Conditional belief types

Alfredo Di Tillio, Joseph Halpern () and Dov Samet

Games and Economic Behavior, 2014, vol. 87, issue C, 253-268

Abstract: We study type spaces where a player's type at a state is a conditional probability on the space. We axiomatize these spaces using conditional belief operators, examining three additional axioms of increasing strength. First, introspection, which requires the agent to be unconditionally certain of her beliefs. Second, echo, according to which the unconditional beliefs implied by the condition must be held given the condition. Third, determination, which says that the conditional beliefs are the unconditional beliefs that are conditionally certain. Echo implies that conditioning on an event is the same as conditioning on the event being certain, which formalizes the standard informal interpretation of conditional probability. The game-theoretic application of our model, discussed within an example, sheds light on a number of issues in the analysis of extensive form games. Type spaces are closely related to the sphere models of counterfactual conditionals and to models of hypothetical knowledge.

Keywords: Conditional probability; Type spaces; Hypothetical knowledge; Counterfactuals (search for similar items in EconPapers)
JEL-codes: C70 C72 D80 D82 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:87:y:2014:i:c:p:253-268

DOI: 10.1016/j.geb.2014.05.012

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