"Randomization, Communication and Efficiency in Repeated Games with Imperfect Public Monitoring"

The present paper shows that the Folk Theorem under imperfect (public) information (Fudenberg, Levine and Maskin (1994)) can be obtained under much weaker set of assumptions, if we allow communication among players. Our results in particular show that for generic symmetric games with at least four players, we can drop the FLM condition on the number of actions and signals altogether and prove the folk theorem under the same condition as in the perfect monitoring case.

Folk theorem with communication

Abstract This paper proposes an alternative folk theorem for repeated games with private monitoring and communication, extending the technique o

Perfect Communication Equilibria in Repeated Games with Imperfect Monitoring.

This paper introduces an equilibrium concept called perfect communication equilibrium for repeated games with imperfect private monitoring. This concept is a refinement of Myerson's [Myerson, R.B., 1982. Optimal coordination mechanisms in generalized principal agent problems, J. Math. Econ. 10, 67–81] communication equilibrium. A communication equilibrium is perfect if it induces a communication equilibrium of the continuation game, after every history of messages of the mediator. We provide a characterization of the set of corresponding equilibrium payoffs and derive a Folk Theorem for discounted repeated games with imperfect private monitoring.Repeated games; Imperfect monitoring; Communication equilibria;

The bounded memory folk theorem

We show that the Folk Theorem holds for n-player discounted repeated games with bounded-memory pure strategies. Our result requires each player’s payoff to be strictly above the pure minmax payoff but requires neither time-dependent strategies, nor public randomization, nor communication. The type of strategies we employ to establish our result turn out to have new features that may be important in understanding repeated interactions

A folk theorem with codes of conduct and communication

We study self-referential games in which players have the ability to commit to a code of conduct—a complete description of how they play and their opponents should play. Each player receives a private signal about each others’ code of conduct and their codes of conduct specify how to react to these signals. When only some players receive informative signals, players are allowed to communicate using public messages. Our characterization of the effect of communication on the equilibrium payoffs yields a folk theorem and players share their private information truthfully in equilibrium. We also provide an application of codes of conduct: games that are played through computer programs.Juan Block acknowledges support from the Cambridge-INET Institute, and David Levine thanks the National Science Foundation (Grant SES-0851315) and the European University Institute for financial support.This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s40505-016-0107-

A folk theorem with codes of conduct and communication

This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s40505-016-0107-yWe study self-referential games in which players have the ability to commit to a code of conduct—a complete description of how they play and their opponents should play. Each player receives a private signal about each others’ code of conduct and their codes of conduct specify how to react to these signals. When only some players receive informative signals, players are allowed to communicate using public messages. Our characterization of the effect of communication on the equilibrium payoffs yields a folk theorem and players share their private information truthfully in equilibrium. We also provide an application of codes of conduct: games that are played through computer programs.Juan Block acknowledges support from the Cambridge-INET Institute, and David Levine thanks the National Science Foundation (Grant SES-0851315) and the European University Institute for financial support

The Folk Theorem in Dynastic Repeated Games

A canonical interpretation of an infinitely repeated game is that of a "dynastic" repeated game: a stage game repeatedly played by successive generations of finitely-lived players with dynastic preferences. These two models are in fact equivalent when the past history of play is observable to all players. In our model all players live one period and do not observe the history of play that takes place before their birth, but instead receive a private message from their immediate predecessors. Under very mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax) can be sustained as a Sequential Equilibrium of the dynastic repeated game with private communication. The result applies to any stage game for which the standard Folk Theorem yields a payoff set with a non-empty interior. Our results stem from the fact that, in equilibrium, a player may be unable to communicate effectively relevant information to his successor in the same dynasty. This, in turn implies that following some histories of play the players’ equilibrium beliefs may violate "Inter-Generational Agreement."Dynastic repeated games, Private communication, Folk theorem

The Folk Theorem in Dynastic Repeated Games

A canonical interpretation of an infinitely repeated game is that of a "dynastic" repeated game: a stage game repeatedly played by successive generations of finitely-lived players with dynastic preferences. These two models are in fact equivalent when the past history of play is observable to all players. In our model all players live one period and do not observe the history of play that takes place before their birth, but instead receive a private message from their immediate predecessors. Under very mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax) can be sustained as a Sequential Equilibrium of the dynastic repeated game with private communication. The result applies to any stage game for which the standard Folk Theorem yields a payoff set with a non-empty interior. Our results stem from the fact that, in equilibrium, a player may be unable to communicate effectively relevant information to his successor in the same dynasty. This, in turn implies that following some histories of play the players' equilibrium beliefs may violate "Inter-Generational Agreement."Dynastic Repeated Games, Private Communication, Folk Theorem

The Folk Theorem in Dynastic Repeated Games

A canonical interpretation of an infinitely repeated game is that of a “dynastic” repeated game: a stage game repeatedly played by successive generations of finitely-lived players with dynastic preferences. These two models are in fact equivalent when the past history of play is observable to all players. In our model all players live one period and do not observe the history of play that takes place before their birth, but instead receive a private message from their immediate predecessors. Under very mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax) can be sustained as a Sequential Equilibrium of the dynastic repeated game with private communication. The result applies to any stage game for which the standard Folk Theorem yields a payoff set with a non-empty interior. Our results stem from the fact that, in equilibrium, a player may be unable to communicate effectively relevant information to his successor in the same dynasty. This, in turn implies that following some histories of play the players’ equilibrium beliefs may violate “Inter-Generational Agreement.”Dynastic Repeated Games, Private Communication, Folk Theorem