Conditional belief types

• 成果类型: Article
• 署名作者: Di Tillio, Alfredo; Halpern, Joseph Y.; Samet, Dov
• 署名单位: Bocconi University; Bocconi University; Cornell University; Tel Aviv University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2014.05.012
• 发表日期: 2014
• 页码: 253-268
• 关键词: Conditional probability; type spaces; Hypothetical knowledge; Counterfactuals

摘要

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. (C) 2014 Elsevier Inc. All rights reserved.