Publications

Journal Article

The author proves the existence of a greatest and a least interim Bayesian Nash equilibrium for supermodular games of incomplete information.

There are two main differences from the earlier proofs in Vives (1990) and Milgrom and Roberts (1990): (a) the author uses the interim formulation of a Bayesian game, in which each player's beliefs are part of his or her type rather than being derived from a prior; (b) the author uses the interim formulation of a Bayesian Nash equilibrium, in which each player and every type (rather than almost every type) chooses a best response to the strategy profile of the other players.

Given also the mild restrictions on the type spaces, the author has a proof of interim Bayesian Nash equilibrium for universal type spaces (for the class of supermodular utilities), as constructed, for example, by Mertens and Zamir (1985). The author also weakens restrictions on the set of actions.