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Cooperation and Signaling with Uncertain Social Preferences

  • John Duffy
  • Felix Munoz-Garcia

This paper investigates behavior in finitely repeated simultaneous and sequential-move prisoner's dilemma games when there is one-sided incomplete information and signaling about players' concerns for fairness, specifically, their preferences regarding "inequity aversion." In this environment, we show that only a pooling equilibrium can be sustained, in which a player type who is unconcerned about fairness initially cooperates in order to disguise himself as a player type who is concerned about fairness. This disguising strategy induces the uninformed player to cooperate in all periods of the repeated game, including the final period, at which point the player type who is unconcerned about fairness takes the opportunity to defect, i.e., he "backstabs" the uninformed player. Despite such last-minute defection, our results show that the introduction of incomplete information can actually result in a Pareto improvement under certain conditions. We connect the predictions of this "backstabbing" equilibrium with the frequently observed decline in cooperative behavior in the final period of finitely-repeated experimental games.

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File URL: http://www.ewi-ssl.pitt.edu/econ/files/faculty/wp/130905_wp_DuffyJohn_signaling_social_preferences_may2013.pdf
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Paper provided by University of Pittsburgh, Department of Economics in its series Working Papers with number 491.

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Date of creation: Mar 2012
Date of revision: May 2013
Handle: RePEc:pit:wpaper:491
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  1. Fehr, Ernst & Schmidt, Klaus M., . "A theory of fairness, competition, and cooperation," Chapters in Economics, University of Munich, Department of Economics.
  2. John Duffy & Felix Munoz-Garcia, 2009. "Patience or Fairness? Analyzing Social Preferences in Repeated Games," Working Papers 2009-12, School of Economic Sciences, Washington State University.
  3. Anderhub, Vital & Engelmann, Dirk & Guth, Werner, 2002. "An experimental study of the repeated trust game with incomplete information," Journal of Economic Behavior & Organization, Elsevier, vol. 48(2), pages 197-216, June.
  4. 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.
  5. Falk, Armin & Fischbacher, Urs, 2001. "A Theory of Reciprocity," CEPR Discussion Papers 3014, C.E.P.R. Discussion Papers.
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  7. Dufwenberg, M. & Kirchsteiger, G., 1998. "A Theory of Sequential Reciprocity," Discussion Paper 1998-37, Tilburg University, Center for Economic Research.
  8. 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.
  9. 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.
  10. Bolle, Friedel & Ockenfels, Peter, 1990. "Prisoners' Dilemma as a game with incomplete information," Journal of Economic Psychology, Elsevier, vol. 11(1), pages 69-84, March.
  11. Stefano Demichelis & Jörgen Weibull, 2009. "Language, meaning and games A model of communication, coordination and evolution," Working Papers hal-00354224, HAL.
  12. Andreoni, James A & Miller, John H, 1993. "Rational Cooperation in the Finitely Repeated Prisoner's Dilemma: Experimental Evidence," Economic Journal, Royal Economic Society, vol. 103(418), pages 570-85, May.
  13. Cho, In-Koo & Kreps, David M, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, MIT Press, vol. 102(2), pages 179-221, May.
  14. Fong Yuk-Fai, 2009. "Private Information of Nonpaternalistic Altruism: Exaggeration and Reciprocation of Generosity," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-32, January.
  15. Camerer, Colin & Weigelt, Keith, 1988. "Experimental Tests of a Sequential Equilibrium Reputation Model," Econometrica, Econometric Society, vol. 56(1), pages 1-36, January.
  16. Clark, Kenneth & Sefton, Martin, 2001. "The Sequential Prisoner's Dilemma: Evidence on Reciprocation," Economic Journal, Royal Economic Society, vol. 111(468), pages 51-68, January.
  17. David Kreps & Robert Wilson, 1999. "Reputation and Imperfect Information," Levine's Working Paper Archive 238, David K. Levine.
  18. Rabin, Matthew, 1993. "Incorporating Fairness into Game Theory and Economics," American Economic Review, American Economic Association, vol. 83(5), pages 1281-1302, December.
  19. Banks, Jeffrey S. & Sobel, Joel., 1985. "Equilibrium Selection in Signaling Games," Working Papers 565, California Institute of Technology, Division of the Humanities and Social Sciences.
  20. Paul J. Healy, 2007. "Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market," American Economic Review, American Economic Association, vol. 97(5), pages 1751-1773, December.
  21. von Siemens, Ferdinand A., 2009. "Bargaining under incomplete information, fairness, and the hold-up problem," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 486-494, August.
  22. 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.
  23. Charles Bellemare & Sabine Kröger & Arthur van Soest, 2008. "Measuring Inequity Aversion in a Heterogeneous Population Using Experimental Decisions and Subjective Probabilities," Econometrica, Econometric Society, vol. 76(4), pages 815-839, 07.
  24. repec:ner:tilbur:urn:nbn:nl:ui:12-376716 is not listed on IDEAS
  25. Brandts, Jordi & Figueras, Neus, 2003. "An exploration of reputation formation in experimental games," Journal of Economic Behavior & Organization, Elsevier, vol. 50(1), pages 89-115, January.
  26. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-36, July.
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