A folk theorem for repeated games played on a network

I consider repeated games on a network where players interact and communicate with their neighbors. At each stage, players choose actions and exchange private messages with their neighbors. The payoff of a player depends only on his own action and on the actions of his neighbors. At the end of each stage, a player is only informed of his payoff and of the messages he received from his neighbors. Payoffs are assumed to be sensitive to unilateral deviations. The main result is to establish a necessary and sufficient condition on the network for a Nash folk theorem to hold, for any such payoff function.

[1]  Tristan Tomala,et al.  Communication equilibrium payoffs in repeated games with imperfect monitoring , 2004, Games Econ. Behav..

[2]  Matthew K. Franklin,et al.  Secure Communication in Minimal Connectivity Models , 1998, Journal of Cryptology.

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

[4]  S. Crawford,et al.  Volume 1 , 2012, Journal of Diabetes Investigation.

[5]  Yann Bramoullé,et al.  Public goods in networks , 2007, J. Econ. Theory.

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

[7]  Tristan Tomala,et al.  Learning the state of nature in repeated games with incomplete information and signals , 2004, Games Econ. Behav..

[8]  Reinhard Diestel,et al.  Graph Theory , 1997 .

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

[10]  E. Lehrer.  Lower equilibrium payoffs in two-player repeated games with non-observable actions , 1989 .

[11]  Ichiro Obara,et al.  Folk theorem with communication , 2009, J. Econ. Theory.

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

[13]  Johannes Hörner,et al.  How Robust is the Folk Theorem , 2009 .

[14]  Pierre Rochus,et al.  Hu, Luojia , Estimation of a censored dynamic panel data model,Econometrica. Journal of the Econometric Society , 2002 .

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

[16]  Tristan Tomala,et al.  Probabilistic Reliability and Privacy of Communication Using Multicast in General Neighbor Networks , 2008, Journal of Cryptology.

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

[18]  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 .

[19]  Tristan Tomala,et al.  Fault Reporting in Partially Known Networks and Folk Theorems , 2011, Oper. Res..

[20]  H. Hotelling.  Stability in Competition , 1929 .

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

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

[23]  Alexander Wolitzky,et al.  Cooperation with Network Monitoring , 2013 .

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

[25]  S. Goyal.  Connections: An Introduction to the Economics of Networks , 2009 .

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

[27]  Éva Tardos,et al.  Network games , 2004, STOC '04.

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

[29]  Johannes Hörner,et al.  The folk theorem for games with private almost-perfect monitoring , 2005 .

[30]  D. Fudenberg,et al.  An approximate folk theorem with imperfect private information , 1991 .

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