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A Detail-free Mediator and the 3 Player Case

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  • Peter Vida

    () (Universitat Autonoma de Barcelona, IDEA)

Abstract

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.

Suggested Citation

  • Peter Vida, 2005. "A Detail-free Mediator and the 3 Player Case," IEHAS Discussion Papers 0511, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  • Handle: RePEc:has:discpr:0511
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    File URL: http://econ.core.hu/doc/dp/dp/mtdp0511.pdf
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    References listed on IDEAS

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    Cited by:

    1. Françoise Forges, 2006. "Correlated Equilibrium in Games with Incomplete Information Revisited," Theory and Decision, Springer, vol. 61(4), pages 329-344, December.

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