Type space on a purely measurable parameter space

Summary. 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 and 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.Received: 12 August 2002, Revised: 1 March 2004, JEL Classification Numbers: C70, C79, D80, D82.Miklós Pintér: The author wishes to thank Péter Tallos, Tamás Solymosi, and an anonymous referee for their suggestions and comments. This work was supported by OTKA grant T046194.