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Sobel (2005) - Interdependent Preferences and Reciprocity

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Journal of Economic Literature Vol. XLIII (June 2005), pp. 392–436 Interdependent Preferences and Reciprocity JOEL SOBEL 392 Sobel: University of California, San Diego. I present- ed a version of this paper at the First World Congress of the Game Theory Society and to my colleagues at the Center for Advanced Study in the Behavioral Sciences. I thank Eli Berman, Antonio Cabrales, Miguel Costa- Gomes, Vincent Crawford, David M. Kreps, Herbert Gintis, Mark Machina, Efe Ok, Luís Pinto, Matthew Rabin, Paul Romer, Klaus Schmidt, Uzi Segal, Joel Watson, and Kang-Oh Yi for discussions, references, and comments. I am especially grateful to two referees who supplied detailed, intelligent, and constructive comments on an earlier version of the manuscript and to John McMillan for his advice and encouragement. I worked on this project while a Fellow at the Center for Advanced Study in the Behavioral Sciences. I thank my classmates at the Center for conversations and encouragement and the Center for financial and clerical support. NSF funding is also gratefully acknowledged. 1. Introduction M uch of economic analysis stems from the joint assumptions of rationality and indi- vidual greed. Common sense and experimen- tal and field evidence point to the limits of this approach. Not everything of interest to econ- omists can be well understood using these tools. This paper reviews evidence that narrow conceptions of greed and rationality perform badly. The evidence is consistent with the view that economic incentives influence decision making. Hence there is a role for optimizing models that relax the assumption of individual greed. I discuss different ways in which one can expand the notion of preferences. I pay particular attention to how reciproc- ity influences decision making. Reciprocity refers to a tendency to respond to perceived kindness with kindness and perceived mean- ness with meanness and to expect this behavior from others. I introduce models of intrinsic reciprocity in section 3.4. Intrinsic reciprocity is a property of prefer- ences. The theory permits individual prefer- ences to depend on the consumption of others. Moreover, the rate at which a person values the consumption of others depends on the past and anticipated actions of others. An individual whose preferences reflect intrinsic reciprocity will be willing to sacri- fice his own material consumption to increase the material consumption of others in response to kind behavior while, at the same time, be willing to sacrifice material consumption to decrease someone else’s material consumption in response to unkind behavior. It is more traditional to view reciprocity as the result of optimizing actions of selfish agents. Responding to kindness with kind- ness in order to sustain a profitable long- term relationship or to obtain a (profitable) reputation for being a reliable associate are examples of instrumental reciprocity. Economics typically describes instrumental reciprocity using models of reputation and
  • Journal of Economic LiteratureVol. XLIII (June 2005), pp. 392436

    Interdependent Prand Reciproc


    Sobel: University of California, San Diego. I present-ed a version of this paper at the First World Congress ofthe Game Theory Society and to my colleagues at theCenter for Advanced Study in the Behavioral Sciences. Ithank Eli Berman, Antonio Cabrales, Miguel Costa-Gomes, Vincent Crawford, David M. Kreps, HerbertGintis, Mark Machina, Rabin, Paul Romer, KlWatson, and Kang-Oh Yicomments. I am especialsupplied detailed, intelligon an earlier version oMcMillan for his advice athis project while a FelloStudy in the Behavioral Scthe Center for conversatiCenter for financial and also gratefully acknowledg

    1. Introduction

    Muchjoinvidual gretal and fieapproach.omists catools. Thisconceptiobadly. Thethat econmaking. Hmodels thgreed. I dcan expan

    I pay pe

    o sitricc h


    c ise

    in response to kind behavior while, at thesame time, be willing to sacrifice materialconsumption to decrease someone elsesmaterial consumption in response to unkindbehavior.Efe Ok, Lus Pinto, Matthewaus Schmidt, Uzi Segal, Joel for discussions, references, andly grateful to two referees whoent, and constructive commentsf the manuscript and to Johnnd encouragement. I worked onw at the Center for Advancediences. I thank my classmates at

    ons and encouragement and the

    It is more traditional to view reciprocity asthe result of optimizing actions of selfishagents. Responding to kindness with kind-ness in order to sustain a profitable long-term relationship or to obtain a (profitable)reputation for being a reliable associate areexamples of instrumental reciprocity.392

    clerical support. NSF funding ised.

    Economireciprocieferences ity

    articular attention to how reciproc-nces decision making. Reciprocitya tendency to respond to perceived with kindness and perceived mean-h meanness and to expect this from others. I introduce models of reciprocity in section 3.4.reciprocity is a property of prefer-e theory permits individual prefer-

    depend on the consumption oforeover, the rate at which a persone consumption of others dependsst and anticipated actions of others.idual whose preferences reflectreciprocity will be willing to sacri- own material consumption tothe material consumption of others of economic analysis stems from thet assumptions of rationality and indi-ed. Common sense and experimen-ld evidence point to the limits of this Not everything of interest to econ-n be well understood using these paper reviews evidence that narrowns of greed and rationality perform evidence is consistent with the viewomic incentives influence decisionence there is a role for optimizing

    at relax the assumption of individualiscuss different ways in which oned the notion of preferences.

    ity influrefers tkindnesness wbehaviointrinsIntrinsiences. Tences others. values on the pAn indintrinsifice hincreascs typically describes instrumentalty using models of reputation and

  • Sobel: Interdependent Preferences and Reciprocity 393

    repeated interaction. This approach is quitepowerfural settinlong-termcould arare unncounterareciprocintuitiveic phenoty of intruseful pe

    The nple that imodels. informalical appSection Section in which3 may reviews lences. Sments aga conclu

    2. An

    We reor recenerty, sabgoing pworkplacent injusto take drage. Thunlikely fired empensatedpenaltiesFor conhigh-rana compahis job wday on thdocumenputer fillater. In

    introduce and motivate the ideas I review inu



    n p

    ms t





    s l ahesxyi


    ju05_Article 2 6/10/05 1:40 PM Page 393l as essentially all exchanges in natu-gs can be viewed as part of some interaction. Consequently one

    gue that the models of section 3.4ecessary. This essay presents thergument that models of intrinsicity can provide clearer and more explanations of interesting econom-mena. An openness to the possibili-insic reciprocity leads to a new andrspective on important problems.

    ext section contains a stylized exam-llustrates the limitations of standardI use the example to provide an introduction to alternative theoret-roaches and motivate the paper.3 introduces these models formally.4 describes some economic settings the modeling approaches of sectionbe particularly useful. Section 5iterature on the evolution of prefer-ection 6 responds to stylized argu-ainst the approach and section 7 is


    Informal Guide to the Concepts

    gularly read accounts of dissatisfiedtly fired employees destroying prop-otaging computer files, or evenostal and killing people at theire. The sense of outrage at an appar-tice is real. Many people are willingestructive actions as part of the out-is kind of destructive behavior isto be in the material interest of aployee: it takes time, it is not com-, and it carries the risk of criminal. How should we think about it?

    creteness, imagine that Paul was aking executive who had worked forny for more than ten years. He losthen business turned bad. On his laste job, Paul destroyed vital companyts and continued to sabotage com-

    es until he was caught six monthsthis section, I will use Pauls story to

    the man

    2.1 Des

    Theredestructas an emnomic aily. PaulMarsha,are comMarshareduce Marsha atric conher howcostly ouevaluate

    I willconsistetion anPaul mamonetathis avapotentiaprovide

    2.1.1 St

    Hypoeconommaximizdependmateriaincomeimmedirather tthese dhypothePaul ma

    Analdestructwould leto ratioassumpimmedihim bacto stop elaboratscript.


    are several ways to react to Paulsve activity. One response is to treat itotional response not subject to eco-alysis. We should not give up so eas-may be crazy, but his former boss,probably is not. Unless Pauls actionsletely unrelated to the environment,will want to understand how tothe chance of adverse behavior.

    ay need to hire lawyers or psychi-ultants (instead of economists) to tello deal with Paul or reduce the risk oftbursts by employees, but she shouldher options using economic models.oncentrate on descriptions that aret with the hypotheses of optimiza-equilibrium. Once we allow that

    imizes something more that his ownreward, there are many stories like

    able. This section introduces somedescriptions informally. Section 3

    a more systematic treatment.

    tic Income Maximization

    hesis. The narrowest version ofc theory assumes that Paul seeks toe his utility and that his utility

    on the quantities of the private goods he consumes. In staticmaximization, Paul balances thete cost and benefits of actionsan the long-term implications ofcisions. In simple settings, thisis reduces to the assumption thatimizes his monetary income.sis. Paul would carry out hisve action only if he imagined that itad to direct material gain. It is hardalize Pauls behavior under theseons. His actions may advance histe material interests if Marsha gives his job or if he receives a payment

    abotaging the company, but a more description seems necessary.

  • 394 Journal of Economic Literature, Vol. XLIII (June 2005)

    2.1.2 Interdependent Preferences

    Hypofunctiontion of m

    Analythe matebe willinbeing toexplain Marsha, until aftepossibilitemploymharm Mwill fire great puMarsha.

    Alterntution beincome ia result oished PaMarsha works iflower therwise adisruptiv

    For ththat Pauincome. approachfice mateof others

    2.1.3 PreCo

    Hypofunctiongoods ththrough

    Analypossiblebehaviorketable ctype of pis not afrcapable

    security. By hurting Marsha, Paul gainshe positions himself to get another









    l ict

    iy fewh

    ul tae

    ju05_Article 2 6/10/05 1:40 PM Page 394thesis. Paul maximizes a utilitythat depends on Marshas consump-aterial goods in addition to his own.sis. If Pauls utility is decreasing inrial wealth of Marsha, then Paul willg to sacrifice his own material well punish Marsha. These preferenceswhy Paul would wish to harmbut do not explain why he waitsr he is fired to do so. There are twoies. In the midst of an ongoingent relationship, Paul does not

    arsha because he fears that Marshahim, which would be a sufficientlynishment to deter him from hurting

    atively, the marginal rate of substi-tween Paul and Marshas material

    n Pauls preferences may change asf Pauls termination. The impover-ul is willing to sacrifice to makeworse off. This explanation only

    Pauls income after being fired isan after a voluntary separation (oth-ny separation would trigger Paulse behavior).e example, it makes sense to assumels utility is decreasing in MarthasThe interdependent preference permits Paul to be willing to sacri-rial welfare to decrease the income.

    ferences over Generalnsumption Goods

    thesis. Paul maximizes a utilitythat is a function of consumptionat are derived from marketed goods

    a personal production process.sis. This approach generates severalstories. One possibility is that Paulsdemonstrates that he has a mar-

    haracteristicthat is, he is not theerson who can be pushed around, heaid to stand up for injustice, or he isof identifying weaknesses in a firms

    becausejob (wha bookcircumsdefinedhis senincreasiwilling tincreasehonor bmonetareduces

    Anothure direhis prefment (his matorientedwhy Paufired. Pthe emurge tothis explevelsemploy

    2.1.4 In

    Hypomateriaperceptthe direginal uincreaseMarshaMarsha

    Analunfairlyhis pre(more) return t

    2.1.5 Co

    Hypoutility fmateriaself to best inth he may be less likely to lose) or sellbout his experiences. Under theseances, Paul may have preferencesover both his monetary wealth ande of honor. If the preferences areg in both arguments, then he will bemake material sacrifices in order toin honor. If Paul only cares aboutcause it enables him to increase hisy payoff, then this explanationto income maximization.er possibility is that Paul takes pleas-tly from the act of sabotage. That is,rences contain an additional argu-abotage). Paul will not maximizerial payoff, but he is selfish and goal. This explanation does not explainl turns to sabotage only after he wasrhaps the advantage of maintainingloyment relationship deterred hisestroy files until he was fired, but

    anation suggests that the sabotageould be the same whether thee was fired or separated voluntarily.

    rinsic Reciprocity

    thesis. Pauls utility depends on thewealth of Marsha. Moreover, Pauls

    on of Marshas behavior determinestion of Pauls preferences. The mar-ility of Paul with respect to anin Marshas income increases when

    is kind to Paul and decreases whens unkind.sis. Paul believes that Marsha actedwhen she fired him. Consequently,rences changed and he becomesilling to sacrifice his own income toe insult he received.


    thesis. Paul seeks to maximize anction that depends only on hisconsumption. He can commit him-king future actions that are in hisrest when he makes his plans, but

  • Sobel: Interdependent Preferences and Reciprocity 395

    1 Alternor announcdestructive

    may not be in his best interest when heenacts his plans.

    Analysis. If fired workers retaliate,Marsha might be reluctant to fire people orshe may offer attractive separation packages.These actions benefit workers, so if workerscould cobeing firto do soconcludean emplonation foafter heconceptsFor this as a descand optargumencommitm

    2.1.6 Rep

    Hypomaterial tionship engagedand he sof single

    Analyfuture parium bemaximizPauls dterm coson MarsEquilibroften speplayer foum behapunishmtrigger tishmentsPauls wmight bethat lead

    This hypothesis works like the commit-ment hythe samecarry ouFor the Paul mu

    ss (s



    t a

    ohlniedm ar




    ju05_Article 2 6/10/05 1:40 PM Page 395atively, Marsha might institute tighter securitye that she will seek severe punishments for


    mmit to destructive actions aftered, then it might be in their interest.1 Marsha fired Paul because shed that he would do more damage asyee than not, but there is no expla-r why Paul carried out his threat

    was fired. Standard equilibrium rule out this kind of commitment.reason, I do not treat commitmentription consistent with equilibriumimization. I discuss evolutionaryts for why individuals may maintainent ability in section 5.

    eated Games

    thesis. Paul seeks to maximize hisconsumption, but he views the rela-as ongoing. More precisely, he is

    in a repeated game with Marsha,eeks to maximize a discounted sum-period payoffs.sis. Actions have implications foryoffs in repeated games, so equilib-

    havior does not require short-termation. It is natural to assume thatestructive action imposes a short-t on Paul but an even greater costha, punishing her for firing him.ium strategies in repeated gamescify that one player punish anotherllowing a deviation from equilibri-vior. In the simplest cases, potentialents deter the behavior that wouldhem. So one would never see pun-. When Marsha is uncertain aboutillingness or ability to sabotage, it in her best interest to take actions to Pauls destructive behavior.

    punisheotherwibecauseparties he puni

    2.2 Sort

    In thexplanata concepdifferento do sothe explgame-thdistinctiapproactermino

    At adescriptPauls blead to environsatisfiedparticulto constspectivethat is ctaxonomtestablefamily omechanrejectin

    Natuhypothesome sithey habenefit may dislong Panature known much dpothesis in this example, and it has problem: Paul lacks incentives to

    t his threat after he loses his job.repeated-game hypothesis to apply,st expect to receive benefits after he Marsha that he would not receivee. These benefits may comePaul receives rewards from thirdfriends or future employers) afterhes Marsha.

    ng out the Explanations

    s section, I have presented severalry models in an informal context. At

    tual level, it is sometimes difficult toiate the models. I make an attemptin the next section, where I discussnations more precisely in an explicit

    eoretic context. Nevertheless, then is often linguistic: The differentes sometimes just use different

    ogy to describe the same thing. empirical level, the differentons identify different reasons forhavior. Fully specified models willifferent ways to organize the workent in response to the threat of dis-

    workers. On the other hand, given ar observation, it is usually possibleuct a just-so story from the per-of ones favorite class of descriptionsonsistent with the observation. Myy does not generate a fully specifiedmodel in each category, but rather af models with the same underlyingsm. Rejecting a model is easy, an approach is nearly impossible.al formulations of the differentes do have different implications inuations, however, in part becausee different conceptions of what theof Pauls actions are. Factors thattinguish the descriptions are howl has worked for Marsha and thef their relationship, how widelyis destructive actions become, howscretion Marsha has in her decision,

  • 396 Journal of Economic Literature, Vol. XLIII (June 2005)

    and how old Paul is when he is fired. I closethe secti

    In thepunishesreturns. age andchange, he is to sin the reior to depay he employeintrinsic behavioron interdict thatemploye

    On thon reciprwould bethought him or ifreward hOne wodecreasehas accuThe consis fired aesis of restory or g

    The siior baserelationsdestroys it knownto the cohurt MaadvertisiFor at leon genrepeatedation wit

    The insis prediMarsha ifires Pauto coordof emplo

    di lxi

    The different implications of the hypothe-ly that more precise versions of thean be supported or rejected by data.

    ferent hypotheses also suggest differ-s for Marsha to modify the environ-o sl la.


    eler irl

    a dete.ff2fsisnete rlf


    ju05_Article 2 6/10/05 1:40 PM Page 396on with a few examples. repeated-game explanation, Paul Marsha to influence his futureIf his future returns decrease with the cost of sabotage does notthen the older Paul is, the less likelyabotage Marsha. It is not necessarypeated-game story for Pauls behav-pend on the amount of severancereceived or the number of otheres laid off. Simple stories based onreciprocity would not predict Pauls to depend on his age. Stories baseddependent preferences would pre- the wealth of Marsha and otheres would influence Pauls behavior.e other hand, considerations basedocity are largely retrospective. Paul less inclined to punish Marsha if hethat she had no choice but to fire steps were taken to inform him andim for service prior to separation.

    uld expect destructive behavior to with the amount of goodwill Marshamulated during their relationship.equences of Pauls behavior after here less important under the hypoth-ciprocity than in the repeated-gameeneral consumption good story.

    mplest explanation of Pauls behav-d on reciprocity involves only thehip between Paul and Marsha. Pauldata to hurt Marsha. He may want that something bad has happenedmpany because this revelation mayrsha, but he gains nothing fromng his own connection to the crime.ast some of the explanations basederalized consumption goods or games, it is important Pauls associ-h the sabotage becomes public.terdependent-preference hypothe-

    cts less punishment if it is clear thats suffering material losses when shel. It would be to Marshas advantageinate firings with reductions in payyees under these circumstances.

    2 The permits afitness ma

    ses impstories cThe difent wayment tthoughtized conbest expior, shemaniputhe firmmotivatwould femploy



    Severoped toof nonscomplefindingsfrom disection the difMarshations ramaintaihave wbehave ject to rthere isbehavioterm seway to mly depePreferein the mscussion of evolutionary models in section 5ess arbitrary identification of selfishness withmization.

    improve outcomes. If Marshathat the repeated-game or general-umption good hypotheses were theanations of Pauls destructive behav-would try to reduce sabotage byting Pauls incentives after he leaves If Marsha thought that Paul wasd by intrinsic reciprocity, then shecus on changing behavior during theent.

    3. Models

    ver a theory appears to you as the only one, take this as a sign that you have

    understood the theory nor the problemt was intended to solve. Popper

    l different models have been devel-escribe and organize the evidence

    lfish behavior. No model provides a description of the observational

    A sensible approach will take ideaserent models. This section parallels. It introduces formal models forerent descriptions of Paul and conflict and the theoretical ques-ed by the use of these models. I the assumption that individualsll defined preferences and theyo maximize their preferences sub-source constraints. For this reason,a clear sense in which all of the I discuss is selfish. I will use theish preferences in a more limitedean preferences that do not direct-d on the consumption of others.2

    ces are altruistic if they are increasingterial consumption of others.

  • Sobel: Interdependent Preferences and Reciprocity 397

    3 Reciprthat adjectmeanings Marshall Sa(Service 19other for dereciprocity. ized and bato describebadly. On threciprocity dopened and(Sahlins 196nary confusstructive recreciprocity. Richard D. ity to descrreceiving a the benefit comes fromeralized recreciprocity. describe restrong recip

    The narrowest formulation of rationalitydemands that an economic agent maximize autility function that depends only on his cur-rent consumption of material goods. Thisformulation is easily refuted, but it is anunnecessarily restrictive view of rationality.General models of rational behavior permita wider range of arguments to enter utilityfunctions. Somewhat arbitrarily, I classifythe models according to the way they extendpreferences. Section 3.2 looks at models inwhich an individual cares about people otherthan himself. Section 3.3 discusses models inwhich preferences depend on more thingsthan marketed goods.

    Pauls behavior toward Marsha illustratesan apparent willingness to risk material wellbeing in order to damage someone else. Spite,outrage, moralistic aggression, and the desirefor revenge are behaviors that are as familiarto social scientists as they are inconvenient tothe econoBut whilharm enhelp theiness withty and construc

    FSn Ne. r t

    an intrinsic preference for reciprocity willhave different preferences over allocationsdepending on the context. Unkind behaviorof their neighbors induces destructive reci-procity while kindness induces constructivereciprocity. Section 3.4 examines models inwhich the process that creates outcomesinfluences preferences. These models are formal re

    Sectionment po3.6 discuinteractiobehave aothers. Tof instrum

    Throuels usingtum gamthe hypoand equi


    . ceree

    mdivar pimle

    ju05_Article 2 6/10/05 1:40 PM Page 397ocity has many definitions, so it is not surprisingives modifying reciprocity take on differentdepending on the author. Anthropologistshlins (1968, page 82) and Elman R. Service66, pages 14 and 15) generously credit eachfinitions of generalized, balanced, and negativeWhile economists do not use the terms general-lanced reciprocity, they use negative reciprocity the tendency to punish people who treat youe other hand, for Sahlins and Service negativeescribes many standard economic transactions conducted towards net utilitarian advantage8, page 83). To avoid unnecessary interdiscipli-ion, I propose the terms destructive and con-iprocity as alternatives to negative and positive

    This is not the only possible source of confusion.Alexander (1987) uses the term direct reciproc-ibe bilateral exchanges of favors: the personbenefit compensates the person who generatedand indirect reciprocity when the return favor a third party. Robert L. Trivers (1971) uses gen-iprocity in the sense that Alexander uses indirectHerbert Gintis (2000) uses weak reciprocity tociprocal interactions that are instrumental androcity in the way that I use intrinsic reciprocity.

    mists narrow notion of self interest.e people will go out of their way toemies, they will make sacrifices tor friends. I will call repaying unkind- unkindness destructive reciproci-repaying kindness with kindnesstive reciprocity.3 Individuals with

    4 ErnstKlaus M. this sectio

    5 It is aand for thequal to sbecause itoffers less

    tions. Inbargainfixed sizchoose s [0,1]either arespondproposerespondboth rec

    Gameto maxitwo preall positin subgproposefeasiblethe min

    The ufor expehr and Simon Gchter (2000) and Fehr andchmidt (2003) also review of the material in.ash equilibrium for the proposer to offer s > 0

    responder to accept any offer greater than orThis equilibrium fails to be subgame perfectelies on the responders threat to reject positivehan s.

    presentations of intrinsic reciprocity. 3.5 briefly discusses how commit-

    wer influences predictions. Sectionsses how the theory of repeatedns may lead selfish individuals tos if they cared about the welfare ofhis provides a foundation for theories

    ental reciprocity.4

    ghout this section, I illustrate mod- the ultimatum game. The ultima-e provides a powerful challenge tothesis that income maximization

    librium describe economic interac- the ultimatum game, two playersver the distribution of a surplus of 1. The first player (proposer) canany distribution of the surplus The second player (responder) thencepts or rejects the proposal. If ther accepts the proposal s, then thes monetary payoff is 1 s and thers monetary payoff is s. Otherwise,ive nothing.theory, assuming that players seekize their monetary payoff, makes

    ictions. First, in Nash Equilibrium,e offers must be accepted. Second,

    me-perfect Nash Equilibrium, the must offer s = 0 (or, if the set ofroposals is discrete, either s = 0 orum positive proposal).5

    timatum game is a beautiful subjectrimental study. It is simple. The

  • 398 Journal of Economic Literature, Vol. XLIII (June 2005)

    6 See WSchwarze (and Alvin E

    combination of payoff maximization andrationality leads to sharp predictions.Experimental subjects repeatedly violate thetheoretical predictions.6 The violations aresystematic: low (s < .2) proposals are rare;proposalthe seconplus (so equal orcommonin typicafrom theThis finmuch wediction choose apayoffs tciated wto hold u

    Beforebasic notenvironmof agens = (s1,determingame thassumptipreferenagent is a utilitycomes. Wish behadefinitioconsump

    3.1 Incom

    In thisis an alloincreasinxj for j private geach placonsumpvate goo

    payoffs. For simplicity, xi will refer to amonetaris simplepredictiomany int



    s i


    tx mpep m.aaodyo

    sn a vChtimin t

    i (

    ju05_Article 2 6/10/05 1:40 PM Page 398erner Gth, Rolf Schmittberger, and Bernd1982) for early experiments and Gth (1995b). Roth (1995) for reviews.

    s are rejected; proposals rarely gived player more than half of the sur-that s > .5 is rarely observed); and nearly equal splits (.4 < s .5) are, occurring more than half the timel experiments. In addition, rejections responder decrease as s increases.ding is consistent with, althoughaker than, the stark theoretical pre-

    since subjects are more likely toctions that maximize their materialhe larger the (material) benefit asso-ith doing so. These results continuender a range of conditions. describing the models, I introduceation. Limit attention to a strategicent with I agents. The strategy set

    t i is si. Any strategy profile ,sI) (where si Si for all i = 1,,I)es an outcome O(s). Conventionaleory adds to this formulation theon that agents have well definedces over outcomes. Assume thatpreferences can be represented by function ui(.) defined over out-

    ithout additional assumptions, self-vior is not defined. The abstractn of outcome does not identify ation bundle for each agent.

    e Maximization

    setting, O(s) = (x1,,xI), where xication to player i and ui(O(s)) is ang function of xi and independent ofi. That is, the outcome consists ofoods allocated to each player and

    yer cares only about his or her owntion. In many applications the pri-ds are one-dimensional monetary

    combinuse (sugies, thfirst plain the u

    3.2 Inte

    This assumedefinedtions onprefereof other

    As inO(s) = (xi is theinterdeabout thnot simui(O(s))for j i

    Severfunctionences. Fare onetary pathese m


    The prefereij isaltruismto decreincreasea negati

    Gary and Fecations papers ij is on only

    uy payoff in this section. This model and leads to clear predictions. Thens are systematically wrong in

    eresting situations. It is this model,d with the assumption that playersgame perfect) equilibrium strate-t leads to the prediction that theer demands essentially everythingtimatum game.

    dependent Preferences

    ubsection describes models thatndividuals seek to maximize well-preferences, and that base predic- equilibrium behavior, but permitces to depend on the consumption.he case of income maximization, let1,,xI) denote the outcome, where

    aterial allocation of player i. Withendent preferences, agents care distribution of material goods andly their own allocation. That is,ay now depend nontrivially on xj,

    l authors have proposed specificl forms for interdependent prefer-r these authors, material allocationsimensionalconformable to mone-offs in an experiment. To reviewdels, consider the utility function


    implest form of interdependentces consistent with (1) arises whenconstant. A positive ij reflects(in the sense that an agent is willingse his own consumption in order tothe consumption of another agent);e ij reflects spite.harness and Matthew Rabin (2002)

    r and Schmidt (1999) offer specifi-hat are special cases of (1). These

    pose the further restriction thatdependent of i and j and depends

    he sign of xi xj.

    x x x x xij i

    ij i j j) = + ( )

  • Sobel: Interdependent Preferences and Reciprocity 399

    Charness and Rabin (2002) opt for anaverage tive weithe monwell offthis spewhen xplaces pof otherconsumpis than o

    For thgested bif xi > xjspecificamonetarto reducthe twoOckenfeReciprocsimilar functionBolton aerences ear) fun


    The spreferendescribemaximizexampleij = she is ofs (1 then thetum gam

    offer th

    which isThis r

    suggeststhe ultimand notexpect able cont



    his opponent in a dictator-game version ofatum game (in which the second

    required to accept any feasible pro-Allowing the sign of to changeng on the income distribution isnt with this behavior.7

    K. Levine (1998) assumes that theo which agents care about anothermea





    ju05_Article 2 6/10/05 1:40 PM Page 399of functional forms that place posi-ght on the selfish monetary payoff,etary payoff received by the least

    agent, and the total payoff. Withcification, ij > 0, but is greateri > xj. That is, individual i alwaysositive weight on the consumptions and places more weight on thetion of individuals poorer than hen richer individuals.e inequity aversion approach sug-

    y Fehr and Schmidt, ij is positiveand negative if xi < xj. Under thistion, an agent cares about his owny payoff and, in addition, would likee the inequality in payoffs between players. Gary E. Bolton and Axellss (2000) ERC (for Equity,ity, and Competition) model has a

    motivation, but proposes a utility that is not in form (1). Instead,nd Ockenfels assume agent is pref-are an increasing (possibly nonlin-ction of xi and agent is relative


    implest model of interdependentces provides the flexibility to

    some observed violations of incomeation in the ultimatum game. For, if the responder is spiteful, so thatis constant and negative, then whenfered the share s she will reject it if s) < 0. If both players have (0,1), unique equilibrium of the ultima-e would be for the first player to

    e second player the share ,

    positive but less than one half.esolution is unsatisfactory. Intuition that at least some of the behavior inatum game comes from generosity

    fear of rejection. One would not spiteful individual to make charita-ributions or give a positive share to

    1 +






    7 Modepositive oHence Chfunctionalin order behavior in

    the ultimplayer isposal). dependiconsiste

    Davidextent tplayers of a purism parassumeswhich thple carenice pemaximiz

    Hereer i andprefereni placesof js dweight iism paracase of (the weiganotherthat playwants touses thiresults.playerspreferenof incomwant tothat theinferencple. Thiarise ins choos of interdependent preferences predict allfers are accepted when ij is nonnegative.rness and Rabin (2002) also combine theirorm with preferences that depend on contexto explain some of the observed responder ultimatum games.

    aterial utility is a weighted average altruism parameter and the altru-meter of the other player. Levinethat people differ in the degree toey care about others and that peo-more about the material payoffs ofple. Formally, he assumes that is


    i is the altruism parameter of play-i is the weight player i places on js

    ces. If i = 0, then the weight playern js material payoff is independentgree of altruism; otherwise, thean increasing function of js altru-

    meter. This specification is a special1). In contrast to inequity aversion,ht placed on the material payoff ofplayer depends on the identity ofer. In Levines model, an individualbe kind to a kind person. Levinemodel to describe experimental

    n order to do so, he assumes thatre uncertain about their opponentsces and solves for the equilibriumplete information games. Agents

    dentify altruistic (high ) people socan be nice to them. Players draws from the strategies of other peo-permits a form of reciprocity to

    equilibrium. If agents with higherse nicer strategies, then players

    x xij i

    i i j





  • 400 Journal of Economic Literature, Vol. XLIII (June 2005)

    8 Jacob Kto test for thsum paymebargaining tent with ththese paymthe bargain

    place higher weights on the material pay-offs of people who play nice strategies,because playing nice strategies signals thatyou really are nice.

    Models of interdependent preferencesraise theoretical issues about how to deter-mine the arguments of the utility function.Imagine an agent who is motivated by thedesire toreflects inity entersthis utilisubject cpayoff inher earnbehaviorfor inequRead, Geand Richcerns outhe decissecond learned would shIf experimto play a rium printerestewould threduced?positionstest of grandom day of tattempt torder to wealth oparticula

    Concetal settiShould t



    the subjects utility function? Subjects havesome idea that the experimenter is budgetconstrained (or at least the money from theexperiment comes from somewhere). So allallocations are just transfers. Since the totalmonetary payments are constant, utilitari-an objecsubjects


    se toldyone

    set telyt ot ir hnios

    ju05_Article 2 6/10/05 1:40 PM Page 400. Goeree and Charles A. Holt (2000) attemptis effect in the laboratory. They vary the lump-

    nt received by subjects in a perfect-informationgame. Results from the experiment are consis-

    e hypothesis that subjects take into accountents, which are irrelevant to standard models ofing process.

    maximize a utility function thatequity aversion. Exactly whose util- into this function and how should

    ty be measured? An experimentalould try to maximize her monetary the laboratory and then redistributeings to deserving people later. This would be appropriate if the concernity was broadly bracketed (Danielorge Loewenstein, and Rabin 1999ard H. Thaler 1999) in that con-

    tside of the laboratory entered intoion making in the laboratory. If theplayer in the ultimatum gamethe proposer was relatively poor,e be willing to accept small offers?8

    ental subjects had to earn the rightrole in a game in which the equilib-ediction (assuming narrowly self-d behavior) gave unequal payoffse effect of inequity aversion be Would it matter whether attractive were allocated by scoring high on aeneral intelligence or by a pseudo-device, like being born on an oddhe year? Do winners of lotterieso find out the names of the losers inreduce inequality (or increase the

    f the agent who did poorly on thisr transaction)?rns that always arise in experimen-ngs are especially salient here.he experimenters payoff enter into

    9 On thmay have the laboraexperimenselfish is t

    more thmental bring ththe lab,ness or experimdecision

    An opplaces pers coucarefullnature This ageent preftory, soindifferewinningto decrpossibiliaccountratory, experim(narrowple musers mayorder toutside

    Thereels of modeleifying tgame aapplicatonly abticipant contrary, one could also argue that subjectsore incentive to curb their selfish instincts inry than in other settings if convincing fellow

    al subjects and experimenters that they are note best way to gain future riches.

    tives are not relevant. Also, themust be aware that they maken one decision during an experi-ession. Even if subjects do not

    eir lifetime decision problem intothey may impose notions of fair-ocial preferences across the entirental session rather than just oneat a time.imizing agent whose utility functionsitive weight on the wealth of oth- allocate income outside the lab

    so that one could not infer the truef preferences from lab behavior.t would optimize his interdepend-rences before entering the labora-

    at the margin he would bent between allocating his laboratory to increase his personal income orase inequality. If one accepts they that laboratory behavior takes intodecisions made outside of the labo-hen this argument suggests thatnts overestimate the amount of) selfish behavior, since selfish peo-

    be selfish in all situations and oth-appear selfish in the laboratory in pursue their nonselfish interestshe laboratory more effectively.9

    are tacit assumptions in the mod-nterdependent preferences. Themakes the assumptions when spec-e identities of the players in thed their initial wealth levels. In

    ons, subjects are assumed to careut the welfare of other active par- in the game and to make relative

  • Sobel: Interdependent Preferences and Reciprocity 401

    income comparisons based only on thematerial (and necin whichments (choice useems esdependeing how understautility of the expethese momust ddefined othe contrmodels decide wacross laworkers,jobs. Oninvoke andeterminagents mover long

    3.3 PrefeGood

    The Cusing theed agentmentaprices, explain aena. Thein the woBecker 1977). Thsibility thtion. Prmarketedthat indigoods. Mnot requtheir decpayoffs.

    Stiglermaker (h

    (2) U(Z1,,Zm)










    l m cinyailyhioa d


    ju05_Article 2 6/10/05 1:40 PM Page 401payoffs of the game. It is typicalessary) to identify a small world to apply decision-theoretic argu-particularly in models involvingnder uncertainty). The problempecially critical when using inter-nt preferences, however. In decid-to interpret these models, one mustnd why the subject cares about theother subjects, but not the utility ofrimenter. In deciding how to applydels to a contracting problem, one

    ecide whether preferences arever coworkers or just the parties toact. In deciding how to apply theseto the labor market, one musthether workers care about inequitybor and management, across all

    or only across workers in similare must also decide whether to interdependent utility function toe decisions separately or whetherake decisions that reduce inequityer intervals.

    rences over General Consumptions

    hicago School pursues the goal of optimizing models of self-interest-s constrained by a market environ- limited endowment, existingand economic institutionsto broad range of economic phenom- approach is advocated powerfullyrk of George J. Stigler and Gary S.

    (for example, Stigler and Beckere theory explicitly exploits the pos-at self interest has a broad defini-

    eferences are not defined over goods, but general commodities

    viduals transform into consumptionodels in this tradition therefore doire that experimental subjects baseisions solely on their own monetary

    and Beckers posit that the decision-ousehold) has a utility function

    where f

    (3) Zi

    Zi are ti is thity i, Xgood, tkis the hYi repreand prihold selject to (of markThe quaIn thehowevefunctionand, indsumptiothe mod

    Whileis firmlyomistsmaximizview am(1968, pomy ofuncommmateriathat thethe gaingood thlook beundersteconomexplicitgood tthe notcedes thvated byeven in

    Whenthe Stiglmakersvariableon somr i = 1,,m

    i(X1i,,Xni,t1i,,t1i,S1,,Sl,Yi)e generalized consumption goods,e production function for commod-is the quantity of the jth marketin the time input of individual k,Skman capital of the kth person, andents all other inputs. Given wageses for the market goods, a house-cts Xji and tki to maximize (2) sub-). In any application, the definitiont goods will not be controversial.tities Xji and tki will be observable.

    eneral specification of the theory,the levels of human capital, the

    l form of the production functions,ed, the nature of generalized con-goods can be freely selected by

    ler.the approach of Stigler and Beckergrounded in ideas familiar to econ-budget constraints and individualtionit also reflects a commonng cultural anthropologists. Sahlinsge 9), who provides a useful taxon-reciprocity, observes that in anon number of tribal transactionsutility is played down, to the extent

    ain advantages appear to be social,oming in good relations rather thangs. Sahlins recognizes the need toond immediate material gain tond the workings of simplees. While Stigler and Becker do not substitute good relations forings, their formulation broadensn of consumption good and con-t economic exchange may be moti-more than short-term material gaineveloped market economies.stripped to its mathematical core,rBecker model posits that decision-ave preferences over their choiceand that these preferences depend

    thing that is determined in part by

  • 402 Journal of Economic Literature, Vol. XLIII (June 2005)

    10 In thutility funcheterogenevariables.

    11 I useorder to cothat I intro

    choices and in part by other factors that areleft unconstrained in the basic formulation.10

    Everything can be written

    (4) ui(O(s);(s;))

    where s = (s1,,sI) is strategy profile (indi-vidual i chooses si), describes personalcharacteristics, and is a parameter.11 Inmaking tchoice vof markadditionother inized condoes nogenerali

    The d(2) appeagents ugeneralireducedthe entipendentindividuthe prodments tFurther,restrictiochoices human ction of the othemizationdepende

    What the modinterdeping decisdistributaspects tgenerali

    require that the outcome is a vector ofobservabgeneralizof the gobut are goods. Tquantitielike a wa


    rn p, rBch qg is


    aiivd ereifniahlos bteic


    ju05_Article 2 6/10/05 1:40 PM Page 402e StiglerBecker formulation, the householdtion does not depend on the household, butity may enter through the human capital

    this formulation rather than simply Ui(s,) innnect this model to explicitly strategic modelsduce in section 3.4.

    he transformation, si represents theariables of the household (quantitieset goods and labor); denotes theal parameters (human capital andputs); O(s) denotes those general-sumption goods whose production

    t depend on and (s;) all otherzed consumption goods.escription of the utility function inars to rule out externalities, since antility is a function only of his ownzed consumption goods. The-form (4) allows utility to depend onre outcome, so it permits interde- utilities. Characteristics of otherals in the economy enter throughuction function: it includes as argu-he human capital of all agents. since the general model makes nons on the relationship between

    of other agents and their level ofapital on one hand and the defini-

    generalized consumption goods onr, nothing prevents agent is opti- problem from having an arbitrarynce on agent ks market decisions.distinguishes this formulation fromels of income maximization and

    endent preferences is that optimiz-ions can be based on more than theion of material goods. There are twoo this difference. First, the model ofzed consumption goods does not

    differenconsumcomes mthe repprefereon theobserve

    The Stiglerapproaappears

    Geor(2000)sthe dec

    (5) U

    where the indassignecharactindicatple in dsituatio719). Gselects action c

    Akerreduceable aassociaacterist(s;) =Akerlofthus mthat thare assooften ar

    The tconsistele private allocations. Models withed consumption goods permit someods to be standard private goods,flexible enough to include publiche arguments could also includes that cannot be measured directly,rm glow from giving. The seconde is that in models of generalizedtion goods preferences over out-ay vary with parameters. In terms ofesentation in (4), an individualsces over outcomes O can dependarameter , which is difficult tolet alone control.educed-form description of theecker model also connects it to an that, at least on the surface,uite different.

    e A. Akerlof and Rachel E. Krantonformulation of identity posits thationmaker has a utility function


    is the action of individual i, Ii isiduals identity, ci is the individualssocial categories, i is individual isistics, and P are prescriptions that the behavior appropriate for peo-ferent social categories in differents (Akerlof and Kranton 2000, pageven ci, i, P, and ai, individual ki to maximize Ui. In this theory,oices are observable.f and Krantons model alsoto (4) by denoting the action vari-y s, letting contain the variablesd with social and individual char-s and prescriptions, and defining

    Ii(ai,ai;ci,i,P). The models ofKranton and StiglerBecker arehematically identical. It is curiouse formally equivalent approachesiated with schools of thought that viewed as opposites.eories are identical because they aret with precisely the same set of

  • Sobel: Interdependent Preferences and Reciprocity 403

    12 Theendowmein additiDecisionfixed com

    observations. Any observation consistentwith the first must be consistent with the sec-ond and conversely. The theories have differ-ent social scientific implications because theylead one to look for different ways to describeobservations. For example, the Chicagoschool may assume that generous behavior isa consuutility fance ofuture)an indaccorditherefooffersloses u

    GertPosnerexamplmodeldependsumptious speexpenditems. Iity functo capting statpreferement oincomeitems avariablagentstheir stbe consfrom segest thsurplusistic. Benhancbetter





    interest in the future. The decision to sacri-fice nonconspicuous consumption forincreased status is a standard economictradeoff. Proposers will not make low offersin the ultimatum game for the same reasonand also to avoid challenging the secondplayers status.13 Responders reject low

    the ultimatum game in order to sig-small amounts of money are not

    nt to them. Voluntary contributionsc goods arise if status is enhanced byting to charitable projects.ling and Posner presumably wish ton the Chicago tradition and basep




    net etuth

    ju05_Article 2 6/10/05 1:40 PM Page 403 fixed component of status derives from geneticntinherited wealth, titles, race, and genderon to other attributes obtained in the past.s made in the current period cannot influence theponent of status.

    mption good that directly enters theunction (possibly because the appear-f kindness that will be useful in the. Akerlof and Kranton might posit thatividuals identity required behavingng to accepted norms of fairness (andre the proposer loses utility if heunequal divisions or the respondertility if she accepts unequal divisions).rud M. Fremling and Richard A.

    (1999) provide a more elaboratee of this approach. They sketch a

    in which an individuals utilitys on status and nonconspicuous con-

    on. In this formulation, nonconspicu-nding is the category that summarizesitures on standard consumptionnserting a status argument in the util-tion provides a reduced-form meant

    ure the instrumental value of increas-us. Agents have the same underlyingnces, but differ in their given endow-f status.12 Individuals allocate theirover nonconspicuous consumption

    nd expenditures that influence theire component of status. Becausewill forgo consumption to increaseatus, this formulation is sufficient toistent with many apparent departureslf interest. Fremling and Posner sug-at dictators will not take the entirein order to signal that they are altru-eing known as a generous persones your status, which will put you in aposition to advance your material self

    13 Thisso the difmust deperejected in

    14 Alexmorality cFremling altruistic selfish mothe broadsuch condly untestaif we are difficulty

    offers innal thatimportato publicontribu

    Fremmaintaitheir exstatus rthat hetdifferenof statuway toFurtherresponsbehavioefforts tstatus.

    Fremspecifieoperatioargumenot obswhich iry.14 Thwhy stanor do the formffect should arise in the dictator game as well,rence in proposer behavior in the two gamesd on some expectation that low offers will bethe ultimatum game.ders (1987) discussion of the evolution of

    ntains discussions consistent with the view ofnd Posner. In his discussion of (apparently)ving on pages 159 and 160, Alexander raisesivations for generous behavior. He is aware ofess of the theory and writes (page 160): Iftions seem to render the propositions virtual-le, that is simply a problem that we must solveo deal in a better way with the unparalleledf understanding ourselves.

    lanations of differences in giventher than preferences. They arguerogeneous behavior arises becauseagents have different endowments

    , but their formulation provides nomeasure endowments of status.

    this position is a bit strainedto heterogeneity of laboratory

    , since experimenters make greatsuppress information about given

    ing and Posners model is not fully. They do not provide a complete,al definition of status. The status

    t that enters their utility function isrvable. Hence there is no way incan be controlled in the laborato-y do not provide an explanation ofs should enter the utility function,ey place substantial restrictions on

    that it enters. Yet their motivation

  • 404 Journal of Economic Literature, Vol. XLIII (June 2005)

    15 Andreone approatages for exother intanmodels rath

    16 This income acrvant for exp

    is powerful and consistent with casual intu-ition. There have been successful attemptsto incorporate status concerns in prefer-ences, which means that one can derivepreferences like the ones proposed byFremling and Posner from a more detailedmodel.15 Still, the lack of guidance about howstatus influences preferences is disconcert-ing. Fremin whichstatus an(for examing unprwhich mments inmodel co

    Whiletheir mocompleteImplicitlan obsersomethinthe formthat maincome. does in presumautility futhird paforms inincome wrium of aeven thePosner p

    3.4 Intri

    Gameuations, relation process does no

    e 02

    identity and generalized commodities per-mit preferences over outcomes to depend onthe context in which the outcome wasreached. Formally, this means only that appears tion despreferendepend o

    exneylpp t5te0el isfeot el



    ju05_Article 2 6/10/05 1:40 PM Page 404w Postlewaite (1998) provides an overview ofch. This article also argues that there are advan-plicitly incorporating the reasons why status (orgible arguments) should matter into formaler than relying on reduced-forms.interpretation suggests that differences inoss experimental subjects would be both rele-erimental results and difficult to control.

    ling and Posner describe situations conspicuous spending increases

    d others in which conspicuous thriftple, buying a modest car or wear-

    etentious clothes) enhances status,akes me suspect that ex post adjust- their status variable will make theirnsistent with any observation.

    Fremling and Posner describedel as a signaling model, it is notly clear what is being signaled.

    y, status is important because it isvable way for third parties to learng important about an individual. Inal model, the only characteristicy be hidden is an individualsIf status does signal income (as it

    many of the informal stories), thenbly it is not status that enters thenction, but income (as perceived byrties).16 The function that trans-vestment in status into perceivedould be determined as an equilib- signaling game and need not have

    weak properties that Fremling andosit.

    nsic Reciprocity

    theory assumes that, in strategic sit-players act to maximize a preferenceover outcomes. As a result the

    by which the outcome is reachedt matter. I argued that models of

    17 SomRabin (20

    Contpreferegame bduced bof the uthe pro8020 sversion,8020, games, respondand a 0ences dmateriaher decbeen ofplayer split. Instrategymore likwhen pequal dare avaArmin (2003) c

    Assumtwo reainfluencmatum adding selectiogames ito accepequilibrences oindiffertwenty of the experiments reported in Charness and) have a similar flavor.

    in the utility function. This subsec-cribes a framework in which theces that players optimize in a gamen the game itself.t matters in a strategic situation if

    ces over outcomes depend on theing played. The idea is best intro- an example. Consider two versionstimatum game. In the first version,oser can make only two offers: anlit and a 2080 split. In the secondhe proposer can make three offers:050, and 2080. In both of thesehere exists an opportunity for ther to choose between 8020 division division. If the responders prefer-pend only on the distribution ofpayoffs available when she makesion, then her decision after she hasred 20 cannot depend on whether

    ne could have proposed an equaluition suggests that the additionalmight matter, with the responderly to reject the unfair 8020 split

    ayer one could have offered anision than when only unequal splitsable. The experimental results ofalk, Fehr, and Urs Fischbachernfirm this intuition.17

    ing equilibrium behavior, there areons why adding strategies might the responders choice in the ulti-ame. The first possibility is that

    trategies changes the equilibrium. This could only happen if the sub- which responder decides whether or reject a proposal have multiple. For appropriately defined prefer-

    er outcomes, the responder may bent between accepting or rejectingnits out of one hundred, but it is an

  • Sobel: Interdependent Preferences and Reciprocity 405

    18 If thindifferenparametrbetween explainedrium seleof feasibloutcomes

    implausible way to explain experimentalbehavior.18

    The second possibility is that preferencesdepend on more than final payoffs. In theultimatum game, if player 2s preferencesdepend only on final outcomes and she has astrict preference between accepting the8020 split and turning it down, then shemust make the same choice on the equilibri-um patbe avaion the comes than juthe 80unavailiprocitythe acexamplwhetheultimatmust pmore t

    Rabispecificgames text to lation uintroduPearcePsychoto entemodel,materiation of intentiobeliefs)posed game t

    (6) u

    nf a

    In this expression, G is the game, s = (si,sj), s = (si,sj), vi denotes player isutility function over outcomes, and O(s) isthe outcome obtained if the players play s. 19

    Rabin interprets si as the strategy choice ofplayer i, strategy believes is strate



    ie t








    ju05_Article 2 6/10/05 1:40 PM Page 405e responders preferences over outcomes left hert between 00 and 8020, then for all popular

    izations of (1), she would have a strict preference00 and 7921. Consequently a model that the experimental results on the basis of equilib-ction predicts that small perturbations in the sete offers would dramatically change experimental.

    h whatever the other strategies maylable to player 1. Hence I concentratepossibility that preferences over out-at a decision point depend on morest final payoffs. Player 2s rejection of20 offer when the equal split isable is an example of destructive rec-. In situations where beliefs abouttions of others are irrelevant (fore, when the second player decidesr to accept or reject an offer in theum game), any descriptive modelermit allow preferences to depend onhan the distribution of income.n (1993) was the first to propose a model of equilibrium behavior inwhere players take into account con-determine their behavior. His formu-ses the theory of psychological gamesced by John Geanakoplos, David, and Ennio Stacchetti (1989).logical games permit players beliefsr into their preferences. In Rabins the weight placed on an opponentsl payoffs depends on the interpreta-that players intentions. He evaluatedns by using beliefs (and beliefs about over strategy choices. Rabin pro-that agent i pick his strategy si in ao maximize a function of the form:

    i(si;s) = vi(O(s)) + Gi (s)vj(O(s)).

    19 Rabibutions oCharness

    are accusi = si. player igame a

    The uences ovon expemaximizutility wG(s) dadditioninterpreextent tmateriation (Gisentatiotypicallypreferenthan histrategicspecificGi inless imptive if inegativenasty. Iintrinsicment raopponemaking own mathat of h

    The individusumptio (1993) assumes that the outcomes are distri-money x and that vi() depends only on xi.

    nd Rabin (2002) relax the second assumption.

    sj as player is beliefs about player jschoice, and si as what player ithat player j believes about playergy choice. In equilibrium, beliefsrate, so that j actually plays sj and Gi is a function of the beliefs of It is this feature that makes thesychological game.

    tility function ui expresses is prefer-er his own strategies (si) conditionedted behavior (s). A player seeks to

    e a weighted average of his materialth that of his opponent. The weightpends on the game being played into the strategy profile. The naturalation of G(s) is as a measure of the which player i cares about player jswelfare. The conventional formula- 0) is a special case of this repre-. When Gi is not constant, as is

    the case in Rabins model, player isces over strategies depend on more preferences over outcomes: the context matters. Rabin presents afunctional form for the coefficient(6). The form of the coefficient isrtant than its content. Gi is posi-

    thinks that js behavior is nice and if he thinks that the behavior is this way, (6) provides a model ofreciprocity. Kind (unkind) treat-

    ises (lowers) the weight placed onts material payoff is preferences,n agent more willing to sacrifice his

    terial payoff to increase (decrease)is opponent.ptimization problem (4) faced byl agents in the generalized con-

    n model appears to include the

  • 406 Journal of Economic Literature, Vol. XLIII (June 2005)

    problem (6) as a special case. There is a sub-tle differmodels tthe strategiven ans fixed. IModels btion gooconditionevolutionof a statdecisionmdirectly anical impthat prefprobabiltence ofargumenExistencAkerlofwithout cavity of(4). The the prob


    The mfor a stAssume form (6) and Gi (Fand Gi (Ffor i = Roa naturalpates coon his owhile ondinate bnegativeAssume s = (Figplace a npayoff athan dev

    equilibrium outcome. When (Fight,Opera)xe vigee

    r n


    , i(ss sa(ifut hdeius e



    np6e ij2s ry



    ju05_Article 2 6/10/05 1:40 PM Page 406ence in the way that one closes theo compute equilibria, however. Ingic models, agent i takes context as

    d chooses si to maximize (6) holdingn equilibrium, one must have s = s.ased on the generalized consump-

    d idea often require a consistency (the condition may describe the of human capital or the magnitudeus argument), but in general theaker controls si as it enters both

    nd indirectly in (4). There is a tech-lication of the difference. Assumingerences over outcomes are linear inities, the standard assumption, exis- equilibrium follows from standardts in the game-theoretic models.e would not be guaranteed in theKranton or StiglerBecker settingsassumptions that lead to quasicon- the reduced-form preferences infollowing example illustrates part oflem.ple 1. Consider the game:

    atrix describes the material payoffsandard battle-of-the-sexes game.that payoffs can be written in thewith vi as given in the payoff matrixight,Fight) = Gi (Opera,Opera) = .8

    light,Opera) = Gi (Opera,Fight) = .8w and Column. These weights have

    interpretation: a player who antici-ordination places positive weight r her opponents material payoff,e who anticipates a failure to coor-lames the other player and places weight on that persons payoffs.that the players expect the outcomeht,Opera). Then each player willegative weight on the other playersnd will prefer playing as expectediating: That is, (Fight,Opera) is an

    is the ethat thopera eto the fshe is bthe matto lowe

    Alteras the identityhave thThat isui(s) = vsame a(v1(s),v2(Coordincharge thoughtfailure becauseas selfisconfuseNow, thequilibrplayer iresponses his midentity

    The dtions is player cchange In the eequilibrbut in between

    The mences ience apvi() in (outcomplayers,player Rabin (assumeerencesmoneta








    1,2pected outcome, the man believeswomen is planning to go to the

    en though she believes he is goinght. In this situation, he thinks thating nasty and is willing to give uprial value of coordination in orderher payoff.atively, one can view the payoffsresult of Akerlof and Krantonstheory. Assume that preferences same representation as before.they can be written in the form) + Gi (s)vj(s), where i j, Gi is thebefore, and the material payoffs

    )) are given in the payoff matrix.tion permits the man to feel inf the outcome is (Fight,Fight)) orl (if the outcome is (Opera,Opera));

    o coordinate leads to negative the man does not want to be viewed (if the outcome is (Fight,Opera)) or (if the outcome is (Opera,Fight)). outcome (Fight,Opera) is not anm because given that the columngoing to the opera, the mans best

    is to go there as well. Doing so rais-aterial payoff and also changes his increases from .8 to .8).fference between the two formula-at, when considering a deviation, an change his identity but cannotis view of his opponents intentions.ample, Rabins model had a largerm set than Akerlof and Krantons,

    general there is no relationship the two sets.odels of context-dependent prefer-clude the interdependent prefer-roach. The underlying preferences) are defined over outcomes. If an specifies a material payoff to botht is permissible for vi to depend ons material payoff. Charness and002) propose a functional form thatthat the vi are interdependent pref-that place positive weight on js payoff (with the weight changing

  • Sobel: Interdependent Preferences and Reciprocity 407

    to reflect concern for the player with the loFischbconcertions. come measurprefereoutcomwas obcares oFalk athe flaOckenf(1999).

    Sincesectionerencebroadethat prthe gaminto the

    Therdence tsufficiementalbe worsic reci

    Ken Ponti, (2002) tive-offtest wbackwapaper libriuminterdeward idepartuis eviderium bences. preferehow onexperimPonti, tradict models

    e ei

    results is a tribute to their flexibility ratherual support for the formulation. 20

    el Costa-Gomes and Klaus G.(2001) analyze data from ultimatumperiments and estimate utility func-



    l te








    ju05_Article 2 6/10/05 1:40 PM Page 407west monetary payoff). Falk andacher (2005) also attempt to separatens for equity and concerns for inten-Their model contains a pure out-concern parameter. This numberes the degree to which a playersnces in the game depend only on thee and not on the context in which ittained. At one extreme, a playernly about the outcome. In this case,nd Fischbachers (2005) model hasvor of the models of Bolton andels (2000) and Fehr and Schmidt

    the approach outlined in this sub- generalizes the interdependent pref- approach, without restrictions, it hasr descriptive powers. To the extenteferences over outcomes depend one, reciprocity models provide insight observations.e is substantial experimental evi-hat the distributional approach is notnt to explain and organize experi- findings, which suggests that it wouldthwhile investigating models of intrin-procity.Binmore, John McCarthy, Giovanni

    Larry Samuelson, and Avner Shakedcompare one- and two-stage alterna-er bargaining games in an effort tohether experimental subjects obeyrd induction for these games. Theobserves that subgame-perfect equi- strategies played by agents withpendent preferences satisfy back-nduction. They discover systematicres from backward induction, whichnce against the hypothesis of equilib-ehavior with interdependent prefer-Context-dependent models permitnces over outcomes to depend upone reached the outcome. Hence theental results of Binmore, McCarthy,

    Samuelson, and Shaked do not con-these models. The fact that these are consistent with experimental

    20 Uzi Sargumentsgames govthese restr

    than actMigu

    Zauner game extions oftion thagame wmethodinterdepterminarejects the samficient the estishould bis not thpreferenbut on h

    Therepreferendistribuand Mucomes oer propbetweensecond proposathe secosecond posal (aIf the seon the tplayer rtwo plaand Niebehaviothe paymwho recer is moshe knohigh pathe rejethird pgal and Joel Sobel (2004) show that dominancehave power to rule out some predictions inrned by preferences represented by (6), but

    ctions are weak.

    he form vi + vj under the assump- agents play an equilibrium to aith perturbed preferences. Theirontains an indirect test of the pure

    endent preference approach. In allnodes in which the second player

    he proposal, monetary payoffs are (zero for each player). If the coef-does not depend on actions, thenated variance in the error term

    e the same after all rejections. This case, providing some evidence thatces depend not just on the outcome,ow the outcome was reached.are other ways to demonstrate thatces depend on more than the finalion of wealth. Yoella Bereby-Meyeriel Niederle (2005) compare out- three-player games. The first play-ses a division of a fixed quantity

    himself and the second player. Thelayer either accepts or rejects this

    . The third player is nonstrategic. Ifd player accepts, then the first and

    layers get paid according to the pro-d the third player receives nothing).ond player rejects, then (dependingeatment) either the first or the thirdceives a payment, while the otherers receive nothing. Bereby-Meyererle find that the second players

    depends both on the quantity ofent given following a rejection andives this payment. The second play-e willing to reject a small offer whens that doing so will not lead to a

    off for the proposer (either becausetion payment is low or because theayer receives the payment). To

  • 408 Journal of Economic Literature, Vol. XLIII (June 2005)

    explain this behavior with some form ofinterdepplayer wences thmonetarneed to off differgame. Mstrategievide a coition thato sacrifpunish pmakes a punish (action) dplayer re

    Jamescomes oseparatedesignedbehaviorbasic expdivided group recontribuThe memthree timbers of thof the trafers are abers of tin the Tsecond gTreatmenot movsame coTreatmeamountsMemberfers as intransfersence thethen dectrast betand C prthe powences to

    mover cares only about the distribution of toi

    amsn ae

    nWp tnb

    dsen cnu 3o

    y dd d weinomt plt eh tn

    ju05_Article 2 6/10/05 1:40 PM Page 408endent preferences, the secondould not only need to have prefer-at depended non trivially on they payoffs of others, but she wouldweigh an opponents monetary pay-ently depending on his role in theodels that permit preferences overs to depend on strategy choices pro-nvenient way to capture the intu-

    t the second player might be willingice her material payoff in order to

    layer one when the first playersmall offer. Naturally, the ability toand therefore the second playersepends on whether the first or thirdceives a payment after a rejection. C. Cox (2004) compares the out-f three related games designed to predictions from different models to identify the source of nonselfish in experimental trust games. In theeriment (Treatment A), subjects areinto two groups. Those in the firstceive $10 and decide how much tote to a member of the second group.

    ber of the second group receiveses the contribution. Finally, mem-e second group can return any partnsfer he or she received. (All trans-nonymous.) In Treatment B, mem-

    he first group decide on transfers asreatment A while members of theroup do not have a move. In the

    nt C, members of the first group doe. Instead, experimenters make thentributions that were made in thent A (and subtract the appropriate from members of the first group).s of the second group receive trans- the Treatment A, are told how the are generated (and how they influ- endowment of first movers), andide how much to return. The con-ween the results of Treatments Aesent the evidence most relevant toer of the interdependent prefer- describe outcomes. If the second

    payoffs,same inThe secmoney betweenlarge trsecond generou

    In cocontext,influenccomes iset up. their opers maypreferedraws aon the observeon the (becausgies castrategy

    Expautility f3.2 andsion thein utilitcapturecommoare notthe moredefineway in influencshould an outction of strategyin the uthat noreceivesalso theable to tlogicallyfurther preferethen contributions should be thehese two treatments. They are not.nd mover tended to return moren Treatment A. The difference the amount returned is largest afternsfers, suggesting that in part theover acted to reward intentionally

    behavior.trast to the models that focus ondding strategies to a game does not a players preferences over the out- the original game in Levines (1998)

    hen players are uncertain aboutonents preferences, however, play-ry to use their actions to signal theirces. The inferences one playerout his opponents payoffs dependstrategies available. Consequently, preferences over outcomes dependtrategic context in Levines model changing the set of available strate- change the signaling content ofhoice).

    ding the set of arguments in thenction, as in the models of sections.3, is consistent with standard deci-retic methods. The new argumentsfunctions are externalities and fully by expanding the definition ofity. The models in this subsectiontraditional. One attempt to returnels to the standard framework is tothe notion of an outcome. If thehich one arrives at an outcome

    s preferences, then the outcomeclude that information. Formally,e would need to include a descrip-

    he entire game and an anticipatedrofile. Specifically, the 8020 offer

    timatum game leads to an outcome only specifies that player one80 and player two receives 20, butxistence of other possibilities avail-e first player. This transformation ispossible, but hardly useful. Note

    hat the representation (6) specifiesces over player is own strategies

  • Sobel: Interdependent Preferences and Reciprocity 409

    conditional on a strategy profile s; it is not autility function defined over outcomes. Afterredefiniextend t

    Theremodels ences. Tfication Martin D(2004), Rabin (forms foitive arexperimdescribetions onWithoutand Sobry that about be

    Anothbe posssented bpreferenmade inObservasetting informatthis exemany dioffs vibehaviorchoice bble to sfrom pre

    The tpretatioioral randomit requiron eachferent oHence mixed-sbeliefs. situationthe pureequilibr

    result of incomplete information regardingthe oppo


    ra eee,h




    nsn) bn ite

    ju05_Article 2 6/10/05 1:40 PM Page 409ng the outcomes, one would need tohe preferences to this new space. are several problematic aspects ofbased on context-dependent prefer-he most basic problem is the speci-of . Charness and Rabin (2002),ufwenberg and Georg Kirchsteiger

    Falk and Fishbacher (2005), and1993) present explicit functionalr , all motivated by plausible intu-guments and appeals to selectedental evidence, but no one hasd observable behavioral assump- that best describe behavior.

    a model of this parameter, Segalel (2004) demonstrate that the theo-makes few definitive predictionshavior.er problem is identification. It shouldible to separate preferences repre-y vi and ui in (6) through revealedce analysis. Observation of decisions a nonstrategic setting determine vi.tions of decisions made in a strategicdetermine ui. Adding incompleteion about preferences complicatesrcise, however. On the other hand,fferent combinations of material pay-and weight will lead to the same in strategic settings. Looking only atehavior in games it will not be possi-eparate preferences for reciprocityferences over outcomes.hird problem deals with the inter-n of mixed strategies. The behav-interpretation of deliberate

    ization is somewhat strained becausees a player to select a precise weight pure strategy in spite of being indif-ver at least two pure strategies.it is often attractive to interprettrategy equilibria as equilibria inThe important idea is that in somes an agent must be uncertain about-strategy choice of his opponent in

    ium, but that uncertainty may be the

    due to of the othe chadependstrategiences dnent, thexamplemakes t


    Columowner wcome ihomeowAM, inearns 1owner, owner rthe pluappointall day; with thover strover ouequilibrand a chomeowplumbeeach pu

    Now prefereput a poin respodinationto nastycares othe twogame wue to bnents characteristics rather thannscious randomization on the partponent. In standard game theory,cterization of equilibrium does noton the interpretation of mixed

    s. In games where a players prefer-pend on the intentions of his oppo- interpretation matters. A simple taken from Segal and Sobel (2004),e point clearly.ple 2. Consider the game:

    n is a plumber and Row is a home-ith a leaky faucet. The plumber can the AM or in the PM while thener can arrange to be at home in thehe PM, or ALL day. The plumber if she coordinates with the home-ut nothing otherwise. The home-ceives a payoff of 10 if he can meetber and only cancel half of hisents; he receives 7 if he stays home

    e receives 0 is he fails to coordinate plumber. If players preferencestegies agreed with their preferencescomes, then the game has threeum outcomes: (AM,AM), (PM,PM),ntinuum of equilibria in which thener stays home all day and the places probability of at least .3 one strategy.assume that the homeowner hasces over strategies that lead him toitive weight on the plumbers payoffse to nice behavior (apparent coor- and a negative weight in responseehavior. (Assume that the plumber

    ly about her own payoffs.) Clearly,pure-strategy equilibria from theh standard preferences will contin-equilibria. But if randomization by












  • 410 Journal of Economic Literature, Vol. XLIII (June 2005)

    the plumber is purposeful, then the home-owner mrandominasty beprobabilciently noffs, theeither AMall day. Clibrium the plumAM andno longe

    The abpretationcations, homeowpopulatiodency totendencyhomeowty to a dthen it isnot placepayoff. Iequilibriowner alwith proplumber

    Many tance of cally dyndo not pDufwenbFalk andsive-formgic-formgood prlike seqSince it sive-formapplies treasons. there is dmation lcomplica

    In stancal prefe

    l lae


    of equilibria. Multiple equilibrium problemssible, but less pervasive for the para-

    odels of extended preferences usedterature. Coordination problems ariseeferences are interdependent. Playersstuck in nasty equilibria in which theynasty behavior from their opponents it or in nice equilibria in which posi-eeal



    i cr




    a bs f o brt

    ju05_Article 2 6/10/05 1:40 PM Page 410ay well think that a plumber whozes equally between AM and PM iscause this behavior minimizes theity of coordination. With a suffi-egative weight on the plumber pay- homeowner may prefer to play

    or PM rather than to stay at homeonsequently, there may be an equi-

    in which both the homeowner andber randomize equally between

    PM, while ( ) isr an equilibrium.ove analysis depends on the inter- of mixed strategies. In many appli-it is appropriate to treat the

    ner as if he is matched against an of plumbers, some with a ten-

    come in the morning, others with a to come in the afternoon. If the

    ner does not attribute his uncertain-eliberate strategy of the plumber, reasonable to assume that he does a negative weight on the plumbers

    n this case, however, there will be anum in beliefs in which the home-ways stays at home (and he believesbability greater than .3 that the

    will come at any time).of the motivations for the impor-context and intentions are intrinsi-amic, but dynamic considerationslay a role in the basic formulation.erg and Kirchsteiger (2004) and Fischbacher (2005) study exten- games. They argue that the strate-

    approach of Rabin does not lead toedictions in extensive-form gamesuential prisoners dilemma games.is possible to represent any exten- game in strategic form, the model

    o extensive-form games for standardEven for standard game theory,ispute about whether this transfor-

    oses information. This issue is moreted when intentions matter.dard examples, the notion of recipro-rences tends to increase the number

    ALL AM PM, 1212+

    21 Segaallowing penlarges th

    22 Thisplayers arbest respo

    are posmetric min the liwhen prcan get expect and gettive expexistencin applicof possibequilibrobserva

    3.5 Com

    Allowlibriumof prefepower function

    (7) ui(

    where Bresponsegy as gsistent prefereish respthen shonly accno betteExperimare brothat thepower, ability irange o

    The snot be athe otheior is noand Sobel (2004b) formalize the intuition thatyers preferences to depend on context generally set of equilibria.ormulation leaves open how the other I 1ve at best responses and what to do when these correspondence is not single valued.

    ctations are fulfilled.21 While the of multiple equilibria may be usefultions, the possibility broadens the sete predictions from the theory so thatm analysis places few restrictions on

    le behavior.


    ng commitment changes the equi-oncept rather than the specificationences. A player with commitment

    elects his strategy to maximize aof the form:


    Ri(si) is the strategy profile of bests for all other agents, taking is strat-en.22 Commitment models are con-ith more general specifications ofces. In the ultimatum game, if a self-nder had full commitment power, would announce that she wouldpt s = 1 and the proposer could do than to offer her the entire surplus.ental results in the ultimatum gamedly consistent with the hypothesisresponder has partial commitmentut merely assuming commitmentnot sufficient to handle a broader

    empirical regularities.lution si of problem (7) typically willest response to the strategy choices of players. That is, commitment behav- consistent with Nash Equilibrium. I

  • Sobel: Interdependent Preferences and Reciprocity 411

    23 That iin a given psolve: maxsi

    find it more useful to assume that all feasiblecommitment abilities are described in thespecification of the strategic environment.

    3.6 Repeated Games

    The thconventiapparently repeatgame, obthe gamPayoffs fed sumsoffs. Straplay in ebehaviorlarge setrepeatedsible, instage gamperfect einfinitely

    To comapproachtion in waction si t

    (8) (1

    where ufunction;describesthe contiry . In value funfolk theotions on Vstate thatformally consumptake an feasible pno reasofor playethe actio


    In a repeated interaction, an agent exclu-sively interested in his material consumptioncould rationally forgo short-term utility inorder to obtain future benefits. If an appar-ently unselfish action is part of a repeated

    ion between patient agents, then theoer tilreunrita







    ju05_Article 2 6/10/05 1:40 PM Page 411s, if equilibrium strategies specify the actions s

    eriod, then there is no reason to expect that siui(si,si).

    eory of repeated games provides aonal framework in which to explainly unselfish behavior. In an infinite-ed game, agents play a given staticserve its outcome, and then play

    e again and again, without end.or the repeated game are discount- of the individual static-game pay-tegies are rules that specify how toach repetition as a function of past. Repeated games typically haves of equilibria. The folk theorem of games states, roughly, that any fea-dividually rational payoff for the

    e can be obtained as a subgame-quilibrium payoff for the associated repeated game.pare repeated games to the earlier

    es, consider a reduced-form descrip-hich player i selects a stage-gameo maximize

    )ui(si,si) + Vi((s)),

    i(s) is player is stage-game payoff (0,1) is a discount factor; the history of play; and Vi() givesnuation (average) value given histo-this formulation, the continuationction is endogenous. Thanks to therem, however, there are few restric-

    i. So although it is not possible to models of repeated interaction areidentical to those based on generaltion goods, it is clear that if Vi canarbitrary individually rational andayoffs and is close to one, there is

    n that an equilibrium action choicer i will be a myopic best response tons of his opponents.23

    24 The Service 1motivation

    interactfolk thethe obsbehaviothe folkreciprocterm semore ptheir eqtreatmebehaviobut punfear thafuture pthe actihis futusufficieincentiv

    Embeed-gamway to dwith a inconsisapproacrepeateask: Wa way th

    The athem no

    Becaucontrol results n

    In orargumeimportathere mpunish tions faiselfish bnthropologists (for example Sahlins 1968 and6) studying exchange clearly recognize this

    rem of repeated games can explainrvation as a part of equilibrium

    between selfish agents. The logic ofheorem is the logic of instrumentalty.24 Individuals forgo their short-fish gains because being nice (or,cisely and more generally, playingilibrium strategy) will lead to nicet in the future. Punishing nasty serves to discourage nasty behavior,shment only occurs because players a failure to punish will lower theiryoffs. This argument requires thatns an agent takes today influencese payoffs and that the influence istly great to counter short-terms.ding an interaction into a repeat-

    setting is a powerful and acceptedescribe behavior that, when viewedstatic perspective, appears to beent with selfish behavior. Like the of generalizing consumption,

    game theory forces the observer toat does that player stand to gain? int often leads to useful insights.proach has limits. I discuss some of.

    se laboratory experiments carefullyfor repeated-game effects, theseeed a different explanation.er for conventional repeated-gamets to apply, the future must bet. Agents must be patient andst be opportunities to reward anddays behavior. When these condi-

    , theory predicts a return to myopicehavior. Relationships do end, and

  • 412 Journal of Economic Literature, Vol. XLIII (June 2005)

    25 ClassiFudenberg

    while it is easy to find evidence of myopicself interest at the end of relationships, it isalso easy to cite examples of employees whodo not shirk as retirement approaches andfamiliesFitting trepeatedawkward

    Repetum behaty of punfor the pso, the qpunish?punish bished thmust bewilling toishers antificationdirect ananswer sprocity:get utilitof people

    Repeastrategicences buIn orderrepetitiostatic gaence futupreferentions abogame cosubgamesubgameabandonpredict from rep

    Condithat thersubgamefor adopries may


    for all players. For example, the grim trig-ger strategy specifies that players neveragain cooperate following a noncooperativeaction in the prisoners dilemma. The princi-





    s ex d

    ju05_Article 2 6/10/05 1:40 PM Page 412c treatments are Dilip Abreu (1988) and Drew and Eric Maskin (1986).

    that stand by dying relatives.his behavior into an individualistic-game framework is possible, but.

    ition increases the range of equilibri-vior because it creates the possibili-ishment. Punishment may be costlyunisher as well as the punished. Ifuestion arises: Why should anyoneThe theoretical answer is: Peopleecause otherwise they will be pun-emselves. Of course, the argumentrepeated to ensure that people are

    punish the punishers of the pun-d so on. Theory provides elegant jus-for this answer.25 The theory is lessd, perhaps, less convincing than theupplied by models of intrinsic reci-Punishment arises because peopley directly from lowering the welfare

    who have hurt them.ted-game theory incorporates context, not by changing prefer-t by changing the way people play. to obtain equilibria distinct fromns of equilibria of the underlyingme, the history of play must influ-re play. History does not influence

    ces, but it does influence expecta-ut behavior. The principle of sub-nsistency would require play in a to be independent of where the arises in a larger game. One must subgame consistency to in order torepeated-game behavior distinctetitions of static equilibria.tioning on history is so descriptivee is little resistance to abandoning consistency. There is some supportting a weaker principal. Some histo- trigger punishments that are bad

    26 AbreFarrell an

    pal of reof possum payin the payoffs inition iate at equilibrnever aPareto Renegohistory tory cancontinuweaker equilibrnated balready is not stproofnethe resproofnepredicti

    Finalpredictitions anqualitatity of cotoo manis oftentheory ainterest

    This settingsinterestThese esupportextende, Pearce, and Stachetti (1993) and Joseph Maskin (1989) are two approaches.

    egotiation proofness identifies a setle (renegotiation-proof) equilibri-

    ffs with the property that no payoffset are Pareto-dominated by other the set. The logic behind this def-

    that if players are able to renegoti-e beginning of each period on them that they will play, then they will

    ree to play an equilibrium that isnferior to another equilibrium.ation proofness says, in effect, thatn influence future play, but no his-induce players to select inefficienttion. The idea is controversial (theosition that players will not play anm whose payoffs are Pareto domi- another equilibriums payoffs isontroversial for one-shot games). Itightforward to define renegotiation

    s in infinitely repeated games andictions imposed by renegotiations do not lead to more descriptivens.26

    , repeated game theory providesns consistent with many observa-

    also gives strong intuitions aboute features that increase the possibil-peration. But repeated games haveequilibria and the selection process

    ailored to particular examples. Theit is typically used does not produceg refutable hypotheses.

    4. Using the Models

    ection describes several economicin which narrow notions of self-d behavior provide limited insight.amples provide further evidence inof developing models that assume preferences and illustrates the way

  • Sobel: Interdependent Preferences and Reciprocity 413

    27 Andre

    in which the different approaches of section3 provide alternative predictions.

    4.1 Charity

    It is contribuan indiviwealth. charitab

    Contrthe econconsistenexamplemarginalof givingered facthat are dard ecoRobert C(1998) rtions incthe chartributioncontribuare less economi

    The mreasonsmodelswhat inflciple cancusses sogiving an

    Altruisvalue ondicts posthe contcrowdineffect shdistributmotivatethe incothe poorvalue of feature people g


    income, but they do not care about thenature of transfers that determines incomedistribution.28

    s Andreonis (1990) warm-glow theo-aritable giving fits within the tradi-

    of preferences over generalpb







    t teo

    ju05_Article 2 6/10/05 1:40 PM Page 413oni (2001) is a survey.

    difficult to rationalize charitabletions as optimizing behavior fromdual who cares only about materialNevertheless, people do make

    le contributions.ibutions appear to be sensitive toomic environments in ways that aret with conventional theory.27 For

    , changes in tax laws that reduce the cost of giving increase the amount. Social psychologists have discov-tors that influence contributionsless obvious consequences of stan-nomic assumptions. For example,. Cialdini and Melanie R. Trosts

    eview essay suggests that contribu-rease in response to small gifts fromity. There is also evidence that con-s are an increasing function of thetions of others. These predictionsobvious consequences of standardc assumptions.odels of section 3 suggest differentwhy people give to charity. Thesemake different predictions aboutuences charitable giving and in prin-

    be distinguished. This section dis-me theoretical models of charitabled relevant experimental evidence.m, modeled