Equilibrium Existence and Uniqueness in Cournot Games: Closing the Gap

Abstract

We establish sufficient and necessary conditions for equilibrium existence and uniqueness in Cournot games, with a particular focus on unbounded payoff functions, a case not previously addressed but of significant relevance in both industrial organization and the economics of decentralized finance. To establish existence, we adopt a limiting approach that leverages existing results for bounded payoff functions. Uniqueness is demonstrated by employing the aggregate backward response correspondence. Our results provide new insights into how equilibrium existence and uniqueness are shaped by agent competition and strategic interaction. Sufficient and easily verifiable conditions for uniqueness are also developed, subsuming all existing results in the literature.

Keywords: Cournot competition, Contests, Industrial organization, Decentralized finance, Nash equilibrium