Equilibrium existence in games with a concave Bayesian potential

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Abstract

We establish existence of a pure-strategy Bayesian Nash equilibrium in Bayesian games that have a continuous and concave potential at all states of nature, without assuming absolute continuity of information. As an application, we show that Bayesian Nash equilibrium exists in many well-known games that have semi-quadratic payoffs (including Bertrand and Cournot oligopolies with linear demand), for general information structures.

Original languageEnglish
Pages (from-to)288-294
Number of pages7
JournalGames and Economic Behavior
Volume123
DOIs
StatePublished - 1 Sep 2020

Keywords

  • Absolute continuity
  • Bayesian games
  • Bayesian potential
  • Concave payoffs
  • Equilibrium existence
  • Information structures

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