Introduction to Repeated Games with Private Monitoring

Abstract We present a brief overview of recent developments in discounted repeated games with (imperfect) private monitoring. The literature explores the possibility of cooperation in a long-term relationship, where each agent receives imperfect private information about the opponents' actions. Although this class of games admits a wide range of applications such as collusion under secret price-cutting, exchange of goods with uncertain quality, and observation errors, it has fairly complex mathematical structure due to the lack of common information shared by players. This is in sharp contrast to the well-explored case of repeated games under public information (with the celebrated Folk Theorems), and until recently little had been known about the private monitoring case. However, rapid developments in the past few years have revealed the possibility of cooperation under private monitoring for some class of games. Journal of Economic Literature Classification Numbers: C72, C73, D43, D82, L13, L41.

[1]  Olivier Compte,et al.  On Failing to Cooperate When Monitoring Is Private , 2002, J. Econ. Theory.

[2]  Elchanan Ben-Porath,et al.  Communication in Repeated Games with Private Monitoring , 1996 .

[3]  Olivier Compte.  Communication in repeated games with imperfect private monitoring , 1998 .

[4]  Olivier Compte,et al.  On Sustaining Cooperation without Public Observations , 2002, J. Econ. Theory.

[5]  Tadashi Sekiguchi.  Efficiency in Repeated Prisoner's Dilemma with Private Monitoring , 1997 .

[6]  Jeffrey C. Ely.  Correlated Equilibrium and Private Monitoring , 2000 .

[7]  E.E.C. van Damme,et al.  Games with imperfectly observable commitment , 1997 .

[8]  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 .

[9]  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 .

[10]  R. Radner.  Repeated Partnership Games with Imperfect Monitoring and No Discounting , 1986 .

[11]  Tadashi Sekiguchi.  Existence of nontrivial equilibria in repeated games with imperfect private monitoring , 2002, Games Econ. Behav..

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

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

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

[15]  M. Amarante.  Recursive structure and equilibria in games with private monitoring , 2003 .

[16]  Masaki Aoyagi,et al.  Collusion in Dynamic Bertrand Oligopoly with Correlated Private Signals and Communication , 2002, J. Econ. Theory.

[17]  Hitoshi Matsushima,et al.  The Folk Theorem with Private Monitoring and Uniform Sustainability , 2000 .

[18]  Ichiro Obara,et al.  Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring , 2002, J. Econ. Theory.

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

[20]  David Pearce,et al.  Information and timing in repeated partnerships , 1991 .

[21]  Stephen Morris,et al.  Repeated Games with Almost-Public Monitoring , 2002, J. Econ. Theory.

[22]  Eric van Damme,et al.  Moral Hazard and Private Monitoring , 2002, J. Econ. Theory.

[23]  Ichiro Obara,et al.  Efficiency in Repeated Games Revisited: The Role of Private Strategies (with M. Kandori) , 2004 .

[24]  K. Bagwell.  Commitment and observability in games , 1995 .

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

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

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

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

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

[30]  Michihiro Kandori.  Check Your Partners' Behavior by Randomization: New Efficiency Results on Repeated Games with Imperfect Monitoring , 1999 .