This is a brief survey describing some of the recent progress and open problems in the area of cooperative games with incomplete information. We discuss exchange economies, cooperative Bayesian games with orthogonal coalitions, and issues of cooperation in non-cooperative Bayesian games.

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 fin nitely long (but...

If the allocations of a differential information economy are defined as incentive compatible state-contingent lotteries over consumption goods, competitive equilibrium allocations exist and belong to the (ex ante incentive) core. Furthermore, any competitive equilibrium allocation can be viewed...

In a differential information economy with quasi–linear utilities, monetary transfers facilitate the fulfillment of incentive compatibility constraints : the associated ex ante core is generically nonempty. However, we exhibit a well–behaved exchange economy in which this core is empty, even...

We identify particular exchange economies with asymmetric information in which the ex ante incentive compatible core is nonempty provided that coalitions can allocate goods by means of random mechanisms. Both the use of random mechanisms and the restriction to a specific class of economies are...

Radner (1968) proved existence of a competitive equilibrium for differential information economies with finitely many states. We extend this result to economies with infinitely many states of nature. Each agent observes a public and a private signal. The publicly observed signal may take...

We consider exchange economies with a continuum of agents and differential information about finitely many states of nature. It was proved in Einy, Moreno, and Shitovitz (2001) that if we allow for free disposal in the market clearing (feasibility) constraints then an irre- ducible economy has...

We survey selected results on strategic information transmission. We distinguish between "cheap talk" and "persuasion". In the latter model, the informed player's message set depends on his type. As a benchmark, we first assume that the informed player sends a single message to the decision...

This paper characterizes geometrically the sets of all Nash and perfect Bayesian equilibrium payoffs achievable with unmediated communication in persuasion games, i.e., games with an informed expert and an uninformed decisionmaker in which the expert's information is certifiable. The first...