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Nash Equilibrium Existence without Convexity

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  • Conrad Kosowsky

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.

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  • Conrad Kosowsky, 2023. "Nash Equilibrium Existence without Convexity," Papers 2308.11597, arXiv.org.
    • Handle: RePEc:arx:papers:2308.11597
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    File URL: http://arxiv.org/pdf/2308.11597
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