A game with no Bayesian approximate equilibria

• 成果类型: Article
• 署名作者: Hellman, Ziv
• 署名单位: Bar Ilan University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2014.06.005
• 发表日期: 2014
• 页码: 138-151
• 关键词: Existence of equilibria; Bayesian games; incomplete information; Approximate equilibria

摘要

Harsanyi [4] showed that Bayesian games over finite games of payoff uncertainty with finite sets of belief types always admit Bayesian equilibria. That still left the question of whether Bayesian games over finite games of payoff uncertainty with infinitely many types are guaranteed to have equilibria. Simon [7] presented an example of a Bayesian game with no measurable Bayesian equilibria, even though the underlying game of payoff uncertainty is finite. We present a new and shorter proof of Simon's result using a simpler Bayesian game that moreover does not even have measurable approximate equilibria. That game in turn is used as the basis for constructing another Bayesian game which has no Bayesian equilibria at all, even in non-measurable strategies, in a construction complementary to one appearing in Friedenberg and Meier [1]. (C) 2014 Elsevier Inc. All rights reserved.