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Patience or Fairness? Analyzing Social Preferences in Repeated Games

  • John Duffy
  • Felix Munoz-Garcia


    (School of Economic Sciences, Washington State University)

This paper investigates how the introduction of social preferences affects players’ equilibrium behavior in both one-shot and infinitely repeated versions of the Prisoner’s Dilemma game. We first show that defection survives as the unique equilibrium of the stage game if at least one player is not too concerned about inequity aversion. Second, we demonstrate that in the infinitely repeated version of the game, fairness concerns operate as a “substitute: for time discounting, as fairness helps sustain cooperation for lower discount factors. We then extend our results to more general simultaneous-move games, and more general preferences. Furthermore, we examine how the introduction of incomplete information about players’ social preferences can help in the selection of the efficient cooperative outcome. Finally, we point out the implications of our findings for the design and analysis of experiments involving repeated games. In particular, repeated game equilibria which are thought to be supported by sufficiently large discount factors, may in fact be sustained by a combination of discounting and social preference parameters, an observation that may help rationalize recent experimental findings.

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Paper provided by School of Economic Sciences, Washington State University in its series Working Papers with number 2009-12.

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Length: 27 pages
Date of creation: May 2009
Date of revision:
Handle: RePEc:wsu:wpaper:munoz-4
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  1. Urs Fischbacher & Simon Gaechter, 2008. "Social Preferences, Beliefs, and the Dynamics of Free Riding in Public Good Experiments," CESifo Working Paper Series 2491, CESifo Group Munich.
  2. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Oxford University Press, vol. 38(1), pages 1-12.
  3. John Duffy & Felix Munoz-Garcia, 2010. "Signaling Concerns about Fairness: Cooperation under Uncertain Social Preferences," Working Papers 2010-19, School of Economic Sciences, Washington State University.
  4. Maria Montero, 2007. "Inequity Aversion May Increase Inequity," Economic Journal, Royal Economic Society, vol. 117(519), pages C192-C204, 03.
  5. Duffy, John & Ochs, Jack, 2009. "Cooperative behavior and the frequency of social interaction," Games and Economic Behavior, Elsevier, vol. 66(2), pages 785-812, July.
  6. Oechssler, Jörg, 2011. "Finitely repeated games with social preferences," Working Papers 0512, University of Heidelberg, Department of Economics.
  7. Axel Ockenfels & Gary E. Bolton, 2000. "ERC: A Theory of Equity, Reciprocity, and Competition," American Economic Review, American Economic Association, vol. 90(1), pages 166-193, March.
  8. Pedro Dal Bo & Guillaume R. Frechette, . "The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence," Working Papers 2007-7, Brown University, Department of Economics.
  9. Drew Fudenberg & David G. Rand & Anna Dreber, 2012. "Slow to Anger and Fast to Forgive: Cooperation in an Uncertain World," American Economic Review, American Economic Association, vol. 102(2), pages 720-49, April.
  10. Fehr, Ernst & Schmidt, Klaus M., 1999. "A theory of fairness, competition, and cooperation," Munich Reprints in Economics 20650, University of Munich, Department of Economics.
  11. Yuichi Yamamoto, 2010. "The use of public randomization in discounted repeated games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 431-443, July.
  12. Esther Hauk, 1999. "Multiple prisoner's dilemma games with (out) an outside option: An experimental study," Economics Working Papers 391, Department of Economics and Business, Universitat Pompeu Fabra.
  13. Hector Chade & Pavlo Prokopovych & Lones Smith, . "Repeated Games with Present-Biased Preferences," Working Papers 2173938, Department of Economics, W. P. Carey School of Business, Arizona State University.
  14. Gabriele Camera & Marco Casari, 2009. "Cooperation among Strangers under the Shadow of the Future," American Economic Review, American Economic Association, vol. 99(3), pages 979-1005, June.
  15. Matthias Blonski & Peter Ockenfels & Giancarlo Spagnolo, 2011. "Equilibrium Selection in the Repeated Prisoner's Dilemma: Axiomatic Approach and Experimental Evidence," American Economic Journal: Microeconomics, American Economic Association, vol. 3(3), pages 164-92, August.
  16. Russell Cooper & Douglas V. DeJong & Thomas W. Ross, 1992. "Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games," Papers 0036, Boston University - Industry Studies Programme.
  17. William Neilson, 2006. "Axiomatic reference-dependence in behavior toward others and toward risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 681-692, 08.
  18. Anderhub, Vital & Güth, Werner & Engelmann, Dirk, 1999. "An experimental study of the repeated trust game with incomplete information," SFB 373 Discussion Papers 1999,97, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  19. Brandts, J. & Figueras, N., 1997. "An Exploration of Reputation Formation in Experimental Games," UFAE and IAE Working Papers 404.97, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  20. Paul Healy, . "Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market," GSIA Working Papers 2006-E6, Carnegie Mellon University, Tepper School of Business.
  21. Hans-Theo Normann & Brian Wallace, 2012. "The impact of the termination rule on cooperation in a prisoner’s dilemma experiment," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 707-718, August.
  22. Aoyagi, Masaki & Fréchette, Guillaume, 2009. "Collusion as public monitoring becomes noisy: Experimental evidence," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1135-1165, May.
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