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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-02 DOI:10.1287/moor.2023.0352

Ron Holzman

引用次数: 0

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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无限双人输赢游戏中的最小值属性

我们探讨了具有无限多纯策略的双人输赢博弈的最小定理版本。在可数情况下，我们给出了一个博弈的组合条件，它意味着最小属性。在一般情况下，我们证明当且仅当一个博弈的所有子博弈都不与 "大数博弈 "同构时，该博弈及其所有子博弈都满足最小性质。这概括了 Hanneke、Livni 和 Moran 最近提出的一个定理。我们还提出了我们的结果在博弈论之外的一些应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.