From posteriors to priors via cycles

• 成果类型: Article
• 署名作者: Rodrigues-Neto, Jose Alvaro
• 署名单位: Australian National University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2008.10.003
• 发表日期: 2009
• 页码: 876-883
• 关键词: Consistency; cycle; incomplete information; Join; KNOWLEDGE; Meet; partition; Prior; posterior; Type

摘要

We present new necessary and sufficient conditions for checking if a set of players' posteriors may come from a common prior. A simple diagrammatic device calculates the join and meet of players' knowledge partitions. Each cycle in the diagram has a corresponding cycle equation. Posteriors are consistent with a common prior if and only if all cycle equations are satisfied. We prove that in games of two players, where the join partition has only singletons, a common prior exists if each player's distribution of beliefs over the elements of her opponent's partition is independent of her own private information. Crown Copyright (C) 2008 Published by Elsevier Inc. All rights reserved.