Epistemic Conditions for Equilibrium in Beliefs without Independence

Oscar Volij

Aumann and Brandenburger (1991) describe sufficient conditions on the knowledge of the players in a game for a Nash equilibrium to exist. They assumed, among other things, mutual knowledge of rationality. By rationality of a player, they mean that the action chosen by him maximizes his expected utility, given his beliefs. There is, however, no need to restrict the notion of rationality to expected utility maximization. This paper shows that their result can be generalized to the case where the players preferences over uncertain outcomes can be represented by a continuous function, not necessarily linear in the probabilities.

January, 1992
Published in: 
Journal of Economic Theory 70 (1996), 391-406