THE BAYESIAN FORMULATION OF INCOMPLETE INFORMATION - THE NONCOMPACT CASE

In a game with incomplete information, a player may have beliefs about nature, about the other players' beliefs about nature, and so on, in an infinite hierarchy. We generalize a construction of Mertens & Zamir and show, that if nature is any Hausdorff space, and beliefs are regu lar Borel probability measures, then the space of all such infinite hi erarchies of the players is a product of nature and the types of every player, where a type of a player is a belief about nature and the oth er players' types.