Cheap Talking in Games with Incomplete Information.

The paper studies Bayesian Games which are extended by adding pre-play communication. Let T be a Bayesian game with three or more players. The main result is that if players can send private messages to each other and make public announcements then every communication equilibrium outcome, q, that is rational (i.e. involves probabilities which are rational numbers), can be implemented in a sequential equilibrium of a cheap talk extension of T, provided that the following condition is satisfied: there exists a Bayesian Nash equilibrium s in T such that for each type ot ti of each player i the expected payoff to ti in q is larger than the expected payoff of ti in s.