Repeated Games Played in a Network

Delayed perfect monitoring in an infinitely repeated discounted game is modelled by allocating the players to a connected and undirected network. Players observe their immediate neighbors’ behavior only, but communicate over time the repeated game’s history truthfully throughout the network. The Folk Theorem extends to this setup, although for a range of discount factors strictly below 1, the set of sequential equilibria and the corresponding payoff set may be reduced. A general class of games is analyzed without imposing restrictions on the dimensionality of the payoff space. Due to this and the bilateral communication structure, truthful communication arises endogenously only under additional conditions. The model also produces a network result; namely, the level of cooperation in this setup depends on the network’s diameter, and not on its clustering coefficient as in other models.

[1]  M. Kinateder.  The Repeated Prisoner’s Dilemma in a Network , 2010 .

[2]  Lones Smith,et al.  The Folk Theorem for Repeated Games , 1993 .

[3]  M. Cronshaw,et al.  Algorithms for Finding Repeated Game Equilibria , 1997 .

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

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

[6]  Michihiro Kandori,et al.  Introduction to Repeated Games with Private Monitoring , 2002, J. Econ. Theory.

[7]  M. Marsili,et al.  CLUSTERING, COOPERATION, AND SEARCH IN SOCIAL NETWORKS , 2005 .

[8]  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 .

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

[10]  Jehoshua Bruck,et al.  Networks of relations , 2005 .

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

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

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

[14]  Mark S. Granovetter.  The Strength of Weak Ties , 1973, American Journal of Sociology.

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

[16]  Hao Li,et al.  How complex are networks playing repeated games? , 1999 .

[17]  Lones Smith,et al.  THE FOLK THEOREM FOR REPEATED GAMES: A NEU CONDITION' , 1994 .

[18]  J. Coleman,et al.  Social Capital in the Creation of Human Capital , 1988, American Journal of Sociology.

[19]  Quan Wen,et al.  The "Folk Theorem" for Repeated Games with Complete Information , 1994 .

[20]  Kandori Michihiro,et al.  Randomization, communication, and efficiency in repeated games with imperfect public monitoring , 2003 .

[21]  Roger Lagunoff,et al.  Social Norms, Local Interaction, and Neighborhood Planning , 2000 .

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

[23]  G. Spagnolo,et al.  Networks of Relations and Social Capital , 2005 .

[24]  Elchanan Ben-Porath,et al.  Communication in repeated games with costly monitoring , 2003, Games Econ. Behav..

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