The Idea and the Features of Type Space

Several game theoretical topics require the analysis of hierarchical beliefs, particularly in incomplete information situations. For the problem of incomplete information, Harsanyi 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. We divided this work into two parts. In the first part we introduce the main ideas and features of type space. We follow Heifetz & Samet, however we take some steps out of their work. We also introduce an example to present the usefulness of type space. In the second part we present a complete universal type space, which contains the works of Mertens & Zamir, Heifetz, and Brandenburger & Dekel as a special case. The two parts of this work can be read separately, therefore there are some minor parallelism in this paper.