Communication equilibrium payoffs in repeated games with complete information and imperfect monitoring

J. Renault, T. TOMALA

Games and Economic Behavior

November 2004, vol. 49, n°2, pp.313-344

Departments: Economics & Decision Sciences, GREGHEC (CNRS)

Keywords Plus: 2-PLAYER REPEATED GAMES; PLAYER REPEATED GAMES; NASH EQUILIBRIA; INFORMATION Abstract: We characterize the set of communication equilibrium payoffs of any undiscounted repeated matrix-game with imperfect monitoring and complete information. For two-player games, a characterization is provided by Mertens, Sorin, and Zamir (Repeated games, Part A (1994) CORE DP 9420), mainly using Lehrer's (Math. Operations Res. (1992) 175) result for correlated equilibria. The main result of this paper is to extend this characterization to the n-player case. The proof of the characterization relies on an analogy with an auxiliary 2-player repeated game with incomplete information and imperfect monitoring. We use Kohlberg's (Int. J. Game Theory (1975) 7) result to construct explicitly a canonical communication device for each communication equilibrium payoff