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The minimax property in infinite two-person win-lose games

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  • Ron Holzman

Abstract

We explore a version of the minimax theorem for two-person win-lose games with infinitely many pure strategies. In the countable case, we give a combinatorial condition on the game which implies the minimax property. In the general case, we prove that a game satisfies the minimax property along with all its subgames if and only if none of its subgames is isomorphic to the "larger number game." This generalizes a recent theorem of Hanneke, Livni and Moran. We also propose several applications of our results outside of game theory.

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  • Ron Holzman, 2023. "The minimax property in infinite two-person win-lose games," Papers 2310.19314, arXiv.org.
    • Handle: RePEc:arx:papers:2310.19314
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    File URL: http://arxiv.org/pdf/2310.19314
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