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...

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...

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...

We study information transmission between informed experts and an uninformed decision-maker who only takes binary decisions. In the single expert case, we show that information transmission can only be relatively poor. Hence, even sophiscated communication games do not yield equilibria which (ex...

We show that in a standard symmetric Cournot duopoly with unknown demand, the optimal information disclosure policy of an informed benevolent planner is to fully inform one of the duopolists and disclose no information to the other one. We discuss possible extensions of the result.