld, 2006). cially indebted to Ian Jewitt for valuable suggestions. Be´nabou gratefully acknowledges support from the John Simon These findings extend a large literature in psychol- Guggenheim Memorial Foundation in 2004 and from the Na- ogy documenting how explicit incentives can lead tional Science Foundation (SES-0424015). to decreased motivation and unchanged or re- 1652 VOL. 96 NO. 5 BE´ NABOU AND TIROLE: INCENTIVES AND PROSOCIAL BEHAVIOR 1653 duced task performance (see, e.g. Edward Deci, their self-image. In the words of Adam Smith 1975; Deci and Richard Ryan, 1985). In studying (1759), they make moral decisions by assessing this class of phenomena, however, one cannot their own conduct through the eyes of an “im- simply assume that rewards and punishments sys- partial spectator,” an “ideal mate within the tematically crowd out spontaneous contributions. breast”: “We endeavour to examine our own Indeed, there is also much evidence to support the conduct as we imagine any other fair and im- basic premise of economics that incentives work, partial spectator would examine it. If, upon for instance in workplace contexts (e.g., Robert placing ourselves in his situation, we thor- Gibbons, 1997; Canice Prendergast, 1999; Ed- oughly enter into all the passions and motives ward P. Lazear, 2000a, b). A more discriminating which influenced it, we approve of it, by sym- analysis is thus required. pathy with the approbation of this supposed A second set of issues relates to the fact that equitable judge. If otherwise, we enter into his people commonly perform good deeds and re- disapprobation, and condemn it.” frain from selfish ones because of social pres- In more contemporary terms, psychologists sure and norms that attach honor to the former and sociologists describe people’s behavior as and shame to the latter (e.g., Dan Batson, 1998; being influenced by a strong need to maintain Richard B. Freeman, 1997). Charitable and non- conformity between one’s actions, or even feel- profit institutions make ample use of donors’ ings, and certain values, long-term goals, or desire to demonstrate their generosity and self- identities they seek to uphold.2 Recent studies lessness (or at least the appearance thereof), confirm the importance of such self-image con- with displays ranging from lapel pins and T- cerns in explaining prosocial behavior in anon- shirts to plaques in opera houses or hospitals, ymous settings.3 A very telling experiment by and buildings named after large contributors. Jason Dana et al. (2003) thus shows that when Patricia Funk (2005) finds that the introduction people are given the opportunity to remain ig- of mail voting in Switzerland, which allowed norant of how their choices affect others, or of citizens to vote at a lower cost but simulta- their precise role in the outcome (as with firing neously made unobservable who did their “civic squads, which always have one blank bullet), duty” and who did not, failed to raise the ag- many “altruists” choose not to know and revert gregate voting rate and actually resulted in a to selfish choices.4 decline in small communes. The presence of a To examine this broad array of issues, we social signalling motive for giving is also evi- develop a theory of prosocial behavior that dent in the fact that anonymous donations are combines heterogeneity in individuals’ degrees both extremely rare—typically, less than 1 per- of altruism and greed with a concern for social cent of the total number1—and widely consid- ered to be the most admirable. Conversely, 2 boasting of one’s generous contributions is of- Thus Batson (1998) writes, “The ability to pat oneself on the back and feeling good about being a kind, caring ten self-defeating. Codes of honor, whose strin- person, can be a powerful incentive to help”; he also dis- gency and scope vary considerably across time cusses the anticipation of guilt. Daniel Kahneman and Jack and societies, are another example of norms Knetsch (1992) find that subjects’ stated willingness to pay enforced largely through feelings of shame or for alternative public goods is well predicted by indepen- dent assessments of the associated “moral satisfaction.” glory. To understand these mechanisms, it is Miche`le Lamont (2000) documents the importance attached again important not to posit exogenous social by her interviewees to the presence or absence of the “car- constraints, but rather to model the inferences ing self” not just in others, but also in themselves. and market conditions involved in sustaining or 3 For instance, in an anonymous transportation-related inhibiting them. survey of about 1,300 individuals, Olof Johansson-Stenman and Peter Martinsson (2006) find that people who are asked Finally, as much as people care about the which attributes in a car are most important to them sys- opinion others have of them, they care about tematically put environmental performance near the top and social status near the bottom; but when asked about the true preferences of their neighbors or average compatriots, they 1 See, e.g., the studies reported in Amihai Glazer and Kai give dramatically reversed rankings. Interviews with car A. Konrad (1996, p. 1021). Note that anonymous contribu- dealers show intermediate results. tions have the same tax-deduction benefits as nonanony- 4 For evidence of self-image management in dictator mous ones. games, see also J. Keith Murnighan et al. (2001). 1654 THE AMERICAN ECONOMIC REVIEW DECEMBER 2006 reputation or self-respect. The key property of tional concerns are (endogenously) dominated the model is that agents’ prosocial or antisocial by the avoidance of stigma or the pursuit of behavior reflects an endogenous and unobserv- distinction. The first case occurs when there are able mix of three motivations: intrinsic, extrin- relatively few types with low intrinsic altruism, sic, and reputational, which must be inferred and when valid excuses for not contributing are from their choices and the context. We obtain more rare than events that make participation four main sets of results. inevitable, or unusually easy. The second case applies in the opposite circumstances. Rewards and Punishments.—The presence of extrinsic incentives spoils the reputational value Welfare and Competition.—When setting in- of good deeds, creating doubt about the extent centives, sponsors such as charities, nonprofit to which they were performed for the incentives organizations, or government agencies will ex- rather than for themselves. This is in line with ploit these complementarities or substitutabili- what psychologists term the “overjustification ties, which respectively increase or decrease the effect” (e.g., Mark R. Lepper et al., 1973), to elasticity of the supply curve. Because they do which we give a formal content in terms of a not internalize the reputational spillovers that signal-extraction problem.5 Rewards act like an fall on nonparticipants or on those who contrib- increase in the noise-to-signal ratio, or even ute through other sponsors, however, their pol- reverse the sign of the signal, and the resulting icies will generally be inefficient. Thus, even a crowding out of the reputational (or self-image) monopoly sponsor may offer rewards and motivation to contribute can make aggregate “perks” (preferred seating, meetings with fa- supply downward-sloping over a wide range, mous performers, valuable social networking with possibly a sharp drop at zero. opportunities, naming rights to a building, sta- dium, or professorial chair, etc.) that are too Publicity, Praise, and Shame.—A greater generous from the point of view of social wel- prominence and memorability of contributions fare, and sponsor competition may further ag- strengthens the signaling motive and thus gen- gravate this inefficiency. The socially optimal erally encourages prosocial behavior. When in- incentive scheme, by contrast, subtracts from dividuals are heterogeneous in their image the standard Pigouvian subsidy for public goods concerns, however, it also acts like an increase provision a “tax” on reputation-seeking, which, in the noise-to-signal ratio: good actions be- per se, is socially wasteful. In the market for come suspected of being motivated by appear- prosocial contributions, finally, a form of ances, which limits the effectiveness of policies holier-than-thou competition can also lead based on “image rewards” such as public praise sponsors to offer agents opportunities for repu- and shame. The same concern can lead people tationally motivated sacrifices that will again to refrain from turning down any rewards that reduce social welfare, without any increase in are offered. the supply of public goods.

Social and Personal Norms.—The inferences While a number of related themes have been that can be drawn from a person’s actions de- examined in the literature, none of the existing pend on what others choose to do, creating models provides a unified account of this broad powerful spillovers that allow multiple norms range of phenomena. Standard models of public of behavior to emerge as equilibria. More gen- goods provision or altruistic behavior, whether erally, individuals’ decisions will be strategic based on a concern for others’ welfare, a pure complements or substitutes, as will legal and joy of giving, or reciprocity, are not consistent social sanctions, depending on whether reputa- with a (locally) downward-sloping response of prosocial behavior to incentives, nor with peo- ple choosing not to know how their actions will 5 It is also consistent with the informal explanation pro- affect others and reverting to selfish behavior vided by Frey and Jegen (2001): “An intrinsically motivated person is deprived of the chance of displaying his or her when such ignorance is feasible. Models of giv- own interest and involvement in an activity when someone ing as a signal of wealth explain monetary do- else offers a reward, or orders him/her to do it.” nations but not in-kind prosocial acts such as VOL. 96 NO. 5 BE´ NABOU AND TIROLE: INCENTIVES AND PROSOCIAL BEHAVIOR 1655 volunteering, helping, giving blood, etc. (these membership, with which our analysis of social should instead be avoided, as they signal a low norms shares some important insights. On the opportunity cost of time), the greater admiration other hand, Corneo’s model does not give rise reserved for anonymous contributions, or peo- to crowding out, and while Bernheim does not ple’s choosing to be modest about their good consider the effects of incentives, the similarly deeds. Models that postulate a reduced-form unidimensional structure of his model will also crowding out (or in) of intrinsic motivation by lead to a standard upward-sloping response. incentives do not really explain its source and miss Jerker Denrell (1998) shows how the presence its dependence on the informational environment, of monetary or side benefits in some activity can such as the observability of actions and rewards or destroy the separating equilibrium that would the distribution of preferences in the population. otherwise obtain. While this again does not lead The same is true for models of social norms that to crowding out, a principal may obtain higher assume complementarities in payoffs. profits with a zero reward than with a positive The papers most closely related to the present one.7 Closest to our paper is that of Paul Sea- one take a signaling approach to social interac- bright (2002), where individuals derive from tions, although none share with it the structure participating in a “civic activity” both a direct of multidimensional uncertainty that is essential benefit that depends on their private type and a to generating overjustification effects and net reputation that will make them more desirable crowding out. In Be´nabou and Tirole (2003), a partners in a later matching market. Under a potential conflict between extrinsic and intrinsic sorting condition that makes high types care motivation arises from the fact that giving an more about reputation, a “payment discontinu- agent high-powered incentives may convey bad ity” arises at zero, in that total participation can news about the task or his ability. The idea that be greater when no reward is offered than with the principal has private information about a small positive one.8 these variables applies well to child rearing, The paper is organized as follows. Section I education, and empowerment versus monitoring presents the model and an intuitive illustration of employees, but not to activities such as con- of the image-spoiling effect of rewards. Section tributing to a charitable cause, donating blood, II formally demonstrates the crowding-out phe- voting, etc.6 In B. Douglas Bernheim (1994), nomenon, as well as a related form of the over- individuals take actions designed to signal that justification effect. Section III deals with social their tastes lie close to “the mainstream,” lead- ing to conformity in behavior and multiple so- cial norms. When reputation bears on prosocial 7 Funk (2005) shows how a model of voting that incor- orientation, however, what is valuable is not to porates a motive to signal oneself as a “good citizen” can resemble the average but to appear as altruistic very plausibly account for her empirical findings concerning as possible. Such is the case in Giacomo G. the Swiss policy change discussed earlier. The phenomenon thus captured is also not an instance of crowding out, as Corneo’s (1997) signaling model of union both the cost of voting and its visibility are changed simul- taneously and it is the latter that causes participation to fall. 8 Our paper naturally also ties in to the large literature on 6 The informed-principal approach to rewards remains gifts and donations, such as James Andreoni (1993, 2006), applicable when agents know their own type, however, if Glazer and Konrad (1996), William Harbaugh (1998), An- they care about the principal’s perception of it. Thus, in drea Buraschi and Francesca Cornelli (2002), and Prender- Florian Herold (2004), strong incentives can signal that the gast and Lars A. Stole (2001). Other related papers include principal does not trust the agent, which is bad news for Ronit Bodner and Drazen Prelec (2003) and Be´nabou and other aspects of the (multitask) relationship. In Tore Elling- Tirole (2004b) on self-signaling; Akerlof and Rachel E. sen and Magnus Johannesson (2006), agents derive utility Kranton (2000) on identity; Kjell Arne Brekke et al. (2003) from the principal’s ultimate view of their ability or taste for on moral motivation; Maarten Janssen and Ewa Mendys- the activity. Depending on the curvature of this “esteem” Kamphorst (2004) on rewards and the evolution of social function, strong incentives, which signal unfavorable priors, norms; and Wolfgang Pesendorfer (1995) and Laurie Simon may then damage or enhance the expected return to effort. Bagwell and Bernheim (1996) on ostentatious consump- Whereas all the papers above focus on the ex ante choice of tions as signaling devices. Our work is also technically incentives, Anton Suvorov and Jeroen van de Ven (2005) related to a recent literature on signals that convey diverging show that ex post (discretionary) bonuses may serve to news about different underlying characteristics (Aloisio enhance motivation by functioning as a credible feedback Pessoa de Arau´jo et al., 2004; Philipp Sadowski, 2004; mechanism. David Austen-Smith and Roland G. Fryer, 2005). 1656 THE AMERICAN ECONOMIC REVIEW DECEMBER 2006 norms and more generally the strategic comple- of others—family, friends, colleagues, employ- mentarity or substitutability of individual deci- ers. The value of reputation may be instrumen- sions. Section IV examines the possibility for tal (making the agent a more attractive match, agents to turn down rewards. Section V exam- as in Denrell, 1998, Herbert Gintis et al., 2001, ines the setting of incentives by public or pri- or Seabright, 2004) or purely affective (social vate sponsors and the welfare effects of esteem or shame as a hedonic good). For sim- competition. Section VI concludes. All proofs plicity, we assume that it depends linearly on are gathered in the Appendix. observers’ posterior expectations of the agent’s type v, so that the reputational payoff from choosing a, given an incentive rate y,is I. The Model (2) A. Preferences and Information

R͑a, y͒ ϵ x͓␥a E͑va͉a, y͒ Ϫ ␥y E͑vy͉a, y͔͒, We study the behavior of agents who choose 9 the extent of their participation in some pro- with ␥a Ն 0 and ␥y Ն 0. social activity: contributing to a public good ␥ ␥ or worthy cause, engaging in a friendly ac- The signs of a and y reflect the idea that people tion, refraining from imposing negative exter- would like to appear as prosocial (public-spirited) nalities on others, etc. Each selects a and disinterested (not greedy), while the factor participation level a from some choice set x Ͼ 0 measures the visibility or salience of their A ʚ ޒ that can be discrete (voting, blood actions: probability that it will be observed by donation) or continuous (time or money vol- others, number of people who will hear about it, unteered, fuel efficiency of car purchased). length of time during which the record will be ␮ ϵ ␥ ␮ ϵ ␥ Choosing a entails a utility cost C(a) and kept, etc. Defining a x a and y x y,an ϵ yields a monetary or other material reward agent with preferences v (va, vy) and reputa- ѥ ␮ ϵ ␮ ␮ ya. The incentive rate y 0 may reflect a tional concerns ( a, y) thus solves proportional subsidy or tax faced by agents in this economy, or the fact that participation (3) max͕͑va ϩ vy y͒a Ϫ C͑a͒ requires a monetary contribution; note also aʦA that a subsidy to a is equivalent to a tax or ϩ ␮ ͑ ͉ ͒ Ϫ ␮ ͑ ͉ ͒ fine on Ϫa. The incentive rate is set by a a E va a, y y E vy a, y }. principal or “sponsor” and, for now, individ- uals take it as given. In the basic version of the model, ␮ is taken to Denoting by va and vy an agent’s intrinsic be common to all agents and thus public knowl- valuations for contributing to the social good edge. In the full version, we also allow for unob- (discussed further below) and for money (con- served heterogeneity in image-consciousness, sumption of market goods), participation at with ␮ distributed independently of v. Finally, level a yields a direct benefit while we shall generally cast the analysis in terms of effortful or time-consuming prosocial (1) ͑va ϩ vy y͒a Ϫ C͑a͒. actions such as volunteering and voting, it is equally applicable to monetary (e.g., charitable) Each individual’s preference type or “identity” v ϵ (v , v ) ʦ ޒ2 is drawn independently from a y 9 Ϫ a continuous distribution with density f(v) and This payoff is defined net of the constant (1 x)(␥ ៮ Ϫ ␥ ៮ ), which corresponds to the case where a ៮ ៮ ava yvy mean (va, vy). Its realization is private informa- remains unobserved. The restriction to payoffs that are tion, known to the agent when he acts but not linear in the posterior distribution over v is without much observable by others. loss of generality, since introducing (monotonic) nonlinear ␸ ͉ payoffs of the form E[ (va) a, y] would be essentially equivalent to redefining the density of va (see also footnote Social Signaling.—In addition to these direct 34). The more restrictive assumption, which we make for payoffs, decisions carry reputational costs and tractability, is that the coefficients in (2) are independent of benefits, reflecting the judgements and reactions the agent’s type v. VOL. 96 NO. 5 BE´ NABOU AND TIROLE: INCENTIVES AND PROSOCIAL BEHAVIOR 1657

donations, with only a simple relabelling of the plicity, this utility from self-image is linear in ␥ Ϫ␥ variables a (dollars contributed) and y (goods or beliefs, with weights a and y on perceived services used as rewards).10 social orientation and greediness, the model is formally equivalent to the social-signaling one. Self-Signaling, Identity, and Moral Senti- ments.—The model admits an important rein- Relation to Altruism and Public Goods.—An terpretation in terms of self-image. When agent’s intrinsic motivation to behave prosocially, making a decision affecting others’ welfare, an va, can stem from two sources. First, he may care individual will often engage in a self-assessment: about the overall level of a public good to which “How important is it for me to contribute to the his action contributes, such air quality. Let this ៮ ␬ ៮ public good? How much do I care about component of utility be wa(na/n ), where a repre- money? What are my real values?” Later on, sents the average contribution, n the size of the ␬ Ն however, this information may no longer be group, and 0 the degree of congestion; wa perfectly “accessible” in memory—in fact, then measures the intensity of the individual’s there will often be strong incentives to recall it “pure” altruism.12 Second, he may experience a in a self-serving way. Actions, by contrast, are “joy of giving” ua (independent of social- or self- much easier to remember than their underlying esteem concerns) that makes him value his own motives, making it rational to define oneself contribution to na៮ more than someone else’s.13 partly through one’s past choices: “I am the Combining these “pure” and “impure” forms of ϭ ϩ ␬ kind of person who behaves in this way.” Sup- altruism (Andreoni, 1988) yields va ua wa/n ; pose, therefore, that the exact feelings or signals in large groups with ␬ Ͼ 0, the second term underlying the participation decision become becomes vanishingly small. The simplest interpre- inaccessible with some probability proportional tation of our model is thus one with a continuum ϭ to x and that, later on, the agent cares about of agents (so va ua) in which the average “what kind of a person he is.”11 If, for sim- contribution generates a public good (␬ ϭ 1), ៮ which an individual values as waa. The model applies equally well, however, to finite groups of ␬ 10 Let a be the dollar amount contributed by an individ- any size n and value . All that matters is that ual with a known utility for income, the concavity of which there be heterogeneity in the intrinsic propensity Ϫ is represented by C(a). Each dollar generates one unit of to contribute or reciprocate, va, no matter its public good and entitles the contributor to y units of gifts, source, and that agents value being perceived, or perks, and privileges (meeting with performers, gala events, networking, etc.), a “currency” for which he has utility . perceiving themselves, as having a high va. This vy ␮ ͉ The case where the sponsor offers matching funds instead of social (self) esteem benefit, aE(va a, y), is per- perks, i.e., rewards contributors in the same currency, cor- haps what corresponds best to the idea of a “warm ϵ ␮ ϵ responds to vy va and y 0. In the discrete specification glow” of giving: gaining social approval, feeling ʦ ϵ used in Sections IIIA to V (a {0, 1} and vy 1), it can also be represented as the sponsor’s reducing an agent’s monetary cost of providing a unit of public good from c ϵ C(1) to c Ϫ y. Prelec (2003) examine contemporaneous self-signaling in a 11 This may reflect pure feelings of pride or guilt from dual-self model. seeing oneself as generous or selfish (e.g., Akerlof and 12 Since we abstract from decreasing marginal utility Dickens, 1982; Botond Ko¨szegi, 2000), an instrumental over the total supply of public goods, it is worth noting that value of providing the motivation to undertake and perse- the standard substitution effect that it would generate (“if vere in long-term relationships (e.g., Juan D. Carrillo and others give more, I should give less”) can never cause Thomas Mariotti, 2000; Be´nabou and Tirole, 2002), or both. equilibrium aggregate supply to be downward sloping. Note The idea that individuals take their actions as diagnostic of also that, at the cost of some additional complexity, one their preferences originated in psychology with Daryl J. could make agents care about social welfare (which is then Bem (1972) and relates closely to cognitive dissonance defined as a fixed point) rather than about the level of the theory (Leon Festinger and James Carlsmith, 1959). While public good per se. psychologists would generally view people as unable to 13 Such would be the effect of feelings of empathy (em- discern precisely their own motives even at the time they act phasized by Batson, 1998) or reciprocity. Equivalently, the (responding only to the overall mix), this is formally equiv- marginal cost of participation may include an individual Ϫ alent to our specification in which preference states become component equal to ua. The term ua could also arise from inaccessible after some (possibly very brief) period. The link agents’ following the Kantian imperative to evaluate their between imperfect recall and intertemporal self-signaling is actions as if they would lead everyone to make those same analyzed in Be´nabou and Tirole (2004b), while Bodner and choices (Brekke et al., 2003). 1658 THE AMERICAN ECONOMIC REVIEW DECEMBER 2006

good about oneself, etc. The important point, B. The Image-Spoiling Effect of Rewards: however, is the need to go beyond the standard Basic Insights dichotomy between “pure” and “impure” altruism and distinguish, within the latter, between fixed We begin with an intuitive presentation of preferences (ua) and motives that relate to what a some key mechanisms. Consider the first-order person’s behavior says about him or her, which condition for an agent’s choice of a, assuming a will depend on the informational and economic well-behaved decision problem over a continu- context, including what others are doing. Finally, ous choice set. By (3), an individual with type note that the action a chosen by agents and giving (v, ␮) who faces a price y equates rise to reputation could be their reaction to some- one else’s behavior, such as cooperation or defec- (4) CЈ͑a͒ ϭ va ϩ vy y ϩ r͑a, y; ␮͒, tion. The model is thus applicable to reciprocity as well as to unconditional prosocial behavior. where the last term is his (marginal) reputa- We now turn to the terms in (3) relating to tional return from contributing at level a: material compensation. That in vyy requires no explanation, except to note that if the individual ѨE͑va͉a, y͒ ѨE͑vy͉a, y͒ (5) r͑a, y; ␮͒ ϵ ␮ Ϫ ␮ . believes that his receiving y reduces the re- a Ѩa y Ѩa sources available to the sponsor for supporting other activities he cares about, it will be atten- Three important points are apparent from (4). uated by an “eviction effect.”14 Consider next First, observing someone’s choice of a reveals the the potential negative reputation attached to sum of his three motivations to contribute (at the Ϫ␮ ͉ “greed” or money-orientation, yE(vy a, y). margin): intrinsic, extrinsic, and reputational. In Note first that all the paper’s results but one general, all three vary across individuals, so that ␮ ϵ (Proposition 3) obtain with y 0 just as well. learning about va or vy corresponds to a signal- It is, nonetheless, natural to allow for such an extraction problem. Second, a higher incentive effect: “greedy” is no compliment, and indeed rate y reduces the informativeness of actions about someone who has a high valuation for money va, while increasing it about vy. Third, heteroge- relative to effort and/or public goods is not a neity in agents’ image concerns ␮ represents an very attractive partner in friendship, marriage, additional source of noise which makes inferences hiring to a position of responsibility, electing to about both va and vy less reliable, and which is office, or other situations where it is difficult to amplified when actions become more visible always monitor behavior or write complete con- (higher x). tracts. Demonstrating a low marginal utility for To gain further insight into the impact of incen- money vy can also be valuable because it signals tives on inferences and behavior, let us now focus high wealth, a motive that figures prominently on the benchmark case where va and vy are inde- ␮ ␮ in the literatures on charitable contributions and pendent random variables, while a and y are on conspicuous consumption (e.g., Glazer and fixed and will be omitted from the notation. Fig- Konrad, 1996; Bagwell and Bernheim, 1996). ure 1 then shows, for any a Ͼ 0, how the set of agents who contribute at least a varies with the reward y. This group, which we shall term “high 14 In experiments on charitable giving (e.g., Gneezy and Rus- contributors,” comprises all agents with tichini, 2000b), it is typically emphasized to subjects that any rewards will come from an entirely separate research budget (6) va ϩ vy y Ն CЈ͑a͒ Ϫ r͑a, y͒, and therefore do not reduce the amount actually donated. In the real world, the presence and magnitude of an eviction effect so its boundary is a straight line corresponding to will depend on individuals’ beliefs about the level at which the budget constraint binds and how they value the alternative uses (4), along which agents choose exactly a. The of funds. Suppose, for instance, that a charity has a fixed same condition applies when the participation de- budget and will use any funds left over to hire “professionals” cision is discrete, a ʦ {0, 1}, as will be the case in who produce ␶ units of a per dollar, or some other public good the second half of the paper, provided we denote of equivalent value. An individual’s valuation of a reward y for ␣ CЈ(1) ϵ C(1) Ϫ C(0) and r(1, y) ϵ R(1, y) Ϫ R(0, his contribution will now be (v Ϫ ␶w /n )y. This simply y a y). Along the boundary, agents are now indifferent amounts to a redefinition of vy, in a way that contributes to making it negatively correlated with va. between participating and abstaining. VOL. 96 NO. 5 BE´ NABOU AND TIROLE: INCENTIVES AND PROSOCIAL BEHAVIOR 1659

FIGURE 1. THE EFFECTS OF REWARDS ON THE POOL OF PARTICIPANTS

When no reward is offered, y ϭ 0, the sepa- ipate can clearly go either way. Similarly, in ͉ rating locus is vertical: an agent’s contribution the continuous case, the reputation E(va a, y) reveals nothing about his vy, but is very infor- attached to contributing exactly a declines (as mative about his va. In the continuous case, that locus pivots to the left), but so does the prosocial orientation is learned perfectly; in the reputation attached to contributing exactly aЈϭ discrete case one learns whether it is above or a Ϫ da, where da is small; the effect on the Ѩ ͉ Ѩ below a known cutoff. marginal return E(va a, y)/ a is thus a priori When a reward y Ͼ 0 is introduced, the slope ambiguous. of the separating locus becomes Ϫ1/y Ͻ 0. If ● The new high contributors are “greedy” types we ignore, in a first step, any changes in the (have a vy above the mean), whereas those who inferences embodied in the intercept, the origi- still contribute below a after the reward is in- nal boundary simply pivots to the left, as shown troduced reveal that they care less about money in Figure 1 (everything works symmetrically for than average. This unambiguously reduces the a fine or penalty, y Ͻ 0). The set of agents reputational incentive to participate, as is clear contributing at least a thus expands, as types in in the discrete case. In the continuous case, this the hatched area (A ϩ B) are drawn in. Since follows from the fact that, after the rotation, the this occurs at every level of a, the distribution of locus for contributing at a Ϫ da lies below that contributions shifts up (stochastically), resulting for contributing a.15 in a higher total supply; this is the standard effect of incentives. In equilibrium, however, If the overall impact of these changes in there are two reputational effects: inferences is negative, r(a, y) Ͻ r(a, 0), as drawn in Figure 1, the reward attracts some ● The new members of the high-contributors’ new participants (more greedy agents in area B) club have lower va’s than the old ones, so to contributing a or more, but repels some ex- they drag down the group’s reputation for isting ones (more public-spirited agents in area prosocial orientation. The reputation of the low-contributors’ group also declines, how- ever, so in the discrete-choice case, the net 15 This is due to the fact that CЈ(a) Ϫ r(a, y) is increasing effect on the reputational incentive to partic- in a, by the second-order condition for (3). 1660 THE AMERICAN ECONOMIC REVIEW DECEMBER 2006

C).16 Overall, the number of agents who con- where everyone has the same reputational con- ␮ ϵ ␮៮ ␮៮ tribute at least a may increase or decrease, de- cerns, ( a, y). We then extend the anal- pending on the weights given to B and C by the ysis to the case where ␮ is also normally distribution f(v). If a net decrease occurs at distributed across individuals.18 every a, the distribution of contributions shifts down (stochastically) and total supply actually A. Material Rewards declines when a reward y Ͼ 0 is introduced, starting from a no-reward situation. With fixed ␮’s, the reputational return (5) is constant across agents and equal to II. The Overjustification Effect and Crowding Out ѨE͑va͉a, y͒ (8) r៮͑a, y͒ ϵ ␮៮ a Ѩa We now turn to the formal analysis, establish- ing three main results. First, we show how the ѨE͑vy͉a, y͒ “overjustification effect” discussed by psycholo- Ϫ ␮៮ . gists can be understood as a signal-extraction y Ѩa problem in which rewards amplify the noise, lead- ing observers (or a retrospecting individual) to Thus, by (4), an agent’s choice of a reveals his ϩ Ј Ϫ ៮ attribute less of a role to intrinsic motivation in va yvy, equal to C (a) r(a, y). Standard explaining variations in behavior. We then iden- results for normal random variables then yield tify the conditions under which monetary incen- tives crowd out reputational motivation—or, (9) E͑va͉a, y͒ ϭ v៮ a ϩ ␳͑y͒ equivalently, legal sanctions undermine social ones—resulting in a supply curve that is down- ͑ka Ϫ v៮a Ϫ v៮y y Ϫ r៮͑a, y͒͒, ward-sloping over a potentially wide range, or exhibits a sharp drop at zero. Finally, we assess (10) E͑vy͉a, y͒ ϭ v៮ y ϩ ␹͑y͒ the effectiveness of nonmaterial rewards and pun- ishments such as public praise and shame, show- ͑ka Ϫ v៮a Ϫ v៮y y Ϫ r៮͑a, y͒͒, ing in particular that it is also limited by a form of overjustification effect. where We use here a specification of the model ␴2 ϩ ␴ that builds on and extends the familiar normal- a y ay (11) ␳͑y͒ ϵ learning setup. Let actions vary continuously ␴2 ϩ 2y␴ ϩ y2␴2 over A ϭ ޒ, with cost C(a) ϭ ka2/2.17 Agents’ a ay y ϵ valuations v (va, vy) are distributed in the and population as y␹͑y͒ ϵ 1 Ϫ ␳͑y͒. ៮ ␴2 ␴ ͩvaͪ ϳ N ͩva ͫ a ayͬͪ (7) , 2 , v v៮ ␴ ␴ Intuitively, the posterior assessment of an y y ay y ͉ agent’s intrinsic motivation, E(va a, y), is a weighted average of the prior ៮ and of the v៮ a ѥ 0, v៮ y Ͼ 0, va marginal cost of his observed contribution, net and at first we continue to focus on the case of the average extrinsic and reputational incen- tives to contribute at that level.

16 This matches William Upton’s (1973) findings that while offering a monetary reward for giving blood predict- 18 As is often the case, normality yields great tractability at ably brought in new donors, it reduced donations by those the cost of allowing certain variables to take implausible neg- who had regularly been giving for free. ative values. By choosing the relevant means large enough, 17 The case of a general convex function C(a) is treated however, one can make the probability of such realizations in Be´nabou and Tirole (2004a). Both here and there, we arbitrarily small; but (7) and (17) below should really be focus attention on equilibria in which the reputation vector, interpreted as local approximations, consistent with the linear- E(v͉a, y), is differentiable in a. ity of preferences assumed throughout the paper. VOL. 96 NO. 5 BE´ NABOU AND TIROLE: INCENTIVES AND PROSOCIAL BEHAVIOR 1661

Finally, substituting (8) into (9) and (10) shows together, the less observing a high contribution ϩ that an equilibrium corresponds to a pair of func- a, or equivalently a high va vyy, represents ͉ ͉ tions E(va a, y) and E(vy a, y) which solve a good news about the agent’s intrinsic valuation system of two linear differential equations. va; and the larger is y, the stronger is this “dis- counting” effect.20 Summing (12) over agents yields the (per PROPOSITION 1: Let all agents have the capita) aggregate supply of the public good ␮៮ ␮៮ ៮ same image concern ( a, y). There is a unique a(y), whose slope, (differentiable-reputation) equilibrium, in which an agent with preferences (va, vy) contributes at v៮ y the level (14) a៮ Ј͑y͒ ϭ ϩ ␮៮ ␳Ј͑y͒ Ϫ ␮៮ ␹Ј͑y͒, k a y v ϩ v y a y reflects both the standard effect of incentives (12) a ϭ ϩ ␮៮ a␳͑ y͒ Ϫ ␮៮ y␹͑ y͒, k and the crowding out or in of reputational mo- tivation they induce. Since the general expres- where ␳( y) and ␹( y) are defined by (11). The sion (provided in the Appendix) is a bit Ѩ ͉ Ѩ ϭ reputational returns are E(va a, y)/ a complicated, we focus here on two benchmark ␳ Ѩ ͉ Ѩ ϭ ␹ ( y)k and E(vy a, y)/ a ( y)k, resulting cases that make clear the main factors at play. ៮ ϭ ␮៮ ␳ Ϫ ␮៮ ␹ in a net value r( y) k( a ( y) y ( y)), The first one is that of independent values, for independent of a. which we show that as long as the reputational concern over either prosocial orientation or The effects of extrinsic incentives on infer- money-orientation is above some minimum ences and behaviors can now be analyzed. level, there exists a range over which incentives While a higher y increases agents’ direct payoff backfire. ϩ from contributing, va vyy, it also tends to reduce the associated signaling value along both dimensions. In the benchmark case of no corre- PROPOSITION 2 (Overjustification and crowd- ␴ ϭ ␴ ϭ ␪ ϵ ␴ ␴ lation ( ay 0), for instance, ing out): Let ay 0 and define y/ a. Incentives are counterproductive, a៮Ј(y) Ͻ 0, at 1 all levels such that ␳͑ ͒ ϭ (13) y ϩ 2␴2 ␴2 1 y y / a 2 2 2 2 v៮y 2y␪ ␪ ͑1 Ϫ y ␪ ͒ and (15) Ͻ ␮៮ ϩ ␮៮ . k a ͑1 ϩ y2␪2͒2 y ͑1 ϩ y2␪2͒2 y␴2 /␴2 ␹͑ ͒ ϵ y a Consequently, for all ␮៮ above some threshold y ϩ 2␴2 ␴2 , a 1 y y / a ␮ Ն *a 0, there exists a range [y1, y2] such that ៮ a(y) is decreasing on [y1, y2] and increasing ޒ ␮៮ Ͻ ៮ ␪2 ␮ Ͼ so a higher y acts much like an increase in the everywhere else on .If y vy/k , then *a ␪ ϵ ␴ ␴ Ͻ Ͻ ␮៮ noise-to-signal ratio y / a, leading observ- 0 and 0 y1 y2; as a increases, y1 rises and ␮៮ Ͼ ៮ ␪2 ers who parse out the agent’s motives to y2 falls, so [y1, y2] widens. If y vy /k , then ␮ ϭ Ͻ Ͻ ␮៮ decrease the weight attributed to social orienta- *a 0 and y1 0 y2; as a increases both ␳ ␮៮ tion, (y), and increase its counterpart for y1 and y2 rise and, for a large enough, [y1, y2] ␹ 19 ␴  greediness, (y). When ay 0, a positive again widens. correlation tends to amplify the decline in ␳(y); a negative one works to weaken or even reverse 20 it. Indeed, the more va and vy tend to move Thus, as the correlation between va and vy rises from Ϫ1 to 0 to 1, the function ␳(y) pivots downward over the range 0 Ͻ y Ͻ 1/␪, from 1/(1 Ϫ ␪y) to 1/(1 ϩ ␪2y2) and then ϩ ␪ ␴ ␹Ј to 1/(1 y). The effect of ay on the slope (y) is more 19 ␹ ϭ Ϫ ␳ ␴2 More precisely, y (y) 1 (y) rises with y every- complex, as it depends on ay; see (A2) and (A3) in the where, but the same is true of ␹(y) only for ͉y͉ Յ 1/␪. Appendix. 1662 THE AMERICAN ECONOMIC REVIEW DECEMBER 2006

more than men: 52 percent versus 28 percent; (b) introducing a monetary payment (of about $7) caused a moderate, statistically insignificant, in- crease in men’s participation rate (to 37 percent), but led to a dramatic collapse in that of women, which fell to 30 percent; (c) when subjects had the opportunity to turn over their fee to a (cancer- related) charity, men’s participation remained es- sentially unchanged (33 percent), but that of women went right back to 53 percent. If one grants that, for easily understood reasons, it is more important for women than for men to be perceived (and think of themselves) as caring and ␮៮ ␮៮ ϭ A. Varying a (with y 0). The straight line compassionate human beings—that is, if they ␮៮ ϭ ␮ corresponds to a 0 (no reputation concern). have a higher a—then Proposition 2 (or Figure 2A) predicts both that they will contribute more in the absence of rewards and that they will be the ones most likely to respond negatively to mone- tary incentives.22 By the same logic, they will also respond the most to the option of turning down or giving away the reward, which restores to the blood donation its original, unsullied meaning.23 The second case we highlight is that of “small rewards,” which is interesting for two reasons. First, some studies find crowding out (a៮(y) decreasing) to occur mostly at relatively low levels, and it is some- times even suggested that the main effect is a dis- continuity at zero in subjects’ response to incentives (Gneezy and Rustichini, 2000b; Gneezy, 2003). Is there something qualitatively different between ␪ ϭ ␴ ␴ “unrewarded” and “rewarded” activities that could B. Varying y / a. The lower straight line ␮៮ ϭ ␮៮ ϭ cause rational agents to behave in this way? We corresponds to a y 0 (no reputation concern), the upper one to ␪ ϭ 0 (standard one-dimensional show that there is, and explain when it will matter. signaling model). The second reason why “small rewards” are of interest is that in real-world situations where time FIGURE 2 has an opportunity cost, they will actually corre- spond to substantial values of y. As illustrated in Figure 2A, crowding out can occur over a fairly wide range, making all but very PROPOSITION 3 (Small net incentives and large rewards inferior to none.21 Most interesting signal-reversal): (1) Small rewards or punish- ␮៮ ៮Ј Ͻ are the comparative statics on a and the cross- ments are counterproductive, a (0) 0, whenever ␮៮ effects between a and y, two predictions for ␴2 Ϫ ␴2 ␴2 which a recent experiment provides a striking v៮ y ␴ay y 2 ay / a (16) Ͻ ␮៮ ͩ ͪ ϩ ␮៮ ͩ ͪ. match. Studying the willingness of 238 subjects to k a ␴2 y ␴2 join a blood-donor program, Carl Mellstro¨m and a a Johannesson (2005) found that: (a) absent mone- tary rewards, women contributed significantly 22 By contrast, the experimental results described above cannot be explained by what would have been the standard interpretation of condition (a) alone, namely that women 21 ϭ ៮ ϭ ៮ ϭ ៮ The values used in Figure 2A are k 1, va 4, vy are, on average, more prosocial than men (have a higher va). ␮៮ ϭ ␪ ϭ ␮៮ ʦ 23 3, y 0, 0.2, and a {0, 20, 25, 30, 36, 44}. In This case is analyzed, in a simpler version of the ϭ ៮ ϭ ៮ ϭ ␮៮ ϭ ␮៮ ϭ Figure 2B, they are k 1, va 3, vy 1, a y 1, and model, in Section IV, where we show that such options or ␪ ʦ {0, 1, 2, 3, 5}. “menus” may not always be so effective. VOL. 96 NO. 5 BE´ NABOU AND TIROLE: INCENTIVES AND PROSOCIAL BEHAVIOR 1663

␮៮ Ͼ (2) Let y 0 and assume that va and vy are If the empirical validity of this signal reversal uncorrelated, or more generally not too were restricted to very small prizes and fines, it ␴ ␴ correlated. Then, as a / y becomes small, would be of somewhat limited interest. The the slope of the supply function at y ϭ 0 third result shows, however, that the relevant tends to Ϫϱ. “tipping point” is not zero (except in laboratory (3) Suppose that participation entails a unit experiments, where subjects, once there, have opportunity cost with monetary value yˆ. no profitable alternative uses of their time) but Then a៮Ј(yˆ) Ͻ 0 and a៮Ј(yˆ) 3 Ϫϱ under the agents’ monetary value of time, which can be conditions stated in (1) and (2) above, re- quite substantial. This also suggests that exist- spectively. ing experiments may not have been focusing on the most relevant scale of costs and benefits, The first term on the right-hand side of (16) and that future empirical work should involve reflects the intuition given earlier about the role situations in which opportunity costs are non- of correlation in generating crowding out—or trivial and vary across subjects. crowding in. Most important is the second term, whose dependence on the noise-to-signal ratio B. Image Rewards ␴ ϭ is illustrated in Figure 2B: letting ay 0, for ៮Ј ϭ ៮ Ϫ ␮៮ ␴ ␴ 2 instance, shows that a (0) vy /k y( y / a) . Public authorities and private sponsors aiming Thus, in situations where there is much more to foster prosocial behavior make heavy use of uncertainty (hence more to learn) about individ- both public displays and private mementos con- uals’ desire for money than about their motiva- veying honor or shame. Nations award medals tion for the specific task at hand, even a minimal and honorific titles, charitable organizations send ␮៮ Ͼ concern about appearing greedy (a small y donors pictures of “their” sponsored child, non- 0) is sufficient to cause a sharply negative re- profit organizations give bumper stickers and T- sponse to small incentives and, in the limit, a shirts with logos, and universities award honorary downward discontinuity in the supply response. “degrees” to scholars.25 Conversely, the ancient This result, moreover, applies whether or not practice of the pillory has been updated in the ␮៮ the task has any prosocial dimension ( a may form of televised arrests, posting on the Internet equal zero), thus also explaining why adverse the names of parents who are delinquent on child effects of small rewards have been found both support and those of sexual offenders, and pub- in experiments involving private, puzzle-solving lishing in local newspapers the license plate num- tasks and others involving public-goods provi- bers of cars photographed in areas known for drug sion. The intuition for why “zero is special” is trafficking or prostitution.26 that, at that point, participation switches from being an “unprofitable” to a “profitable” activity and thus comes to be interpreted as a signal of continuity in a៮(y)aty ϭ 0 with bounded actions (a ʦ {0, 1}) greed rather than disinterestedness. This signal- ␴ ␴ ϭ and a / y 0. reversal effect, operating specifically around a 25 Our previous results may also help one understand cer- zero net reward, creates an additional source of tain common features of the items that charities, public radio or crowding out on top of the general signal- television stations, etc., offer in their mass fundraising cam- jamming effect (decrease in ␳( y)) that was paigns. The relevant interpretation of the model here is that in 24 which a is a monetary donation and y a reward rate in terms of shown to operate at all levels of y. “thank-you gifts” (see footnote 10). Equation (13) then shows that in order to minimize the image-spoiling effect and maxi- mize contributions, the items should not only be cheap com- pared to the donation (low y) but also have little variance in the 24 ␴2 When the two effects are combined, it is easy to get private value that individuals attach to them (low y); hence supply curves that have a sharp local minimum at y ϭ 0, so the offering of standardized goods with commercially available that neither offering rewards (up to a point) nor requiring substitutes, such as mugs, umbrellas, etc., rather than original sacrifices raises supply. Note also that whereas the signal- or personalized ones. The only dimension in which the items a៮Ј ϭϪϱ reversal effect (lim␴a/␴y30[ (0)] ) is a robust and are unique is the logo they bear, which allows the contributor economically intuitive phenomenon, the fact that the am- to “automatically” display a token of his generosity by using plitude ͉a៮(y)͉ near zero also becomes unbounded in the limit them (relatively high x). is only an artefact of the linear-quadratic specification. In 26 Peer groups also play an important role by creating a Be´nabou and Tirole (2004a), we thus obtain a similar dis- rehearsal mechanism: if acquaintances all contribute to a cause, 1664 THE AMERICAN ECONOMIC REVIEW DECEMBER 2006

Formally, greater publicity or prominence An equilibrium then corresponds again to a pair ␮ ͉ ͉ corresponds to a homothetic increase in ( a, of functions E(va a, y) and E(vy a, y) which ␮ y). Our model then confirms the intuitions solve the differential equations (9) and (10), but above, but also delivers important caveats. In this system is now nonlinear, due to the term particular, when agents are heterogeneous in ⍀(a, y)2 in ␳ and ␹. We are able to solve it for their reputational concerns, giving greater scru- the intuitive and important class of solutions tiny to their behavior may not work that well, as where ⍀ is independent of a, so that reputations good actions come to be suspected of being remain linear in a. We cannot a priori exclude image-motivated. To analyze these issues, we the existence of other, nonlinear, equilibria. now allow agents’ image concerns, like their valuations, to be normally distributed: PROPOSITION 4: (1) A linear-reputation equi- ␮ ␮៮ ␻2 ␻ librium corresponds to a fixed-point ⍀(y), so- a ϳ N a a ay (17) ͩ␮ ͪ ͩ␮៮ , ͫ␻ ␻2 ͬͪ, y y ay y lution to: (20) ⍀͑y͒2/k2 ϵ ␻2␳͑ y͒2 ␮៮ a Ն 0, ␮៮ y Ն 0, a

␮ Ϫ ␻ ␳ ␹ ϩ␻2␹ 2 with v and independent. In the first-order 2 ay (y) (y) y (y) , condition (4), the reputational return r(a, y; ␮) is now also normal and independent of v (con- where ␳( y) and ␹( y) are given by (19) with ditionally on a), with mean r៮(a, y) given by (8) ⍀(a, y) ϵ⍀( y). The optimal action chosen and variance by an agent with type (v, ␮) is then ϩ Ѩ ͉ Ѩ ͉ va vy y E(va a, y) E(vy a, y) (21) a ϭ ϩ ␮ ␳͑ y͒ Ϫ ␮ ␹͑ y͒ (18) ⍀͑a, y͒2 ϵ ͩ Ϫ ͪ k a y Ѩa Ѩa Ѩ ͉ and the marginal reputations are E(va a, Ѩ ͉ Ѩ ϭ ␳ Ѩ ͉ Ѩ ϭ ␹ E(va a, y) y)/ a ( y)k and E(vy a, y)/ a ( y)k, 2 ␮ ϭ ␮ ␳ Ϫ ␻ ␻ Ѩa with a net value of r( y; ) ( a ( y) ϫ a ay ϫ ͫ␻ ␻2 ͬ Ѩ ͉ . ␮ ␹( y))k for the agent. ay y ΂ E(vy a, y)΃ y Ϫ Ѩa (2) There always exists such an equilibrium, ␻ ϭ and if ay 0 it is unique (in the linear- The signal-extraction formulas (9) and (10) thus reputation class). remain unchanged, except that the updating co- efficients ␳(y) and ␹(y) are respectively re- A greater variability of image motives, placed by ⍀(y)2 ϭ Var(r(y; ␮)), makes individuals’ be- havior a more noisy measure of their true un- ␴2 ϩ ␴ ␳ a y ay derlying values (va, vy), reducing both (y) and (19) ␳͑a, y͒ ϵ ␹ ␴2 ϩ 2y␴ ϩ y2␴2 ϩ ⍀͑a, y͒2 (y). This variance is itself endogenous, how- a ay y ever, as agents’ reputational calculus takes into and account how their collective behavior affects observers’ signal-extraction problem. This is re- y␴2 ϩ ␴ flected in the fixed-point nature of equation ␹͑ ͒ ϵ y ay (20).27 a, y ␴2 ϩ ␴ ϩ 2␴2 ϩ ⍀͑ ͒2 . a 2y ay y y a, y Proposition 4 allows us to demonstrate how increased publicity gives rise to an offsetting

one is constantly reminded of one’s generosity, or lack thereof. 27 ␻  People indeed volunteer more help in response to a direct When ay 0, there could be multiple equilibria, with request to do so, especially when it comes from a friend, a different degrees of informativeness. Since the general colleague, or family (Freeman, 1997), whose opinion of them theme of multiplicity is investigated in Section IIIA, we do they naturally care about more than that of strangers. not pursue it here. VOL. 96 NO. 5 BE´ NABOU AND TIROLE: INCENTIVES AND PROSOCIAL BEHAVIOR 1665 overjustification effect. Let all the reputational The aggregate social benefit from publicity ␮ ϭ ␮ ␮ ␮៮ ␳ 1/3 weights ( a, y) be scaled up by some a x ( y, x) thus grows only as x , implying prominence or memorability factor, x; the ma- that it is optimal to provide only a finite level terial incentive y remains constant. Aggregate of x even when it has a constant marginal cost, supply is then or even a marginal cost that declines slower than xϪ2/3.29 Policies by parents, teachers, gov- ernments, and other principals that rely on the v៮ a ϩ v៮ yy (22) a៮ ͑y, x͒ ϭ “currency” of praise and shame are thus effec- k tive up to a point, but eventually self-limiting.

ϩ x͑␮៮ a␳͑y, x͒ Ϫ ␮៮ y␹͑y, x͒͒, III. Honor, Stigma, and Social Norms where the dependence on x indicates that all the ␻2 ␻ ␻2 covariance terms ( a, ay, y) in the original The second main issue we explore is that of equation (20), corresponding to x ϭ 1, are now social and personal norms. We first show how multiplied by x2. A greater visibility of actions multiple standards of “acceptable” behavior can (and of any rewards attached to them) thus has arise from the interplay of honor and shame, two offsetting effects on the reputational incen- then examine what characteristics of the “mar- tive to contribute: ket,” such as the distribution of social prefer- ences, the availability of excuses, or the ● A direct amplifying effect, the sign of which is observability of action and inaction, facilitate or ␮ ␳ Ϫ ␮ ␹ that of a (y, x) y (y, x) for an individual impede their emergence. ␮៮ ␳ Ϫ ␮៮ ␹ and a (y, x) y (y, x) on average. For For the remainder of the paper we focus on people who are mostly concerned about appear- the case of a binary participation decision, A ϭ ␮ ӷ ␮ ing socially minded ( a y), this increases {0, 1}, in which the notions of honor and stigma the incentive to act in a prosocial manner, are most sharply apparent. Unless otherwise whereas for those most concerned about not specified, we also assume that all agents share ␮ ӷ ␮ ␮ ϵ ␮ ␮ appearing greedy ( y a), it has the reverse the same reputational concern ( a, y) and effect.28 the same valuation for money, which we nor- ● A dampening effect, as reputation becomes malize to v ϵ 1. Their prosocial orientation v , y Ϫa less sensitive to the individual’s behavior, by contrast, is distributed on some interval [va , ϩ 30 which observers increasingly ascribe to im- va ]. Indeed, whereas two-dimensional uncer- age-seeking. Formally, the “effective noise” tainty is essential to the overjustification and ⍀(y, x) increases with x (in any stable equi- backfiring-incentives effects analyzed earlier, it librium) and ␳(y, x) and ␹(y, x) consequently is not needed for most of the other results. This tend to decrease with it. simplification also removes any potential incen- tive for agents to “burn money” in order to This tradeoff implies that giving increased pub- signal a low vy. licity to prosocial or antisocial behavior may be of We again denote r(y) ϵ R(1, y) Ϫ R(0, y) and somewhat limited effectiveness, even when it is let c ϵ C(1) Ϫ C(0). Thus, an agent now par- Ն Ϫ Ϫ ϵ relatively cheap to do. Consider, for instance, the ticipates if va c y r(y) v*a(y). To ␮ ␻ ϭ case where y is known ( y 0), possibly equal determine this equilibrium threshold of altru- to zero. As x becomes large (more generally, ism, let us define, for any candidate cutoff va, ␻2 ӷ xk a 1), equation (20) yields the conditional means in the upper and lower tails: ␴2 ϩ ␴ 1/3 a y ay (23) ␳͑y, x͒ Ϸ ͩ ͪ xϪ2/3. 2␻2 29 k a On the other hand, there cannot be full crowding out, namely x␳(y, x) actually decreasing with x: otherwise, by (19) and (20), ␳(y, x) would be increasing in x, a contradiction. 28 Ͼ 30 For y 0. We are focusing this discussion, for simplic- The results generalize to the case where va and vy are ity, on the “natural” case where ␳ and ␹ are both positive, independently distributed and reputation bears only on the ␴ ␮ ϭ which occurs as long as ay is not too negative; see (19). former ( y 0). 1666 THE AMERICAN ECONOMIC REVIEW DECEMBER 2006

ϩ (24) M ͑va ͒ ϵ E͑v˜ a͉v˜ a Ն va ͒,

Ϫ (25) M ͑va ͒ ϵ E͑v˜ a͉v˜ a Յ va ͒. The first expression governs the “honor” con- ferred by participation, which is the difference Mϩ between (va) and the unconditional mean ៮ va. The second one governs the “stigma” from ៮ Ϫ MϪ abstention, which is va (va). Since both are nondecreasing functions, the net reputa- Mϩ Ϫ MϪ A. Unique equilibrium tional gain (va) (va) and the marginal agent’s total nonmonetary return to contributing,

ϩ Ϫ (26) ⌿͑va ͒ ϵ va ϩ ␮a ͓M ͑va ͒ Ϫ M ͑va ͔͒

ϵ va ϩ ⌬͑va ͒,

may increase or decrease with overall participa- ϩ tion, [va, va ]. The slopes of these two functions will play central roles in what follows.31 B. Multiple equilibria A. Endogenous Social Norms FIGURE 3 What makes a given behavior socially or ៮ morally unacceptable is often the very fact that between va and the average contribution a, rep- “it is just not done,” meaning that only people resenting a form of “reciprocity”) or other value whose extreme types make them social outliers of “conformity” is required to explain the com- would not be dissuaded by the intense shame mon finding that individuals contribute more to attached to it. In other places or times, different public goods when they know that others are norms or codes of honor prevail, and the fact also giving more.32 that “everyone does it” allows the very same The following results, illustrated in Fig- behavior to be free of all stigma. Examples in- ure 3, characterize the set of equilibria of the clude choosing surrender over death, not going to participation game and the associated supply church, not voting, divorce, bankruptcy, unem- correspondence.33 ployment, welfare dependency, minor tax evasion, and conspicuous modes of consumption. PROPOSITION 5: (1) When ⌿ is increasing, We show here that such interdependencies there is a unique equilibrium, with no partici- between agents’ choices arise endogenously through the inferences made from observed be- haviors, creating the potential for multiple 32 For instance, James H. Bryan and Mary A. Test (1967) found that motorists were more likely to stop and help norms of social responsibility. In particular, no someone with a flat tire, and walkers-by more likely to put assumption of complementarity in payoffs (e.g., money into a Salvation Army kettle, when they had ob- served someone else (a confederate) doing so a few minutes before. See also Jan Potters et al. (forthcoming) on charities’ frequent strategy of publicly announcing “leadership” con- 31 Recall also that, in the discussion of Figure 1, it was tributions and on the higher yields achieved when donors argued that the reputation for prosociality of contributors act sequentially rather than simultaneously. may worsen either more or less than that of noncontributors 33 To pin down off-the-equilibrium-path beliefs when when the separating locus pivots to the left due to the there is full participation, we make the standard assumption presence of a reward y Ͼ 0. Indeed, for any given value of that the support of beliefs is weakly increasing in the level

vy (over which one then integrates), these reputations re- of contribution off the equilibrium path, as is necessarily the Mϩ Ϫ MϪ Ϫ Ͼ Ј ϩ Ј Ϫ spectively correspond to (v*a vyy) and (v*a vyy), case on the equilibrium path: if a a and v (a ) and v (a) whose difference may increase or decrease with y depend- denote the sup and the inf of the two supports, respectively, ing on the slope of Mϩ Ϫ MϪ. then vϩ(aЈ) Յ vϪ(a). VOL. 96 NO. 5 BE´ NABOU AND TIROLE: INCENTIVES AND PROSOCIAL BEHAVIOR 1667

ϭ ϩ Ͻ Ϫ⌿ ϩ Ϫ ⌿Ј Ͻ pation (v*a va ) for y ca (va ), partic- 1, or 0, the resulting net increase in ʦ Ϫ⌿ ϩ ipation increasing in y for y (ca (va ), reputational pressure is strong enough that the Ϫ⌿ Ϫ ϭ Ϫ Ϫ ca (va )), and full participation (v*a va ) marginal agents in [v*a dva, v*a], who initially Ͼ Ϫ⌿ Ϫ for y ca (va ). preferred to abstain, now feel compelled to con- tribute. This further increases participation and (2) When ⌿ is decreasing, there are three equi- confines abstention to an even worse pool, etc., ʦ Ϫ⌿ Ϫ Ϫ libria for all y (ca (va ), ca leading to corner solutions as the only stable ⌿ ϩ ⌬Ј ʦ Ϫ (va )): full participation, no participation, equilibria, as in Figure 3B. When ( 1, 0), and an unstable interior equilibrium de- complementarity is weak enough that the mar- ⌿ ϭ Ϫ ԫ Ϫ fined by (v*a) ca y. For y (ca ginal agents still prefer to stay out, hence sta- ⌿ Ϫ Ϫ⌿ ϩ (va ), ca (va )), there is again a bility obtains. This is a fortiori the case when unique, corner equilibrium. there is substitutability, ⌬Ј Ͼ 0. (3) When ⌿ is nonmonotonic, there exists a Equipped with this general intuition, we now range of values of y for which there are at investigate the main factors that make strategic least two stable equilibria, of which one at complementarity—and thus the existence of least is interior. multiple social norms—more or less likely.

When va is uniformly distributed on [0, 1], ⌿ ϭ ϩ ␮ for instance, (va) va a /2 so the supply Distribution of Social Preferences.—One ex- curve is a standard upward-sloping one, as in pects that stigma considerations will be domi- ϭ Figure 3A. When va has density g(va) 2va on nant when the population includes only a few ⌿ ϭ ϩ ␮ ϩ [0, 1], by contrast, (va) va (2 a /3)(1 “bad apples” with very low intrinsic values, Ϫ1 ␮ Ͼ va) is decreasing for all a 6, resulting in which most agents will be eager to differentiate ␮ ʦ three equilibria, as in Figure 3B. For a (3/2, themselves from. Formally, an increasing den- ⌿ Mϩ Ϫ MϪ 6), is hump-shaped, making the higher- sity g(va) makes it more likely that participation equilibrium interior. is declining: a rise in va hardly increases ͉ Ն E(va v˜a va) but substantially increases ͉ Յ E(va v˜a va), since the weight reallocated at B. Strategic Complementarity and the margin is small relative to that in the upper Substitutability tail, but large relative to that in the lower tail. Conversely, honor will dominate when there are The intuition for the results is that agents’ only a few heroic or saintly types, whom the actions will (endogenously) be strategic com- mass of more ordinary individuals would like to plements or substitutes, depending on whether be identified with.34 it is stigma or honor that is most responsive to the extent of participation. This same condi- tion turns out to play a key role in other issues, PROPOSITION 6: (1) (Jewitt, 2004) If the dis- such as the socially optimal level of incentives tribution of va has a density that is (a) decreas- (see Section VA) and the disclosure or confi- ing, (b) increasing, (c) unimodal, then (Mϩ Ϫ MϪ dentiality of rewards (see Be´nabou and Tirole, )(va) is, respectively, (a) increasing, (b) 2004a). decreasing, (c) quasi convex.

DEFINITION 1: Participation decisions ex- 34 Corneo (1997) provides related insights (but formal ⌬Ј ϵ results only in a quadratic case), based on whether the value hibit strategic complementarities if (va) ␮ Mϩ Ϫ MϪ Ј Ͻ of reputation is assumed to be a concave (“conformist”) or a( ) (va) 0 for all va. a convex (“elitist”) function of someone’s perceived rank (which, by definition, is uniformly distributed) in the dis- When ⌬Ј Ͻ 0, a wider participation (dv Ͻ 0) tribution of altruism. For any such function s(ra) of rank a ϵ ϵ ϭ ؠ worsens the pool of abstainers more than that of r(va) G(va), we can define v˜a s(ra) (s G)(va), which has density g˜ ϵ 1/(sЈ ؠ sϪ1)(˜ ) ϭ 1/(sЈ(r )). Thus all the contributors, so that the stigma from abstention va a ៮ Ϫ MϪ results in Proposition 6.1 on increasing, decreasing, and va (va) rises faster than the honor from unimodal densities immediately carry over to concave, con- Mϩ Ϫ ៮ ⌬Ј Ͻ participation (va) va fades. When vex, and convex-concave payoff functions. 1668 THE AMERICAN ECONOMIC REVIEW DECEMBER 2006

P (2) If the distribution of va has a log-concave (28) M ͑va ; ␦Ј͒ density (more generally, a log-concave distri- ␮ ʦ ϩ bution function), then for all a [0, 1], the ␦Јv៮a ϩ ͑1 Ϫ ␦Ј͓͒1 Ϫ G͑va ͔͒M ͑va ͒ supply function is everywhere upward-sloping. ϭ . ␦Ј ϩ ͑1 Ϫ ␦Ј͓͒1 Ϫ G͑va ͔͒ Part 1 provides sufficient conditions for the monotonicity of Mϩ Ϫ MϪ, which defines The same expressions apply if participation al- complementarity or substitutability. What ulti- ways gives rise to a signal suggesting that the mately matters for uniqueness or multiplicity individual contributed, but nonparticipation can and the slope of the supply curve, however, is go undetected (also lead to such a signal) with ⌿ ϭ ϩ ␮ Mϩ Ϫ MϪ ␦Ј the behavior of (va) va a( ) probability . (va), for which the strength of reputational con- ␮ cerns, a, is also relevant. In part 2 we thus PROPOSITION 7: (1) An increase in the ␮ ʦ show that, for all a [0, 1], uniqueness ob- probability of unobserved forced participation tains as long as g does not increase too fast—a facilitates the emergence of strategic comple- much weaker condition than 1(b). No simple mentarities and multiple social norms, whereas analogue is available for the case of multiplic- an increase in the probability of (unobserved) ity, but it is clear that it corresponds to situa- involuntary nonparticipation inhibits it. ␮ tions where complementarity obtains and a is high enough (as in the example given earlier). (2) The same results hold for, respectively, an increase in the probability that abstention Excuses, Forced Participation, and Observ- may escape detection and an increase in ability.—Thus far, we have assumed that ob- the probability that a good deed goes un- servers (other agents, future “self”) know for noticed. sure that the individual had an opportunity to contribute and, if so, whether he did. This is Empirical and Policy Implications.—The re- often not the case, however. sults of this section have a number of interesting Suppose that with probability ␦ ʦ [0, 1], an implications. First, for behaviors such as crime, individual faces (unverifiable) circumstances from which most people are deterred by either a that preclude participation: not being informed, strong intrinsic distaste (the density of va is having to deal with some emergency, etc. For increasing) or strong extrinsic constraints (a ␦Ј any potential cutoff va, the honor conveyed by high ), stigma avoidance will be the dominant MP ϭ Mϩ participation is unchanged, (va) (va), reputational concern (by contrast, having no while the stigma conveyed by nonparticipation criminal record is not particularly glorious) and is lessened, taking the form of a weighted actions will be strategic complements, poten- average tially leading to substantial variations over time and space. Conversely, opportunities to engage Ϫ in heroic behaviors (risking one’s life for some- ␦v៮ ϩ ͑1 Ϫ ␦͒G͑v ͒M ͑v ͒ MNP͑ ␦͒ ϭ a a a one else, donating an organ or significant (27) va; ␦ ϩ ͑ Ϫ ␦͒ ͑ ͒ . 1 G va wealth) are relatively rare (high ␦) and few people are intrinsically motivated to such great The same expressions are easily seen to apply if feats of abnegation. The signaling motive will abstention never gives rise to a signal that the therefore be dominated here by the pursuit of individual contributed, but a contribution may distinction, making noble acts strategic substi- go unnoticed (fail to generate such a signal) tutes and their prevalence much less variable with probability ␦. than that of (comparably rare, on average) crim- Conversely, suppose that with probability ␦Ј ʦ inal acts. [0, 1], an individual is forced to contribute, or Second, even absent multiplicity, the two draws a temporarily low cost c. The stigma types of behaviors will respond quite differently MNP ϭ from abstention is now unchanged, (va) to public intervention. Since MϪ (va), but the distinction conveyed by par- Ϫ1 ticipation is dulled, and given by (29) a៮ Ј͑y͒ ϭ ͓1 ϩ ⌬Ј͑v*a ͑y͔͒͒ g͑v*a ͑y͒͒, VOL. 96 NO. 5 BE´ NABOU AND TIROLE: INCENTIVES AND PROSOCIAL BEHAVIOR 1669

we see that for crime-like behaviors the effect of or all of the reward.36 For the same reason, offer- legal rewards and punishments (y)isamplified ing menus of rewards cannot benefit the sponsor. by the response of social pressure (crowding By contrast, when the uncertainty is (also) in), whereas for self-sacrifices it is dampened by about vy, which is needed to obtain net crowd- it (partial crowding out). We shall come back to ing out, turning down the reward or part of it this point when analyzing the socially optimal could be used to signal the absence of greed. level of incentives. The idea that offering such “menus” may be a good strategy for increasing contributions (as in the blood-donation experiment discussed ear- IV. Turning Down Rewards lier) is consistent with both our information- based approach to prosocial behavior, which An agent may be eager to engage in a proso- emphasizes individuals’ concerns with the in- cial action, but concerned that the value of his ferences attached to their contributions, and good deed will be sullied by an inference that with the general principle that a principal al- material considerations played a role in the de- ways (weakly) benefits from being able to cision. In some situations, he may then want to screen agents along more dimensions. turn down part or all of the reward (provided the Yet, even in this case, it may be that all incentive scheme is indeed a payment for good agents either just accept y or do not participate, behavior rather than a penalty for bad behavior), but never turn down rewards, so that there is no or even supplement his participation with a gain to introducing the option. The intuition is net monetary contribution.35 that doing so could lead the audience to ques- Naturally, the issue does not arise if give- tion an agent’s motivation along another dimen- backs are not observable by the audience to sion: is he genuinely disinterested, or merely whom agents are trying to signal, or if the concerned about appearances? It is thus linked sponsor can reward them secretly. On the other to the general idea that good deeds that are “too hand, taking secret rewards does not help with obvious” may backfire, which was first encoun- self-image, and may even damage it. tered when studying public prominence in Sec- Suppose now that the realized transfer from tion IIB.37 the sponsor to the agent is effectively observ- To capture this idea, we allow again uncer- ϭ able. When the uncertainty is only about va, the tainty about v (va, vy) to combine with un- net reputational gain from participating for yЈ Յ certainty about agents’ degree of image- Ј ϭ ␮ ϭ ␮ ␮ y, relative to not participating, is r(y ) consciousness ( a, y), but focus here on ␮ ͉ Ј Ϫ ͉ Ј a(E(va 1, y ) E(va 0, y )). The agent there- a very simple case, to avoid what would other- fore cannot signal his type by taking less than y wise be a rather technical analysis. Suppose that ␮ ␮ ϭ ␥ ␥ ␥ ␥ or even giving money to the sponsor: the loss of ( a, y) (x˜ a, x˜ y), where ( a, y) is fixed Ϫ Ј income, vy(y y ), and the net reputational and thus known to the audience, whereas x˜ is Ј Ϫ benefit, r(y ) r(y), are both type-independent. independently distributed from (va, vy) and Consequently, the equilibria studied in Section takes one of two extreme values: agents are ϵ ϭ III (where vy 1) are still equilibria of the either image indifferent (x˜ 0) or image driven enlarged game in which agents can turn down part (x˜ ϭϩϱ). Image-indifferent individuals partic- Ϫ ϩ Ն ipate if and only if va c vyy 0; when they do, they clearly never turn down the reward (or 35 Alternatively, sponsors may respond to contributors’ desire to appear intrinsically rather than extrinsically moti- vated by publicly announcing low rewards. In Be´nabou and Tirole (2004a) we show that: (a) with strategic substitutes 36 It can also be verified that these equilibria satisfy the (⌬Ј Ͼ 0), a sponsor would indeed like to do so, but this Never-a-Weak-Best-Response criterion of In-Koo Cho and creates a commitment problem: if it can later on secretly David M. Kreps (1987). renegotiate with the agents, both will agree to raising y; 37 The same intuition implies that people may want to be (b) with strategic complements (Ϫ1 Ͻ⌬ЈϽ0), on the “modest” about their generosity. Thus one can show, in a contrary, the sponsor offers a higher fee under public simple extension of the model (with again heterogeneity in ␮ disclosure than under confidentiality, and this is renego- a), that agents may refrain from disclosing their good tiation-proof since agents will not agree to secret cuts in deeds, hoping that the audience will come to learn of them their rewards. through other channels. 1670 THE AMERICAN ECONOMIC REVIEW DECEMBER 2006

part of it), as this would be a strictly dominated religious organization) will set incentives and strategy. We shall assume that if the population the welfare properties of the resulting equilib- consisted only of image-indifferent individuals, rium. For these purposes, we first need to make participation would be reputation enhancing explicit again the public-good aspects of agents’ ␥ Ϫ ␥ ͉ ϩ Ն Ͼ (E( ava yvy va vyy c) 0, which contributions, then specify different sponsors’ always holds for y below some threshold). Turn- objective functions. ing now to image-driven individuals, they all pool Recall from Section IA that an individual’s on the actions that yield the highest reputation, intrinsic motivation can, in general, have two ʦ Ј Յ ϭ ϩ ␬ choosing an a {0, 1} and a reward y y that components: va ua wa/n , where ua is a pure Ј ϭ ␥ ͉ Ј Ϫ ␥ ͉ Ј maximize R(a, y ) aE(va a, y ) yE(vy a, y ). “joy of giving,” whereas wa is the marginal utility If, in equilibrium, a positive fraction of them of a public good na៮/n␬ generated by total contri- chose to participate and receive yЈϽy, they butions na៮. To simplify the analysis, we take here would be identified as image-driven types, and ua and wa to be independently distributed (with ϵ ៮ so their reputation would correspond to the prior again vy 1) and denote the mean of wa as wa. ៮ ៮ 38 mean (va, vy). But they would then be strictly Given an incentive rate y, an equilibrium better off pooling with those image-indifferent (unique or not) is determined by a cutoff v*a. agents who participate at price y. The unique Agents’ expected per capita welfare is thus equilibrium thus consists in participation, at the offered price y, by all image-driven individuals ៮ ͑ * ͒ and by those image-indifferent individuals for (30) U v a ; y Ϫ ϩ Ն whom va c vyy 0. ␬ ϵ E͓wa͑na៮/n ͔͒ ϩ E͓a͑ua Ϫ c ϩ y͒ ϩ ␮ava͔

ϩ PROPOSITION 8: Agents may never turn va ϭ ͵ ͓͑n Ϫ 1͒͑w៮ /n␬͒ down the reward, or part of it, even when this a would be publicly observed and there is uncer- va* tainty about money orientation, vy. ϩ va Ϫ c ϩ y]g͑va ͒ dva ϩ ␮av៮ a . It is worth pointing out that in deriving this result, we did not assume any social opprobrium This expression embodies three effects. First, on image consciousness; presumably, this each agent who contributes enjoys a direct util- Ϫ ϩ would only reinforce agents’ reluctance to turn ity va c y and additionally generates for the 39 Ϫ ៮ ␬ down rewards. n 1 others a positive spillover, equal to wa /n on average. Second, the pursuit of esteem is a zero-sum game: the average reputation in soci- ␮ ៮ V. Welfare and Competition ety remains fixed at ava, reflecting the martin- gale property of beliefs.40 Third, because an We now examine the way in which public or agent’s participation decision is based on the private sponsors (social planner, government private reputational return rather than the social agency, nongovernmental organization (NGO), one (which is zero), it inflicts an externality onto others. Thus, starting from equilibrium, the welfare impact of a marginal increase in partic- 38 If they pooled at multiple values yЈ, these would all ipation is need to deliver the same average reputation, which would therefore again correspond to the prior mean. 39 Note also that, while Proposition 8 focuses for sim- 3 ϩϱ 40 ͉ ϭ ៮ plicity on the extreme case where x˜ , the effect it That is, E[E[va a, y]] va. It thus does not matter brings to light is much more general. One can thus show whether we include agents’ utilities from reputation (e.g., van- that: (a) for all finite x, there always exists an equilibrium in ity) in the definition of social welfare. Note that the zero-sum which no one turns down the reward; (b) even in the best property also relies on the linearity of the reputational payoff ␮ equilibrium for the sponsor, the fraction of image-conscious and the independence of a from va. When these assumptions agents who do so remains bounded away from one across all do not hold, the distribution of reputation across agents will values of x, thus limiting the profitability of introducing this have allocative and efficiency consequences—for instance, form of price discrimination. through subsequent matching patterns. VOL. 96 NO. 5 BE´ NABOU AND TIROLE: INCENTIVES AND PROSOCIAL BEHAVIOR 1671

៮ ѨU͑v*a ; y͒ the organization, bundling of a religious mes- (31) Ϫ sage with schooling or poverty relief, or (in Ѩv* a reduced form) the sponsor’s own signaling or career concerns.41 Both B and the weight ␣ ϭ͓͑ Ϫ ͒͑ ៮ ␬͒ ϩ *Ϫ ϩ ͔ ͑ ͒ n 1 wa /n va c y g va placed by the sponsor on social welfare are again normalized by the opportunity cost of ϭ͓͑ Ϫ ͒͑ ៮ ␬͒ Ϫ ⌬͑ ͔͒ ͑ ͒ 42 n 1 wa /n v*a g v*a . funds that it faces. Since rewards that lead to net crowding out, The first term is the standard public-goods exter- a៮Ј(y) Ͻ 0, are never optimal, we assume that ៮ ϵ Ϫ ៮ ␬ ⌿Ј Ͼ nality, which we shall denote e (n 1)(wa/n ). 0, resulting in a unique equilibrium v*a(y) The second term reflects the fact that each mar- which, for simplicity, we take to be interior, and ៮ ϭ Ϫ ginal participant brings down the “quality” of the a supply curve na(y) n[1 G(v*a(y))], with pool of contributors as well as that of noncontribu- elasticity ␧(y) ϵ ya៮Ј(y)/a៮(y) Ͼ 0. We also tors: by the martingale property, the reputational assume that W៮ is strictly quasiconcave in all losses of inframarginal agents on both sides must cases (it always is for ␣ ϭ 1). Using (31) and ៮Ј ϭϪ Ј add up to the gains of the marginal participant, noting that a (y) (v*a) (y) g(v*a(y)), we ⌬ ϭ (v*a) r(y). Equivalently, we can think of (31) have as the difference between a free-riding effect and ៮ a reputation-stealing effect. (33) WЈ͑y͒ ϭ ͓␣͑e៮ Ϫ ⌬͑v*a ͑y͒͒͒ ϩ B Ϫ y͔

A. Sponsors’ Choice of Incentives and the a៮Ј͑y͒ Ϫ ͑1 Ϫ ␣͒a៮͑y͒. Social Optimum For (symmetric) competitive sponsors, the Consider now a public or private sponsor that private-payoff term in (32) is replaced by (B Ϫ ␣ ʦ ៮ ៮ internalizes some fraction [0, 1] of agents’ yi)ai(y), where ai(y) is the share of total contri- welfare and also derives from each one’s par- butions specifically channeled through sponsor ticipation a private benefit, with equivalent i; in equilibrium, all rewards are then driven to monetary value B. We focus first on the case of B.43 We shall denote the values of ␣, B, y, and monopoly or differentiated public goods, then W៮ for the social planner, monopolistic, and consider competition. The sponsor’s expected payoff (normalized by population size n) is thus 41 Sponsors also often care about the quality of partici- pation, not just total enrollment, in cases where it is subject ៮ ៮ to adverse selection or moral hazard. Thus, one argument (32) W͑y͒ ϵ ␣U͑v*a͑y͒; y͒ ϩ ͑B Ϫ y͒a៮͑y͒. for relatively low pay for the military is to select true patriots rather than mercenaries whose main loyalty is to For a social planner whose preferences mirror whoever pays more. Similarly, it is often argued that not paying for blood reduces the fraction of donors with hepa- the ex ante utility of the n potential contributors titis and other diseases. These ideas could be captured by and who has access to lump-sum taxes, ␣ ϭ 1 introducing a hidden action (beyond a ʦ A, which is ob- and B ϭ 0. More generally, B Ն 0 could reflect served) whose marginal cost to the individual decreases ЈϾ a different discounting of the welfare of future with va, leading to a benefit for the sponsor B(va), with B 0. For instance, a purely private sponsor (␣ ϭ 0) would now generations (e.g., with pollution or biodiversity) Ϫ ␮ maximize Ev,␮[(B(va) y)a(v, ; y)]. and ␣ Յ 1 the presence of a shadow cost of 42 It is worth recalling here that the model also applies to public funds: clearly, replacing B Ϫ y by B Ϫ monetary donations, with sponsors offering either a match- (1 ϩ ␭)y in ␲(y) is equivalent to dividing both ing rate or “perks” and other goods or services (in addition B and ␣ in (32) by 1 ϩ ␭. For other actors such to the publicity); see footnote 10. 43 While this is the standard result, it depends here cru- as charities, NGOs, or specialized government ϭ cially on the fact that vy 1 is known. Otherwise, there is agencies, B may reflect the premium placed on a reputational payoff to participating for a lower fee, and a public good by a particularly motivated con- sponsor competition will then lead to rewards being bid stituency (friends of the arts, environmental- down rather than up, leaving firms with positive profits. This “reversal” of Bertrand competition is analyzed in Be´nabou ists), or some purely private benefits tied to the and Tirole (2004a) and shares important similarities with channeling of donations or the delivery of pub- Bagwell and Bernheim’s (1996) analysis of the pricing of lic goods: rents appropriated in the process by conspicuous-consumption goods. 1672 THE AMERICAN ECONOMIC REVIEW DECEMBER 2006 competitive sponsors by the superscripts s, m, tational incentive to contribute is also weakened. and c respectively, with ␣s Ͼ max{␣m, ␣c}. These results provide both some support and an important qualification to arguments (e.g., PROPOSITION 9: (1) The socially optimal in- Geoffrey Brennan and Philipp Pettit, 2004) centive rate is always strictly less than the calling for a shift in public policy from the standard Pigouvian subsidy yP ϵ e៮ ϩ Bs which use of fines and other costly sentences to a leads agents to internalize the full public-good greater reliance on public praise and shame. value of their contribution. When taxation is Esteem-based incentives can adequately re- nondistortionary (␣s ϭ 1), it equals ys ϭ yP Ϫ place material rewards and punishments in ⌬(c Ϫ yP); more generally, it is given by spheres where gaining distinction is the dom- inant reputational concern (self-sacrifice, her-

s s s oism, great inventions), but not in those where ␣ ͓e៮ Ϫ ⌬͑v*a ͑ y ͔͒͒ ϩ B (34) ys ϭ . avoiding stigma is most important (crime, wel- 1 ϩ ͑1 Ϫ ␣s͒/␧͑ ys͒ fare dependency). The intuition for the second result in Propo- (2) A monopoly sponsor with ␣m Ͻ ␣s may sition 9 is that a monopolist setting ym does not offer contributors a reward ym that is too not internalize the reputational losses of infra- generous (or require of them too low a marginal agents to the same extent a planner monetary donation) from the point of view would. This gives it an incentive to attract too of social welfare, resulting in excess par- many “customers,” which works against the ticipation. This is true even when the ben- standard monopolistic tendency to serve too efit it derives from agents’ participation few. The tension between these two forces can coincides exactly with the gap between be seen from the fact that (W៮ s)Ј(ym) Ͻ 0if their social and private contributions to the public good (Bm ϩ ␣me៮ ϭ Bs ϩ ␣se៮). (35) ͑␣s Ϫ ␣m͓͒ym/␧͑ym͒ Ϫ ⌬͑ *͑ym͔͒͒ (3) Competition between sponsors increases v a rewards (or reduces required monetary ϩ Bs ϩ ␣se៮ Ϫ Bm Ϫ ␣me៮ Ͻ 0. contributions) and may thus reduce social welfare, compared to a monopoly (with the same ␣c ϭ ␣m and Bc ϭ Bm). A low supply elasticity ␧ causes the monopolist to offer too low a price, as usual. When repu- The first result shows that the optimal incen- tational concerns are important enough, how- ␮ ⌬ tive scheme should include a tax that corrects ever (a high a and therefore a high ), the for the reputation-seeking motive to contribute, informational externality can dominate, making which in itself is socially wasteful. This repu- the monopolist too “generous” or not demand- tational rent is endogenous to the reward, how- ing enough in the standards it sets for monetary ever. Thus with ␣s ϭ 1, when individual donations. The last two terms in (35), finally, contributions are complements (respectively, represent the total benefits (private benefit plus substitutes), ys ϭ yP Ϫ⌬(c Ϫ yP) responds less internalized contribution to social welfare) de- (respectively, more) than yP to changes in Bs rived by each sponsor from a marginal agent’s (which leave the function ⌬ unchanged). Simi- participation, each normalized by the corre- larly, the optimal penalty for antisocial activi- sponding shadow cost of funds. The effect of ties such as littering, polluting, etc., should their difference on the sign of ym Ϫ ys is “leave space” for the effect of opprobrium, straightforward, and part 2 of the proposition which itself depends on the fine. As to a higher normalizes it to zero as a benchmark. shadow cost of public funds (a proportional Sponsor competition, finally, further exacer- reduction in ␣s and Bs), it naturally tends to bates the inefficiency above, because each firm reduce ys; when contributions are substitutes, now has a much higher incentive to raise its some of this reduced public intervention is offer than a monopolist (it takes the whole mar- made up by increased social pressure, as ⌬ ket), but still inflicts the same reputational cost rises in response to the decline in participa- on all inframarginal noncontributors. This sug- tion. With complements, however, the repu- gests, for instance, that universities may sell the VOL. 96 NO. 5 BE´ NABOU AND TIROLE: INCENTIVES AND PROSOCIAL BEHAVIOR 1673 naming rights to professorial chairs and build- that cL is so large that the low type is never ings too cheaply, relative to the social optimum. willing to sacrifice and will focus on determin- istic contracts offered by sponsors seeking to maximize their private payoff ␲(y); that is, we B. Holier-than-Thou Competition set ␣ ϭ 0 (the results would extend to any ␣ Ͻ 1).

We saw that competition may reduce welfare by inducing excessive participation in prosocial PROPOSITION 10: In the two-type case de- activities that generate only moderate public- scribed above, a monopoly sponsor who wants good benefits but have a high visibility. We will both types to contribute does not screen con- now see that it can reduce welfare (relative to a tributors inefficiently. By contrast, competing monopolist) even without any change in partic- sponsors may require high-valuation individu- ipation, by leading sponsors to screen contrib- als to make costly sacrifices that represent pure utors in inefficient ways. This result formalizes deadweight losses, thereby reducing social in particular the idea of religions and sects com- welfare. peting on orthodoxy, asceticism, and other costly requirements for membership (e.g., Eli The intuition for this result is that nonprice Berman, 2000). Another important example is screening imposes a negative externality on that of charities sponsoring events where low-type agents, the cost of which a monopolist agents, instead of simply donating or raising must fully bear but which competitive sponsors money (or on top of it), engage in time-intensive, do not internalize. Indeed, screening through strenuous activities such as a day-long walk, costly sacrifices has two effects: (a) it inflicts a marathon, or other tests of endurance often re- deadweight loss cH Ϫ c on the high type, which quiring months of preparation.44 the sponsor must somehow pay for; (b) it boosts To capture this phenomenon most simply, let va the high type’s reputation and lowers that of the H ␳ L Ͻ H take values va with probability ,orva va with low type. When the high-type’s reputational Ϫ ␳ ϵ probability 1 , while maintaining vy 1. gain exceeds the cost of sacrifice, the sponsor Assume, furthermore, that the nonmonetary through which he contributes can appropriate cost of contributing is c (possibly zero) unless the surplus, in the form of a lower reward. If this the sponsor demands a “sacrifice,” which it is sponsor is a monopolist who finds it profitable able to verify and publicly certify. The cost then to serve the whole market (which is always the becomes cH for the high type and cL for the low case when ␳ is low enough), he must also com- type, where pensate the low type for his reputational loss. By a now-familiar argument, these losses must (36) c Ͻ cH Ͻ cL. exactly offset the high type’s reputation gains, so the net effect of (b) on agents’ average util- A sacrifice is a pure deadweight loss, whose ity, as well as on the monopolist’s payoff, is nil. only benefit is to help screen agents’ motiva- This leaves only the net cost corresponding to tion. The assumption that cL Ͼ cH reflects the (a), implying that a sponsor serving the whole idea that such a sacrifice is less costly to a more market will never require sacrifices. motivated agent. For simplicity, we will assume Things are quite different under free entry. First, since vy is known, price competition again drives all sponsors to offer B. Second, by re- 44 Camille Sweeny (“The Latest in Fitness: Millions for quiring a sacrifice, entrants can now attract the Charity,” New York Times, July 7, 2005) documents that: (a) high types away from competitors who impose many large, health-related charities in the United States now derive over a third of their revenues from endurance pro- no such requirement, leaving low types (or their grams and challenges; (b) most sponsored participants are sponsors) with the resulting reputational loss. not athletic types or even regular exercisers (leading to a This “cream skimming” leads inevitably to an high rate of injury); (c) while their motivations vary, the equilibrium where a proportion ␳ of the con- fundraising/doing-good aspect is the dominant one (they often have themselves been, or are personally close to, tracts offered by active sponsors requires an victims of the disease which the funds they are raising will inefficient sacrifice and attracts only high types, be dedicated to combat). while the remaining 1 Ϫ ␳ requires only the 1674 THE AMERICAN ECONOMIC REVIEW DECEMBER 2006 normal contribution c and attracts the low sponsors, who in practice often have their own types.45 signaling concerns. A third one, linked to the Turning finally to welfare, one can show that self-image interpretation of the model and pur- both types of agents are better off under compe- sued in Be´nabou and Tirole (2006), is the topic tition than under monopoly (see the Appendix). of identity and the many instances where people The sponsors or their underlying beneficiaries, refuse transactions that seem to be in their best however, must necessarily lose more than all con- economic interest, but which they judge to be tributors gain: total participation remains un- insulting to their dignity. changed (both types still contribute), the same is true of average reputation (by the martingale prop- APPENDIX erty), and rewards are pure transfers. There is now, however, a deadweight loss of ␳(cH Ϫ c), PROOF OF PROPOSITION 1: corresponding to the wasteful sacrifices made by Since y here is a fixed parameter, in what the high types to separate. Therefore, competition follows we will temporarily omit from the no- unambiguously reduces welfare. tation the dependence of all functions on this argument. Differentiating (9) and (10) with re- VI. Conclusion spect to a yields

To gain a better understanding of prosocial dE͑va͉a͒ (A1) ϭ ␳͓k Ϫ r៮Ј͑a͔͒ behavior, we sought, paraphrasing Adam Smith, da to “thoroughly enter into all the passions and motives which influence it.” People’s actions and indeed reflect a variable mix of altruistic moti- vation, material self-interest, and social or self- dE͑vy͉a͒ image concerns. Moreover, this mix varies ϭ ␹͓k Ϫ r៮Ј͑a͔͒. across individuals and situations, presenting ob- da servers seeking to infer a person’s true values from his behavior (or an individual judging Therefore, r៮(a) is a solution to the linear differ- himself in retrospect) with a signal-extraction ential equation r៮(a) ϭ ␮(k Ϫ r៮Ј(a)), where ␮ ϵ ␮៮ ␳ Ϫ ␮៮ ␹ ៮ ϭ problem. Crucially, altering any of the three a y . The generic solution is r(a) components of motivation, for instance through k(␮ ϩ ␨eϪa/␮), where ␨ is a constant of integra- the use of extrinsic incentives or a greater pub- tion. For ␰  0, however, the objective function licity given to actions, changes the meaning of every agent is not globally concave and is attached to prosocial (or antisocial) behavior actually maximized at a ϭϮϱ(depending on and hence feeds back into the reputational in- the sign of ␮␰). The only well-defined equilib- centive to engage in it. rium is thus for ␰ ϭ 0. This simple mechanism leads to many new insights concerning individuals’ contributions PROOF OF PROPOSITIONS 2 AND 3: to public goods, the interactions between formal From (11), we have incentives and social norms, and the strategic ␴2␴2 ϩ ␴ ͑␴2 ϩ 2␴2͒ decisions of public or private sponsors seeking 2y a y ay a y y (A2) ␳Ј͑y͒ ϭ Ϫ , to increase or capture contributions. This line of ͑␴2 ϩ 2y␴ ϩ y2␴2͒2 research could be extended in several interest- a ay y ing directions. A first one concerns organizations, (A3) where high-powered incentives or performance pay could conflict with agents’ signaling mo- ␴2͑␴2 Ϫ y2␴2͒ Ϫ 2␴ ͑ y␴2 ϩ ␴ ͒ tives that arise from teamwork or career concerns. ␹Ј͑ ͒ ϭ y a y ay y ay y ͑␴2 ϩ ␴ ϩ 2␴2͒2 . A second relates to the role and objectives of a 2y ay y y

Substituting into (14) immediately yields part 45 As long as ␳ is not too large, this is the only equilib- 1 of Proposition 3 in the case y ϭ 0, and part ␴ ϭ rium that is robust to the Cho-Kreps (1987) criterion. 1 of Proposition 2 when ay 0. This last VOL. 96 NO. 5 BE´ NABOU AND TIROLE: INCENTIVES AND PROSOCIAL BEHAVIOR 1675 inequality can be rewritten as Since Z(⍀2) is always positive but tends to zero as ⍀2 becomes large, there is always at 2 2 2 ␻ ϭ (A4) Q͑ y͒ ϵ ͑v៮ y /k͒͑1 ϩ y ␪ ͒ least one solution. When ay 0, moreover, Z(⍀2) is the sum of two squared terms that ⍀2 ϩ ␮៮ ␪4y2 Ͻ 2␮៮ ␪2y are decreasing in , so the solution is y a ␻  unique. When ay 0, one cannot rule out ϩ ␮៮ ␪2 ϵ L͑ y͒. multiple equilibria; note, however, that those y that are stable (in a standard, taˆtonnement sense) are those where Z cuts the diagonal The left-hand side is a second-order polyno- from above. Therefore, in any stable equilibrium, mial in y2, hence convex and symmetric over ⍀ is increasing in k, which in turn implies that ޒ ϭ ៮ Ͼ ␳ ␹ ␴ all of , with value Q(0) vy /k 0 at the (y) and (y) are decreasing in k, as long as ay origin. The right-hand side is an increasing is not too negative. Finally, multiplying all the ϭ ␮៮ ␪2 ␮ ␮ linear function with L(0) y . Conse- ( a, y)’s by a common “publicity factor” x has Ն ␮៮ Ͼ 2 quently, if L(0) Q(0), then for any a 0, the same effect on (A5) as multiplying k by x, Ͻ L( y) intersects Q( y) once at some y1 0 and which concludes the proof. Ͼ once at some y2 0. On the other hand, if Ͻ ␮ Ͼ L(0) Q(0), there exists a unique *a 0 PROOF OF PROPOSITION 6: for which L( y) has a (single) tangency point Part 1 is due to Jewitt (2004). To show part 2, Ͼ ␮៮ Ͻ ␮ Ͼ y* 0 with Q( y). For all a *a, Q( y) we can write: L( y) on all of ޒ*, so a៮ Ј( y) Ͼ 0 everywhere. ␮៮ Ͼ ␮ ϩ Ϫ Ϫ For all a *a, however, L( y) intersects v ϩ ␮ ͓M ͑v ͒ Ϫ M ͑v ͔͒ ϭ v Ϫ M ͑v ͒ Ͻ Ͻ a a a a a a Q( y) twice, at points 0 y1 y2. These properties, together with the linearity of L in ϩ ␮ Mϩ͑v ͒ ϩ ͑1 Ϫ ␮ ͒MϪ͑v ͒, ␮៮ a a a a ay and the convexity of Q( y), conclude the proof of Proposition 2. Part 2 of Proposition 3 follows from the fact then observe that both Mϩ and MϪ are in- ␪ ϭ ␴ ␴ 3 ϩϱ Ϫ MϪ ϭ that, given part 1, as y / a , the creasing functions, and so is va (va) ៮Ј ͐va dominant term in a (0) is asymptotically equiv- ( Ϫϱ G(v) dv)/G(va) if the integral of G is Ϫ␮៮ ␪2 Ϫ ␴ ␴ ␴ 2 alent to y [1 2( ay / a y) ], which tends log-concave. Since log-concavity is preserved to Ϫϱ as long as the correlation between v and by integration over convex sets, it suffices that ͌ a vy is less than 1/ 2 in absolute value. G itself be log-concave. In turn, a sufficient condition for this is that g be log-concave.

PROOF OF PROPOSITION 4: PROOF OF PROPOSITION 7: MP Ϫ MNP The only difference with Proposition 1 is To show part 1, rewrite ( )(va; ⍀ 2 ϭ 2 ␦ ϭ Mϩ Ϫ ៮ Ϫ Ϫ ␦ Ϫ the presence of the term ( y) k Var[r( y; ) [ (va) va]/[1 (1 )(1 G(va))] ␮ ␳ ␹ MP Ϫ MNP Ј ␦ Ͼ )] in the denominator of and (see (19)), and observe that if ( ) (va; ) 0, this leading to the fixed-point equation defining expression is also positive for all ␦ЈϾ␦, since ⍀( y): 1 1 ϭ ⍀2 ϭ 2 P NP P NP (A5) k ͑M Ϫ M ͒͑va; ␦Ј͒ ͑M Ϫ M ͒͑va; ␦͒

␴2 ϩ ␴ ͑␦Ј Ϫ ␦͒͑ Ϫ ͑ ͒͒ a y ay 1 G va ϫ ͫ␮ ͩ ͪ ϩ ϩ , Var a ␴2 ϩ ␴ ϩ 2␴2 ϩ ⍀2 M ͑ ͒ Ϫ ៮ a 2y ay y y va va

y␴2 ϩ ␴ and the last term is clearly decreasing in va. Sim- Ϫ ␮ ͩ y ay ͪͬ ilarly, to show part 2, note that in this case(MP Ϫ y ␴2 ϩ ␴ ϩ 2␴2 ϩ ⍀2 Ϫ a 2y ay y y MNP ␦ ϭ ៮ Ϫ M Ϫ Ϫ )(va; ) [va (va)]/[1 (1 ␦ MP Ϫ MNP Ј ␦ Ͻ )G(va)] and that if ( ) (va; ) 0, it ϵ Z͑⍀2͒. is also negative for all ␦ЈϾ␦. 1676 THE AMERICAN ECONOMIC REVIEW DECEMBER 2006

PROOF OF PROPOSITION 9: text), both types of agents are better off than The general formula in part 1 follows from (33) under monopoly: the low type’s payoff rises ៮ s ␮ L ␮ L ϩ L Ϫ ϩ and the assumed strict quasiconcavity of W . For from ava to ava va c B, while the high ␣s ϭ ៮ s Ј ϭ s ϩ ៮ Ϫ Ϫ L Ϫ ϩ 1, we have (W ) (y) [B e y type’s payoff increases by at least va c B, ⌬ ៮Ј ϩ⌬ ϭ Ϫ (v*a(y))] a (y) and v*a(y) (v*a(y)) c y which is positive from the condition that the (interior equilibrium), so (W៮ s)Ј(y) has the sign of monopoly prefers to enlist both types. The fact s ϩ ៮ Ϫ ϩ ៮ s B e c v*a(y). Therefore, W (y) is strictly that sponsors must necessarily lose more than concave and maximized at the point ys such that the agents gain, resulting in a net welfare loss s ϩ s ϩ ៮ ϭ v*a(y ) B e c, which is the standard from competition, was established in the text. Samuelson condition for efficient public-goods s ϭ Ϫ P provision. Substituting v*a(y ) c y into the equilibrium condition yields ys ϭ yP Ϫ⌬(c Ϫ yp). REFERENCES For part 2, note that (35) holds for all Bm ϩ ␣m៮ Յ s ϩ ␣s៮ ⌬ m Ͼ ៮ e B e as long as (v*a(y )) a(y)/ Akerlof, George A., and William T. Dickens. a៮Ј(y), or 1982. “The Economic Consequences of Cog- nitive Dissonance.” American Economic Re- view, 72(3): 307–19. ⌬͑v*͒ g(v*) a a Ͼ Akerlof, George A., and Rachel E. Kranton. 2000. (A6) ⌿Ј͑ ͒ ͩ Ϫ ͪ 1, v*a 1 G(v*a) “Economics and Identity.” Quarterly Journal of Economics, 115(3): 715–53. m where v*a stands for v*a( y ). For instance, for Andreoni, James. 1989. “Giving with Impure ␣m ϭ 0 and va uniformly distributed on [0, Altruism: Applications to Charity and Ricar- m ϭ Ϫ ␮ ϩ Ϫ 1], we have v*a( y ) (c a/2 1 B)/ dian Equivalence.” Journal of Political Econ- ʦ m ϭ Ϫ ϩ Ϫ ␮ 2 (0, 1) and y (B 1 c a/2)/ omy, 97(6): 1447–58. Ͻ Ϫ␮ Ͻ ϩ Ϫ Ͻ Ϫ 2 B as long as a/2 1 B c 2 Andreoni, James. 2006. “Philanthropy.” In ␮ m Ͼ s ϭ ϩ ៮ Ϫ ␮ a/2. Thus, y y B e a/2 whenever Handbook of the Economics of Giving, Rec- ␮ Ͼ ϩ Ϫ ϩ ៮ a 1 B c 2e, which is consistent with iprocity and Altruism, ed. Serge-Christophe ␮ Ͼ ៮ the previous inequalities as long as a 2e. Kolm and Jean M. Ythier, Vol. 2, chap. 18. Part 3, finally, is implied by part 2 as long as Amsterdam: Elsevier Science North-Holland. ym Ͻ Bm ϭ Bc ϭ yc (which is always the case as Arau´jo, Aloisio Pessoa de, Daniel Gottlieb, and long as ␣m is not too large), since W៮ s is declin- Humberto Moreira. 2004. “A Model of Mixed ing to the right of ys. Signals with Applications to Countersignal- ing and the GED.” Getulio Vargas Founda- PROOF OF PROPOSITION 10: tion Economics Working Paper 553. (1) As long as ␳ is not too small, it is optimal Austen-Smith, David, and Roland G. Fryer, Jr. for the monopolist to get both types on board. If 2005. “An Economic Analysis of ‘Acting he does not demand any sacrifice, he sets y so as White’.” Quarterly Journal of Economics, ϭ Ϫ L Ϫ to make the low type indifferent: y c va 120(2): 551–83. ␮ ៮ Ϫ L ៮ ϵ ␳ H ϩ Ϫ ␳ L a(va va), where va va (1 )va is the Bagwell, Laurie Simon, and B. Douglas Bernheim. ␲ ϵ prior mean. The sponsor’s payoff is then 1 1996. “Veblen Effects in a Theory of Con- Ϫ ϭ Ϫ ϩ L ϩ ␮ ៮ Ϫ L B y B c va a(va va). Suppose spicuous Consumption.” American Economic now that the high type is asked to sacrifice. Review, 86(3): 349–73. L ϭ Ϫ L Rewards are then y c va and (from incen- Batson, Dan. 1998. “Altruism and Prosocial Be- H ϭ L ϩ H Ϫ Ϫ ␮ H Ϫ tive compatibility) y y c c a(va havior.” In Handbook of Social Psychology. L ␲ ϭ Ϫ va). The sponsor’s payoff is then only 2 B Vol 2, ed. Daniel T. Gilbert, Susan Fiske, and ␳ H Ϫ Ϫ ␳ L ϭ ␲ Ϫ ␳ H Ϫ Ͻ ␲ y (1 )y 1 (c c) 1. Gardner Lindzey, 282–316. New York: (2) Under free entry, all sponsors offer, and McGraw Hill. all contributors accept, y ϭ B. Moreover, if Bem, Daryl J. 1972. “Self-Perception Theory.” H Ϫ Յ ␮ H Ϫ L c c a(va va), it is now an equilibrium In Advances in Experimental Social Psychol- for the high type to separate from the low type ogy. Vol. 6, ed. Leonard Berkowitz, 1–62. by opting for a sponsor who requires a sacrifice. New York: Academic Press. In the resulting equilibrium (described in the Be´nabou, Roland, and Jean Tirole. 2002. “Self- VOL. 96 NO. 5 BE´ NABOU AND TIROLE: INCENTIVES AND PROSOCIAL BEHAVIOR 1677

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