Perfect Public Ex-Post Equilibria of 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. To analyze these games, we introduce the concept of perfect public ex-post equilibrium (PPXE), and show that it can be characterized with an extenstion of the techniques used to study perfect public equilibria. We then 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.

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

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

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

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

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

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

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

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

[9]  Jonathan Levin Relational Incentive Contracts , 2003 .

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

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

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

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

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

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

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

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

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

[19]  Drew Fudenberg,et al.  Type-Contingent Perfect Public Ex-Post Equilibria ∗ , 2009 .

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

[21]  David M. Kreps,et al.  Sequential Equilibria1 , 1982 .

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

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

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

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

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

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

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

[29]  Robert J. Aumann,et al.  Repeated Games with Incomplete Information , 1995 .

[30]  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 .

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

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

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

[34]  D. Fudenberg,et al.  Efficiency and Observability with Long-Run and Short-Run Players , 1994 .

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

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

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

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

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