The paper studies Bayesian games which are extended by adding pre-play communication. Let G be a Bayesian game with full support and 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 that are rational numbers) can be implemented in a sequential equilibrium of a cheap talk extension of G, provided that the following condition is satisfied: There exists a Bayesian Nash equilibrium s in G such that for each type ti of each player i the expected payoff of ti in q is larger than the expected payoff of ti in s. Journal of Economic Literature classification number: C7. Key words: communication, Bayesian games, sequential equilibrium.
Communication in Repeated Games with Costly Monitoring
with Michael Kahneman
We study repeated games with discounting where perfect monitoring is possible, but costly. It is shown that if players can make public announcements, then every payo. vector which is an interior point in the set of feasible and individually rational payo.s can be implemented in a sequential equilibrium of the repeated game when the discount factor is high enough. Thus, e.ciency can be approximated even when the cost of monitoring is high, provided that the discount factor is high enough. Key words: Repeated games, costly monitoring, Communication.