We study a repeated game with asymmetric information about a dynamic state of nature. In the course of the game, the better-informed player can communicate some or all of his information to the other. Our model covers costly and/or bounded communication. We characterize the set of equilibrium payoffs and contrast these with the communication equilibrium payoffs, which by definition entail no communication costs.

We exhibit a general class of interactive decision situations in which all the agents benefit from more information. This class includes as a special case the classical comparison of statistical experimentsà la Blackwell.More specifically, we consider pairs consisting of a game with incomplete information G and an information structure S such that the extended game Γ(G, S) has a unique Pareto payoff profile u. We prove that u is a Nash payoff profile of Γ(G, S), and that for any information structure T that is coarser than S, all Nash payoff profiles of Γ(G, T ) are dominated by u. We then prove that our condition is also necessary in the following sense: Given any convex compact polyhedron of payoff profiles, whose Pareto frontier is not a singleton, there exists an extended game Γ(G, S) with that polyhedron as the convex hull of feasible payoffs, an information structure T coarser than S and a player i