  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.
