A game with no Bayesian approximate equilibria

Ziv Hellman

Journal of Economic Theory, 2014, vol. 153, issue C, 138-151

Abstract: Harsányi [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].

Keywords: Existence of equilibria; Bayesian games; Incomplete information; Approximate equilibria (search for similar items in EconPapers)
JEL-codes: C62 C72 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:153:y:2014:i:c:p:138-151

DOI: 10.1016/j.jet.2014.06.005

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