On a Fixed Point Theorem for General Multivalued Mappings on Finite Sets with Applications in Game Theory

Shravan Luckraz and Nan-Jing Huang

Journal of Mathematics, 2022, vol. 2022, 1-9

Abstract: We propose a new fixed point theorem that completely characterizes the existence of fixed points for multivalued maps on finite sets. Our result can be seen as a generalization of Abian’s fixed point theorem. In the context of finite games, our result can be used to characterize the existence of a Nash equilibrium in pure strategies and can therefore distinguish pure strategy equilibria from mixed strategy equilibria in the celebrated Nash theorem.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:2477124

DOI: 10.1155/2022/2477124

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