Unmediated Communication in Games with Complete and Incomplete Information

In this paper we study the effects of adding unmediated communication to static, finite games of complete and incomplete information. We characterize SU(G), the set of outcomes of a game G, that are induced by sequential equilibria of cheap talk extensions. A cheap talk extension of G is an extensive-form game in which players communicate before playing G. A reliable mediator is not available and players exchange private or public messages that do not affect directly their payoffs. We first show that if G is a game of complete information with five or more players and rational parameters, then SU(G) coincides with the set of correlated equilibria of G. Next, we demonstrate that if G is a game of incomplete information with at least five players, rational parameters and full support (i.e. all profiles of types have positive probability), then SU(G) is equal to the set of communication equilibria of G.