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.

翻译：条件信念层次结构（Battigalli 和 Siniscalchi 1999）在序贯博弈中解概念的认知分析中占据核心地位。这些层次结构通常通过类型结构进行实用建模，使分析者无需指定无限的条件信念序列即可表示参与者的层次结构。本文研究满足"完备性"这一丰富性属性的类型结构。该属性直接定义在类型结构本身之上，无需显式引用信念层次或其他类型结构。我们给出了完备类型结构能表示所有条件信念层次结构的充分条件，特别地，将Friedenberg（2010）的主要结论扩展到了带条件信念的类型结构。