Strategy investments in zero-sum games

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED Optimization Letters Pub Date : 2024-06-24 DOI:10.1007/s11590-024-02130-z

Raul Garcia, Seyedmohammadhossein Hosseinian, Mallesh Pai, Andrew J. Schaefer

引用次数: 0

Abstract

We propose an extension of two-player zero-sum games, where one player may select available actions for themselves and the opponent, subject to a budget constraint. We present a mixed-integer linear programming (MILP) formulation for the problem, provide analytical results regarding its solution, and discuss applications in the security and advertising domains. Our computational experiments demonstrate that heuristic approaches, on average, yield suboptimal solutions with at least a 20% relative gap with those obtained by the MILP formulation.

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零和博弈中的战略投资

我们提出了双人零和博弈的一种扩展，在这种博弈中，一方可以在预算约束下为自己和对手选择可用的行动。我们提出了该问题的混合整数线性规划（MILP）公式，提供了有关其求解的分析结果，并讨论了在安全和广告领域的应用。我们的计算实验证明，启发式方法平均会产生次优解，与 MILP 公式得到的解至少有 20% 的相对差距。

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

Optimization Letters 管理科学-应用数学

CiteScore

3.40

自引率

6.20%

发文量

116

审稿时长

9 months

期刊介绍： Optimization Letters is an international journal covering all aspects of optimization, including theory, algorithms, computational studies, and applications, and providing an outlet for rapid publication of short communications in the field. Originality, significance, quality and clarity are the essential criteria for choosing the material to be published. Optimization Letters has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time one of the most striking trends in optimization is the constantly increasing interdisciplinary nature of the field. Optimization Letters aims to communicate in a timely fashion all recent developments in optimization with concise short articles (limited to a total of ten journal pages). Such concise articles will be easily accessible by readers working in any aspects of optimization and wish to be informed of recent developments.