Correlated equilibria and communication in games.

Analyse bayésienne; Théorie des jeux; Information privée;

Game theory

game theory

Implementation of Communication Equilibria by Correlated Cheap Talk: The Two-Player Case

We show that essentially every communication equilibrium of any finite Bayesian game with two players can be implemented as a strategic form correlated equilibrium of an extended game, in which before choosing actions as in the Bayesian game, the players engage in a pos-sibly infinitely long (but in equilibrium almost surely finite), direct, cheap talk.Bayesian game, cheap talk, communication equilibrium, correlated equilibrium, pre-play communication

Disappearing private reputations in long-run relationships

For games of public reputation with uncertainty over types and imperfect public monitoring, Cripps et al. [Imperfect monitoring and impermanent reputations, Econometrica 72 (2004) 407–432] showed that an informed player facing short-lived uninformed opponents cannot maintain a permanent reputation for playing a strategy that is not part of an equilibrium of the game without uncertainty over types. This paper extends that result to games in which the uninformed player is long-lived and has private beliefs, so that the informed player's reputation is private. The rate at which reputations disappear is uniform across equilibria and reputations also disappear in sufficiently long discounted finitely repeated games

"Repeated Games, Entry in The New Palgrave Dictionary of Economics, 2nd Edition"

This entry shows why self-interested agents manage to cooperate in a long-term relationship. When agents interact only once, they often have an incentive to deviate from cooperation. In a repeated interaction, however, any mutually beneficial outcome can be sustained in an equilibrium. This fact, known as the folk theorem, is explained under various information structures. This entry also compares repeated games with other means to achieve efficiency and briefly discuss the scope for potential applications.