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arXiv · 2311.06832

Nash's Existence Theorem for Non-compact Strategy Sets

Xinyu Zhang·Cheng Chen·Chunyan Yang
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Abstract

This paper generalizes the Fan-Knaster-Kuratowski-Mazurkiewicz (FKKM) lemma to the case of weak topology, and obtains the Ky Fan minimax inequality defined on non-empty non-compact convex subsets in reflexive Banach spaces, then we apply it to game theory and obtain Nash's existence theorem for non-compact strategy sets, together with John von Neumann's existence theorem in two-player zero-sum games.

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Xinyu Zhang, Cheng Chen, Chunyan Yang. 2023-11-12. Nash's Existence Theorem for Non-compact Strategy Sets. https://arxiv.org/abs/2311.06832

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