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

The Value of Correlation in Strategic Form Games

Every game in strategic form can be extended by adding a correlation device. Any Equilibrium in such an extended game is called a correlated equilibrium (Aumann 1974). Aumann showed that there exist games, where the agents surplus in a correlated equilibrium is greater than their surplus in every equilibrium. This suggests the study of two major measures for the value of correlation: 1. The ratio between the maximal surplus obtained in an correlated equilibrium to the maximal surplus obtained in equilibrium. We refer to this ratio as the mediation value. 2. The ratio between the optimal surplus to the maximal surplus obtained in correlated equilibrium. We refer to this ratio as the enforcement value. In this work we initiate the study of the mediation value and of the enforcement value, providing several general results on the value of correlation as captured by these concepts. We also present a set of results for the more specialized case of congestion games, a class of games that received a lot attention in the recent computer science and e-commerce communities. Indeed, while much work in computer science has been devoted to the study of the ratio between the surplus in optimal strategies to the surplus in the worst Nash equilibrium (the so called "price of anarchy") for congestion games, our work presents and initiates the study of two other complementary measures