Uniform Folk Theorems in Repeated Anonymous Random Matching Games

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.

[1]  Kevin Hasker,et al.  Social norms and choice: a weak folk theorem for repeated matching games , 2007, Int. J. Game Theory.

[2]  Tristan Tomala,et al.  General Properties of Long-Run Supergames , 2011, Dyn. Games Appl..

[3]  Robert A. Meyers,et al.  Encyclopedia of Complexity and Systems Science , 2009 .

[4]  Jeffrey C. Ely,et al.  A Robust Folk Theorem for the Prisoner's Dilemma , 2002, J. Econ. Theory.

[5]  Johannes Hörner,et al.  When is the lowest equilibrium payoff in a repeated game equal to the minmax payoff? , 2010, J. Econ. Theory.

[6]  Julio González-Díaz,et al.  Community Enforcement Beyond the Prisoner's Dilemma , 2009 .

[7]  Tristan Tomala,et al.  Repeated proximity games , 1998, Int. J. Game Theory.

[8]  Ehud Lehrer,et al.  On the equilibrium payoffs set of two player repeated games with imperfect monitoring , 1992 .

[9]  G. Mailath,et al.  Repeated Games and Reputations: Long-Run Relationships , 2006 .

[10]  Ehud Lehrer,et al.  Nash equilibria of n-player repeated games with semi-standard information , 1990 .

[11]  Andrew Postlewaite,et al.  Social Norms and Random Matching Games , 1995 .

[12]  Satoru Takahashi,et al.  Community enforcement when players observe partners' past play , 2010, J. Econ. Theory.

[13]  Michihiro Kandori,et al.  Private Observation, Communication and Collusion , 1998 .

[14]  R. Radner.  Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives , 1980 .

[15]  A. Rubinstein.  Equilibrium in supergames with the overtaking criterion , 1979 .

[16]  Robert J. Aumann,et al.  Long-Term Competition - A Game-Theoretic Analysis , 1994, Essays in Game Theory.

[17]  Robert Boyd,et al.  Group beneficial norms can spread rapidly in a structured population. , 2002, Journal of theoretical biology.

[18]  Michele Piccione,et al.  The Repeated Prisoner's Dilemma with Imperfect Private Monitoring , 2002, J. Econ. Theory.

[19]  Françoise Forges,et al.  A counterexample to the folk theorem with discounting , 1986 .

[20]  Michihiro Kandori.  Social Norms and Community Enforcement , 1992 .

[21]  P. Bó.  Social norms, cooperation and inequality , 2006 .

[22]  Jeffrey C. Ely,et al.  Belief-free Equilibria in Repeated Games , 2005 .

[23]  Tristan Tomala,et al.  Repeated Games with Complete Information , 2009, Encyclopedia of Complexity and Systems Science.

[24]  Ehud Lehrer,et al.  Correlated Equilibria in Two-Player Repeated Games with Nonobservable Actions , 1992, Math. Oper. Res..

[25]  Sergiu Hart,et al.  Nonzero-Sum Two-Person Repeated Games with Incomplete Information , 1985, Math. Oper. Res..

[26]  Joyee Deb.  Cooperation and Community Responsibility: A Folk Theorem for Repeated Matching Games with Names , 2007 .

[27]  Ehud Lehrer,et al.  Two-Player Repeated Games with Nonobservable Actions and Observable Payoffs , 1992, Math. Oper. Res..

[28]  Ariel Rubinstein,et al.  Equilibrium in Supergames , 1994, Essays in Game Theory.

[29]  R. Radner.  Monitoring Cooperative Agreements in a Repeated Principal-Agent Relationship , 1981 .

[30]  Tristan Tomala,et al.  Secret Correlation in Repeated Games with Imperfect Monitoring , 2007, Math. Oper. Res..

[31]  Glenn Ellison.  Cooperation in the Prisoner's Dilemma with Anonymous Random Matching , 1994 .

[32]  Tristan Tomala,et al.  Perfect communication equilibria in repeated games with imperfect monitoring , 2009, Games Econ. Behav..

[33]  D. Fudenberg,et al.  Digitized by the Internet Archive in 2011 with Funding from Boston Library Consortium Iviember Libraries Working Paper Department of Economics an Approximate Folk Theorem with Imperfect Private Information , 2011 .

[34]  Microeconomics-Charles W. Upton.  Repeated games , 2020, Game Theory.

[35]  Tristan Tomala,et al.  Nash Equilibria of Repeated Games with Observable Payoff Vectors , 1999 .

[36]  Sylvain Sorin,et al.  On Repeated Games with Complete Information , 1986, Math. Oper. Res..