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Patience or Fairness? Analyzing Social Preferences in Repeated Games

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John Duffy
Felix Munoz-Garcia

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Abstract

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. 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 University of Pittsburgh, Department of Economics in its series Working Papers with number 383.

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Date of creation: May 2009
Date of revision: May 2009
Handle: RePEc:pit:wpaper:383

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
H43 - Public Economics - - Publicly Provided Goods - - - Project Evaluation; Social Discount Rate
D91 - Microeconomics - - Intertemporal Choice and Growth - - - Intertemporal Consumer Choice; Life Cycle Models and Saving

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  1. Selten, Reinhard & Stoecker, Rolf, 1986. "End behavior in sequences of finite Prisoner's Dilemma supergames A learning theory approach," Journal of Economic Behavior & Organization, Elsevier, vol. 7(1), pages 47-70, March. [Downloadable!] (restricted)
  2. Maria Montero, 2007. "Inequity Aversion May Increase Inequity," Economic Journal, Royal Economic Society, vol. 117(519), pages C192-C204, 03. [Downloadable!] (restricted)
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  3. Matthew Rabin., 1997. "Fairness in Repeated Games," Economics Working Papers 97-252, University of California at Berkeley.
  4. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August. [Downloadable!] (restricted)
  5. Cooper, Russell & DeJong, Douglas V. & Forsythe, Robert & Ross, Thomas W., 1996. "Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games," Games and Economic Behavior, Elsevier, vol. 12(2), pages 187-218, February. [Downloadable!] (restricted)
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  6. Friedman, James W, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Blackwell Publishing, vol. 38(113), pages 1-12, January. [Downloadable!] (restricted)
  7. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory Of Fairness, Competition, And Cooperation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 817-868, August. [Downloadable!] (restricted)
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  8. William Neilson, 2006. "Axiomatic reference-dependence in behavior toward others and toward risk," Economic Theory, Springer, vol. 28(3), pages 681-692, 08. [Downloadable!] (restricted)
  9. Benoit, Jean-Pierre & Krishna, Vijay, 1985. "Finitely Repeated Games," Econometrica, Econometric Society, vol. 53(4), pages 905-22, July. [Downloadable!] (restricted)
  10. Pedro Dal Bó, 2005. "Cooperation under the Shadow of the Future: Experimental Evidence from Infinitely Repeated Games," American Economic Review, American Economic Association, vol. 95(5), pages 1591-1604, December. [Downloadable!]
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  11. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May. [Downloadable!] (restricted)
  12. Gary E. Bolton & Axel Ockenfels, 2000. "ERC: A Theory of Equity, Reciprocity, and Competition," American Economic Review, American Economic Association, vol. 90(1), pages 166-193, March. [Downloadable!] (restricted)
  13. Rabin, Matthew, 1993. "Incorporating Fairness into Game Theory and Economics," American Economic Review, American Economic Association, vol. 83(5), pages 1281-1302, December. [Downloadable!] (restricted)
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