Iterated expectations, compact spaces, and common priors

• 成果类型: Article
• 署名作者: Hellman, Ziv
• 署名单位: Hebrew University of Jerusalem; Hebrew University of Jerusalem
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2010.06.012
• 发表日期: 2011
• 页码: 163-171
• 关键词: Common priors; Iterated expectations

摘要

Extending to infinite state spaces that are compact metric spaces a result previously attained by D. Samet solely in the context of finite state spaces, a necessary and sufficient condition for the existence of a common prior for several players is given in terms of the players' present beliefs only. A common prior exists if and only if for each random variable it is common knowledge that all Cesaro means of iterated expectations with respect to any permutation converge to the same value; this value is its expectation with respect to the common prior. It is further shown that compactness is a necessary condition for some of the results. (C) 2010 Elsevier Inc. All rights reserved.