Bayesian games with a continuum of states

• 成果类型: Article
• 署名作者: Hellman, Ziv; Levy, Yehuda John
• 署名单位: Bar Ilan University; University of Oxford; University of Oxford
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1555-7561
• DOI: 10.3982/TE1544
• 发表日期: 2017-09-01
• 页码: 1089-1120
• 关键词: Bayesian games; Bayesian equilibrium; common priors; continuum of states

摘要

We show that every Bayesian game with purely atomic types has a measurable Bayesian equilibrium when the common knowledge relation is smooth. Conversely, for any common knowledge relation that is not smooth, there exists a type space that yields this common knowledge relation and payoffs such that the resulting Bayesian game does not have any Bayesian equilibrium. We show that our smoothness condition also rules out two paradoxes involving Bayesian games with a continuum of types: the impossibility of having a commonprior on components when a common prior over the entire state space exists, and the possibility of interim betting/trade even when no such trade can be supported ex ante.