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

Ron Holzman ()
Additional contact information
Ron Holzman: Department of Mathematics, Technion – Israel Institute of Technology, Technion City, Haifa 3200003, Israel

Mathematics of Operations Research, 2025, vol. 50, issue 3, 2287-2300

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.

Keywords: Primary: 91A05; Secondary: 91A44; minimax theorem; infinite games; larger number game; convergent series; infinite matrices; hypergraph duality; stable theories; online learning (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/moor.2023.0352 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:50:y:2025:i:3:p:2287-2300

Access Statistics for this article

More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().