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Complete Conditional Type Structures

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  • Nicodemo De Vito

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

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  • Nicodemo De Vito, 2023. "Complete Conditional Type Structures," Papers 2305.08940, arXiv.org, revised Dec 2023.
    • Handle: RePEc:arx:papers:2305.08940
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    1. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 88(1), pages 188-230, September.
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    More about this item

    Keywords

    conditional probability systems; hierarchies of beliefs; type structures; completeness; terminality. jel: c72; d80;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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