Equilibria Existence in Bayesian Games: Climbing the Countable Borel Equivalence Relation Hierarchy

• 成果类型: Article
• 署名作者: Hellman, Ziv; Levy, Yehuda John
• 署名单位: Bar Ilan University; University of Glasgow
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.1135
• 发表日期: 2022
• 页码: 367-383
• 关键词: Incomplete information; common knowledge

摘要

The solution concept of a Bayesian equilibrium of a Bayesian game is inherently an interim concept. The corresponding ex ante solution concept has been termed a Harsanyi equilibrium; examples have appeared in the literature showing that there are Bayesian games with uncountable state spaces that have no Bayesian approximate equilibria but do admit a Harsanyi approximate equilibrium, thus exhibiting divergent behaviour in the ex ante and interim stages. Smoothness, a concept from descriptive set theory, has been shown in previous works to guarantee the existence of Bayesian equilibria. We show here that higher rungs in the countable Borel equivalence relation hierarchy can also shed light on equilibrium existence. In particular, hyperfiniteness, the next step above smoothness, is a sufficient condition for the existence of Harsanyi approximate equilibria in purely atomic Bayesian games.