Type space on a purely measurable parameter space

Abstract

Several game theoretical topics require the analysis of hierarchical beliefs, particularly in incomplete information situations. For the problem of incomplete information, Harsányi suggested the concept of the type space. Later Mertens & Zamir gave a construction of such a type space under topological assumptions imposed on the parameter space. The topological assumptions were weakened by Heifetz, and by Brandenburger & Dekel. In this paper we show that at very natural assumptions upon the structure of the beliefs, the universal type space does exist. We construct a universal type space, which employs purely a measurable parameter space structure.

The existence of an inverse limit of an inverse system of measure spaces — A purely measurable case

“…Since every previous result on this problem -Mertens and Zamir [12], Brandenburger and Dekel [4], Heifetz [8], Mertens at al., Pintér [17] among others -applies topological assumptions and ours do not, the next result is new.…”