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Note on unique Nash equilibrium in continuous games

John Rehbeck

Games and Economic Behavior, 2018, vol. 110, issue C, 216-225

Abstract: This note studies whether any set of finitely supported mixed strategies can be represented as the unique Nash equilibrium of a game. This note shows that if strategy spaces are metric spaces containing infinitely many points, then any set of finitely supported mixed strategies can be represented as the unique Nash equilibrium to a separable game. If the strategy spaces are additionally subsets of Euclidean space with infinitely many cluster points, then any set of finitely supported mixed strategies can be represented as the unique Nash equilibrium to a polynomial game.

Keywords: Continuous games; Separable games; Polynomial games; Nash equilibrium (search for similar items in EconPapers)
JEL-codes: C70 D70 (search for similar items in EconPapers)
Date: 2018
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