Topology-Free Typology of Beliefs

In their seminal paper, Mertens and Zamir (1985) proved the existence of a universal Harsanyi type space which consists of all possible types. Their method of proof depends crucially on topological assumptions. Whether such assumptions are essential to the existence of a universal space remained an open problem. We answer it here by proving that a universal type space does exist even when spaces are defined in pure measure theoretic terms. Heifetz and Samet (1996) showed that coherent hierarchies of beliefs, in the measure theoretic case, do not necessarily describe types. Therefore, the universal space here differs from all previously studied ones, in that it does not necessarily consist of all coherent hierarchies of beliefs.