Implementation of Communication Equilibria by Correlated Cheap Talk: The Two-Player Case

Abstract

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.

Keywords: Bayesian game, cheap talk, communication equilibrium, correlated equilibrium, pre-play communication

JEL Classification: C72, D70