2023/10/30 by Ron Holzman, Holzman, Ron
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Combinatorial game theory #Combinatorics #Combinatorics (math.CO) #Computer Science and Game Theory (cs.GT) #Countable set #Discrete mathematics #Economic theories and models #Example of a game without a value #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Game Theory and Applications #Game Theory and Voting Systems #Game theory #Mathematical economics #Mathematics #Minimax #Minimax theorem #Property (philosophy) #Repeated game #Sequential game #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2310.19314
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.