Existence of pure Nash equilibria in discontinuous and non quasiconcave games

Philippe Bich (1, 2)

1 CES - Centre d'économie de la Sorbonne
2 PSE - Paris School of Economics

In a recent but well known paper, Reny has proved the existence of Nash equilibria for compact and quasiconcave games, with possibly discontinuous payoff functions. In this paper, we prove that the quasiconcavity assumption in Reny's theorem can be weakened: we introduce a measure allowing to localize the lack of quasiconcavity, which allows to refine the analysis of equilibrium existence.

Nous affaiblissons dans ce papier le théorème d'existence d'équilibres de Nash de Reny pour les jeux discontinus, en autorisant un certain type de non-quasiconcavité.

Mots clés: Equilibre de Nash; discontinuité; quasiconcavité

Mots clés: quasiconcavity; Nash equilibrium; discontinuity

Domaines: Economies et finances

Philippe Bich. Existence of pure Nash equilibria in discontinuous and non quasiconcave games. 2009. ⟨halshs-00426402⟩