The ex ante α-core for normal form games with uncertainty

In this paper we study the existence of the α-core for an n-person game with incomplete information. We follow a Milgrom-Weber-Balder formulation of a game with incomplete information. The players adopt behavioral strategies represented by Young measures. The game unrolls in one step at the ex ante stage. In this context, the mixed-extensions of the utility functions are not quasi-concave, and as a result the classical Scarf's theorem cannot be applied. An approximation argument is used to overcome this lack of concavity.