A unifying pair of Cournot-Nash equilibrium existence results

Abstract

For games with a measure space of players a tandem pair consisting of a mixed and a pure CournotNash equilibrium existence result is presented Their generality causes them to be completely mutually equivalent This provides a unifying pair of CournotNash existence results that goes considerably beyond the central result of Theorem The versatility of this pair is demonstrated by the following new applications i unication and generalization of the two equilibrium distribution existence results for anonymous games in ii generalization of the equilibrium existence result for Bayesian di erential information games in iii inclusion of the Bayesian Nash equilibrium existence results in for games with private information in the sense of Harsanyi