Complete conditional type structures

• 成果类型: Article
• 署名作者: De Vito, Nicodemo
• 署名单位: University of Salerno
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2024.10.006
• 发表日期: 2024
• 页码: 427-448
• 关键词: Conditional probability systems; Hierarchies of beliefs; Type structures; completeness; Terminality

摘要

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. Friedenberg (2010) shows that, under specific conditions, a complete type structure with ordinary beliefs represents all hierarchies. This paper shows that Friedenberg's result can be extended to type structures with conditional beliefs. As an ancillary result of independent interest, we provide a construction of the canonical space of hierarchies of conditional beliefs which generalizes the one in Battigalli and Siniscalchi (1999).