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The Minimax Property in Infinite Two-Person Win-Lose Games

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  • Ron Holzman

    (Department of Mathematics, Technion – Israel Institute of Technology, Technion City, Haifa 3200003, Israel)

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.

Suggested Citation

  • Ron Holzman, 2025. "The Minimax Property in Infinite Two-Person Win-Lose Games," Mathematics of Operations Research, INFORMS, vol. 50(3), pages 2287-2300, August.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:3:p:2287-2300
    DOI: 10.1287/moor.2023.0352
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