Correlated equilibria and communication in games.

Analyse bayésienne; Théorie des jeux; Information privée;

Communication in Bayesian games: Overview of work on implementing mediators in game theory.

game theory; Bayesian games;

Computer Science and Game Theory: A Brief Survey

There has been a remarkable increase in work at the interface of computer science and game theory in the past decade. In this article I survey some of the main themes of work in the area, with a focus on the work in computer science. Given the length constraints, I make no attempt at being comprehensive, especially since other surveys are also available, and a comprehensive survey book will appear shortly.Comment: To appear; Palgrave Dictionary of Economic

A Detail-free Mediator and the 3 Player Case

Two players can make use of a trusted third party who mediates and partially resolves their conflict. Usually, the mediator should be aware of the situation and give suggestions to the players accordingly. However, a corrupt mediator can have a big influence on the outcome of the game. We single out a transparent mediator which can be safely applied in any two player game without loss of efficiency. That is, the mediator is independent of the game and the desired outcome. Technically, we show that any correlated equilibrium of any two player game can be obtained as Nash equilibria of the game, extended with cheap, pre-play communication, where players can communicate through the proposed mediator. The key idea is that after the mediated communication the players can have a plain conversation. In particular, the mediating communication device is transparent, controllable and is the same for all games and for all equilibrium distributions. We extend the result to three player games and show that one of the players can play the role of the mediator. We implement the set of correlated equilibrium in Nash equilibria of an extended game where the players have a plain conversation. The central assumption is that players can be invited to eavesdrop a private conversation. We extend the analysis to games with incomplete information and to the set of communication equilibria.cheap talk, communication device, correlated equilibrium, communi- cation equilibrium, detail-free mechanism, mediator

Repeated Communication Through the Mechanism And.

We consider the “and” communication device that receives inputs from two players and outputs the public signal yes if both messages are yes, and outputs no otherwise. We prove that no correlation can securely be implemented using this device, even when infinitely many stages of communication are allowed."And" communication device;

Voluntary Commitments Lead to Efficiency

Consider an agent (manager,artist, etc.) who has imperfect private information about his productivity. At the beginning of his career (period 1, “short run”), the agent chooses among publicly observable actions that generate imperfect signals of his productivity. The actions can be ranked according to the informativeness of the signals they generate. The market observes the agent’s action and the signal generated by it, and pays a wage equal to his expected productivity. In period 2 (the “long run”), the agent chooses between a constant payoff and a wage proportional to his true productivity, and the game ends. We show that in any equilibrium where not all types of the agent choose the same action, the average productivity of an agent choosing a less informative action is greater. However, the types choosing that action are not uniformly higher. In particular, we derive conditions for the existence of a tripartite equilibrium where low and high types pool on a less informative action while medium (on average, lower) types choose to send a more informative signal.signalling, career concerns