Nash's Existence Theorem for Non-compact Strategy Sets
Functional Analysis
2023-11-14 v1
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.
Cite
@article{arxiv.2311.06832,
title = {Nash's Existence Theorem for Non-compact Strategy Sets},
author = {Xinyu Zhang and Cheng Chen and Chunyan Yang},
journal= {arXiv preprint arXiv:2311.06832},
year = {2023}
}
Comments
8 pages