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Implementation of communication equilibria by correlated cheap talk: The two-player case


  • Péter Vida,

    1. Department of Economics, University of Mannheim; vidapet@gmail.com
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  • Françoise Forges

    1. Université Paris-Dauphine and Institut Universitaire de France; Francoise.Forges@gmail.com
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    • Péter Vida proved the main result of this paper as part of his doctoral thesis at the Universitat Autònoma de Barcelona. A preliminary version of the paper, by Péter Vida, circulated under the title “From Communication Equilibria to Correlated Equilibria.” The two authors had discussions on this research in 2005–2006 and completed the present version in 2010–2011. Péter Vida's work on the paper was completed while he was employed by the University of Vienna. We wish to thank Elchanan Ben-Porath, Antoni Calvó-Armengol, Olivier Gossner, Manfred Nermuth, Eilon Solan, Adam Szeidl, and the participants of the workshop “Decentralized Mechanism Design, Distributed Computing and Cryptography” held at Princeton in June 2010. Finally, three referees and, especially, a co-editor of Theoretical Economics raised interesting questions that led us to establish additional results.


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 possibly infinitely long (but in equilibrium almost surely finite), direct, cheap talk.