DOI: 10.1126/science.1078498 , 2216 (2002); 298Science et al.D. W. Stephens,Prisoner's DilemmaDiscounting and Reciprocity in an IteratedThis copy is for your personal, non-commercial use only.. clicking herecolleagues, clients, or customers by , you can order high-quality copies for yourIf you wish to distribute this article to others. herefollowing the guidelines can be obtained byPermission to republish or repurpose articles or portions of articles (this information is current as of April 9, 2010 ):The following resources related to this article are available online at www.sciencemag.org http://www.sciencemag.org/cgi/content/full/298/5601/2216version of this article at: including high-resolution figures, can be found in the onlineUpdated information and services, http://www.sciencemag.org/cgi/content/full/298/5601/2216/DC1 can be found at: Supporting Online Materialfound at: can berelated to this articleA list of selected additional articles on the Science Web sites http://www.sciencemag.org/cgi/content/full/298/5601/2216#related-content http://www.sciencemag.org/cgi/content/full/298/5601/2216#otherarticles, 2 of which can be accessed for free: cites 17 articlesThis article 37 article(s) on the ISI Web of Science. cited byThis article has been http://www.sciencemag.org/cgi/content/full/298/5601/2216#otherarticles 9 articles hosted by HighWire Press; see: cited byThis article has been http://www.sciencemag.org/cgi/collection/psychologyPsychology : subject collectionsThis article appears in the following registered trademark of AAAS. is aScience2002 by the American Association for the Advancement of Science; all rights reserved. The title CopyrightAmerican Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by theScience on April 9, 2010 www.sciencemag.orgDownloaded from26. M. J. Yanovsky, M. A. Mazzella, J. J. Casal, Curr. Biol.10, 1013 (2000).27. C. Helfrich-Forster, C. Winter, A. Hofbauer, J. C. Hall,R. Stanewsky, Neuron 30, 249 (2001).28. Supported by the Novartis Science Foundation (toS.P. and J.B.H.), the National Institutes of Health (MH62405 to I.P.), the National Institute of MentalHealth (MH51573 to S.A.K.), the American CancerSociety (PF-02-108-01-DDC to T.K.S.), and EuropeanUnion grant BMH4-CT97-2327 (to W.J.d.G.). Wethank J. Geskes, S. Kupriyanov, and M. Andahazy fortechnical assistance, S. Carlson and R. McDowell foranimal care and breeding, T. Wiltshire for preliminarymapping of the Opn4 locus, F. A. J. M. van de Klundertfor help in generating the targeting vector, and theanonymous reviewers for their valuable comments.Supporting Online Materialwww.sciencemag.org/cgi/content/full/298/5601/2213/DC1Materials and MethodsFigs. S1 and S22 August 2002; accepted 30 September 2002Discounting and Reciprocity inan Iterated Prisoner’s DilemmaD. W. Stephens,* C. M. McLinn, J. R. StevensThe Iterated Prisoner’s Dilemma (IPD) is a central paradigm in the study ofanimal cooperation. According to the IPD framework, repeated play (repetition)and reciprocity combine to maintain a cooperative equilibrium. However, ex-perimental studies with animals suggest that cooperative behavior in IPDs isunstable, and some have suggested that strong preferences for immediatebenefits (that is, temporal discounting) might explain the fragility of cooper-ative equilibria. We studied the effects of discounting and strategic reciprocityon cooperation in captive blue jays. Our results demonstrate an interactionbetween discounting and reciprocity. Blue jays show high stable levels ofcooperation in treatments with reduced discounting when their opponentreciprocates, but their levels of cooperation decline in all other treatmentcombinations. This suggests that stable cooperation requires both reduceddiscounting and reciprocity, and it offers an explanation of earlier failures tofind cooperation in controlled payoff games.The Prisoner’s Dilemma illustrates the eco-nomic barriers to cooperative action. In thisgame, the defecting (noncooperative) optionis always the best choice for a single play ofthe game, even though both players could dobetter if they cooperated. Axelrod and Ham-ilton (1) argued that cooperation could be agame theoretical equilibrium if (i) the gamewas played repeatedly and (ii) the playersadopted a reciprocating strategy. In their ar-gument, repetition and reciprocity combine tomake mutual cooperation a viable strategy,because although a defector will receive animmediate reward, reciprocity means that itwill suffer for this choice in the long run.Although theoreticians have exploited thisparadigm with great success, it has been mark-edly less successful empirically (2–5). Nonhu-man animals show a strong tendency to defectin experimentally created Prisoner’s Dilemmas(6–9). These studies raise important questions,because we cannot usually confirm that thepayoffs in naturalistic studies conform to thePrisoner’s Dilemma. This uncertainty has led tocontroversy in some cases (10 –12), and in oth-ers, it has led to questions about whether sim-pler explanations of observed behavior mightnot be more appropriate (5, 13, 14). More than20 years after Axelrod declared the Prisoner’sDilemma to be “the E. coli of social psycholo-gy” (15), there is still no single unambiguouscase of stable nonhuman cooperation in a ver-ifiable Prisoner’s Dilemma.One possible explanation for the fragility ofcooperation in the Iterated Prisoner’s Dilemma(IPD) is strong temporal discounting. In theory,animals should cooperate in an IPD becausecooperation leads to higher payoffs in the longrun, but animals may not value these long-termbenefits because they strongly discount the fu-ture. Psychological studies support this idea. Inthese studies (16 –18), experimentalists offeranimals a choice between small immediate andlarge delayed food rewards. These experimentsshow very strong preferences for immediacy.Fitted discounting functions suggest that thefirst second of delay reduces the value of foodreward by as much as 50% (19). These data,therefore, suggest that animal discounting maybe much stronger than rates typically assumedby economists and other students of humanbehavior [e.g., 4% per year (20)].An alternative explanation of the fragilityof cooperative equilibria might hold that an-imals fail to cooperate, not because they dis-count strongly,