Bayesian games with a continuum of states

Ziv Hellman, Yehuda John Levy

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Abstract

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 common prior 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.

Original languageEnglish
Pages (from-to)1089-1120
Number of pages32
JournalTheoretical Economics
Volume12
Issue number3
DOIs
StatePublished - Sep 2017

Bibliographical note

Publisher Copyright:
Copyright © 2017 The Authors.

Keywords

  • Bayesian equilibrium
  • Bayesian games
  • common priors
  • continuum of states

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