Repeated Games with Uncertain Outcomes

This paper studies repeated games with imperfect public monitoring where the players are uncertain both about the payoff functions and about the relationship between the distribution of signals and the actions played. We introduce the concept of perfect public ex-post equilibrium (PPXE), and show that it can be characterized with an extension of the techniques used to study perfect public equilibria. We develop identifiability conditions that are sufficient for a folk theorem; these conditions imply that there are PPXE in which the payoffs are approximately the same as if the monitoring structure and payoff functions were known. Finally, we define type-contingent PPXE, which allows players to condition their actions on their initial private information, and we provide its linear programming characterization.

[1]  Thomas Wiseman,et al.  A partial folk theorem for games with private learning , 2012 .

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

[3]  Yuichi Yamamoto.  A limit characterization of belief-free equilibrium payoffs in repeated games , 2009, J. Econ. Theory.

[4]  Jérôme Renault,et al.  Repeated Games with Incomplete Information , 2009, Encyclopedia of Complexity and Systems Science.

[5]  Antonio Guarnieri,et al.  WITH THE COLLABORATION OF , 2009 .

[6]  I. Obara,et al.  Secret Contracts for Ecient Partnerships , 2008 .

[7]  Sergei Severinov,et al.  Individually rational, budget-balanced mechanisms and allocation of surplus , 2008, J. Econ. Theory.

[8]  Stephen Morris,et al.  Belief Free Incomplete Information Games , 2007 .

[9]  Yuichi Yamamoto.  Efficiency results in N player games with imperfect private monitoring , 2007, J. Econ. Theory.

[10]  Michihiro Kandori.  Weakly Belief‐Free Equilibria in Repeated Games With Private Monitoring , 2007 .

[11]  Drew Fudenberg,et al.  Perfect Public Equilibrium When Players are Patient , 2004, Games Econ. Behav..

[12]  Tristan Tomala,et al.  Belief-free equilibria in games with incomplete information: the N-player case , 2007 .

[13]  Thomas Wiseman,et al.  A Partial Folk Theorem for Games with Unknown Payoff Distributions , 2005 .

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

[15]  I. Obara,et al.  Secret Contracts for Efficient Partnerships ∗ , 2005 .

[16]  Stephen Morris,et al.  Purification in the Infinitely-Repeated Prisoners' Dilemma , 2004 .

[17]  Drew Fudenberg,et al.  Learning to Play Bayesian Games , 2001, Games Econ. Behav..

[18]  David A. Miller.  The dynamic cost of ex post incentive compatibility in repeated games of private information , 2005 .

[19]  Martin W. Cripps,et al.  Some Asymptotic Results in Discounted Repeated Games of One-Sided Incomplete Information , 2003, Math. Oper. Res..

[20]  David M. Kreps,et al.  Relational Incentive Contracts , 2003 .

[21]  Nicolas Vieille,et al.  Strategic learning in games with symmetric information , 2003, Games Econ. Behav..

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

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

[24]  S. Athey,et al.  Optimal Collusion with Private Information , 1999 .

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

[26]  D. Fudenberg,et al.  The Folk Theorem for Repeated Games with Discounting and Incomplete Information , 1998 .

[27]  Drew Fudenberg,et al.  Efficiency and Observability in Games with Long-Run and Short-Run Players , 1994 .

[28]  D. Fudenberg,et al.  Digitized by the Internet Archive in 2011 with Funding from Working Paper Department of Economics the Folk Theorem with Imperfect Public Information , 2022 .

[29]  Michihiro Kandori,et al.  The Use of Information in Repeated Games with Imperfect Monitoring , 1992 .

[30]  S. Hart,et al.  Handbook of Game Theory with Economic Applications , 1992 .

[31]  E. Stacchetti,et al.  Towards a Theory of Discounted Repeated Games with Imperfect Monitoring , 1990 .

[32]  E. Stacchetti,et al.  Optimal cartel equilibria with imperfect monitoring , 1986 .

[33]  Drew Fudenberg,et al.  The Folk Theorem in Repeated Games with Discounting or with Incomplete Information , 1986 .

[34]  R. Radner,et al.  An Example of a Repeated Partnership Game with Discounting and with Uniformly Inefficient Equilibria , 1986 .

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

[36]  Françoise Forges.  Note on nash equilibria in infinitely repeated games with incomplete information , 1984 .

[37]  S. Sorin.  “Big Match” with lack of information on one side (part i) , 1984 .

[38]  Â Sylvain Sorin,et al.  "Big match" with lack of information on one side (Part II) , 1984 .

[39]  R. Porter,et al.  NONCOOPERATIVE COLLUSION UNDER IMPERFECT PRICE INFORMATION , 1984 .

[40]  D. Fudenberg,et al.  Subgame-perfect equilibria of finite- and infinite-horizon games , 1981 .

[41]  J. Hirshleifer.  The Private and Social Value of Information and the Reward to Inventive Activity , 1971 .