Nash Equilibrium Existence without Convexity

Conrad Kosowsky

Papers from arXiv.org

Abstract: In this paper, I prove the existence of a pure-strategy Nash equilibrium for a large class of games with nonconvex strategy spaces. Specifically, if each player's strategies form a compact, connected Euclidean neighborhood retract and if all best-response correspondences are null-homotopic, then the game has a pure-strategy Nash equilibrium. As an application, I show how this result can prove the fundamental theorem of algebra.

Date: 2023-08
New Economics Papers: this item is included in nep-gth and nep-mic
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