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Uniform Folk Theorems in Repeated Anonymous Random Matching Games

Author

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  • Joyee Deb
  • Julio González Díaz
  • Jérôme Renault

Abstract

We study infinitely repeated anonymous random matching games played by communities of players, who only observe the outcomes of their own matches. It is well known that cooperation can be sustained in equilibrium for the prisoner's dilemma, but little is known beyond this game. We study a new equilibrium concept, strongly uniform equilibrium (SUE), which refines uniform equilibrium (UE) and has additional properties. We establish folk theorems for general games and arbitrary number of communities. We extend the results to a setting with imperfect private monitoring, for the case of two communities. We also show that it is possible for some players to get equilibrium payoffs that are outside the set of individually rational and feasible payoffs of the stage game. As a by-product of our analysis, we prove that, in general repeated games with finite players, actions, and signals, the sets of UE and SUE payoffs coincide.
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Suggested Citation

  • Joyee Deb & Julio González Díaz & Jérôme Renault, 2013. "Uniform Folk Theorems in Repeated Anonymous Random Matching Games," Working Papers 13-16, New York University, Leonard N. Stern School of Business, Department of Economics.
  • Handle: RePEc:ste:nystbu:13-16
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    File URL: http://web-docs.stern.nyu.edu/old_web/economics/docs/workingpapers/2013/Deb_UniformFolkTheorems_Nov2013.pdf
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    References listed on IDEAS

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    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
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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