Complete Conditional Type Structures (Extended Abstract)

TL;DR

This paper investigates complete type structures that can represent all hierarchies of conditional beliefs in sequential games, extending existing results to broader classes of such structures.

Contribution

It introduces a new notion of completeness for type structures and provides conditions ensuring they can represent all hierarchies of conditional beliefs.

Findings

Established sufficient conditions for completeness in type structures.

Extended Friedenberg's main result to include conditional beliefs.

Provided a framework for modeling hierarchies of beliefs without infinite regress.

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 practically 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.