Complete Conditional Type Structures

Abstract: Hierarchies of conditional beliefs (Battigalli and Siniscalchi 1999) play a central role for the epistemic analysis of solution concepts in sequential games. They are modelled by type structures, which allow the analyst to represent the players' hierarchies without specifying an infinite sequence of conditional beliefs. Here, we study type structures that satisfy a "richness" property, called completeness. This property is defined on the type structure alone, without explicit reference to hierarchies of beliefs or other type structures. We provide sufficient conditions under which a complete type structure represents all hierarchies of conditional beliefs. In particular, we present an extension of the main result in Friedenberg (2010) to type structures with conditional beliefs. KEYWORDS: Conditional probability systems, hierarchies of beliefs, type structures, completeness, terminality. JEL: C72, D80