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

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  • Shravan Luckraz

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.

Suggested Citation

  • Shravan Luckraz, 2022. "On a Fixed Point Theorem for General Multivalued Mappings on Finite Sets with Applications in Game Theory," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:2477124
    DOI: 10.1155/2022/2477124
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    References listed on IDEAS

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