Strategy investments in zero-sum games

被引：0

作者：

Garcia, Raul ^{[1
]}

Hosseinian, Seyedmohammadhossein ^{[2
]}

Pai, Mallesh ^{[3
]}

Schaefer, Andrew J. ^{[1
]}

机构：

[1] Rice Univ, Dept Computat Appl Math & Operat Res, Houston, TX 77005 USA

[2] Univ Cincinnati, Dept Mech & Mat Engn, Cincinnati, OH 45221 USA

[3] Rice Univ, Dept Econ, Houston, TX 77005 USA

来源：

OPTIMIZATION LETTERS | 2024年 / 18卷 / 08期

基金：

美国国家卫生研究院;

关键词：

Zero-sum games; Matrix games; Strategy investments; Mixed-integer linear programming;

D O I：

10.1007/s11590-024-02130-z

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

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.

引用

页码：1771 / 1789

页数：19

共 50 条

[21] ERGODICITY CONDITIONS FOR ZERO-SUM GAMES
Akian, Marianne
Gaubert, Stephane
Hochart, Antoine
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2015, 35 (09) : 3901 - 3931
[22] ZERO-SUM GAMES WITH MULTIPLE GOALS
COOK, WD
NAVAL RESEARCH LOGISTICS, 1976, 23 (04) : 615 - 621
[23] Zero-Sum Stochastic Stackelberg Games
Goktas, Denizalp
Zhao, Jiayi
Greenwald, Amy
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 35 (NEURIPS 2022), 2022,
[24] Definable Zero-Sum Stochastic Games
Bolte, Jerome
Gaubert, Stephane
Vigeral, Guillaume
MATHEMATICS OF OPERATIONS RESEARCH, 2015, 40 (01) : 171 - 191
[25] On the Complexity of Succinct Zero-Sum Games
Lance Fortnow
Russell Impagliazzo
Valentine Kabanets
Christopher Umans
computational complexity, 2008, 17 : 353 - 376
[26] Convexity in zero-sum differential games
Goebel, R
PROCEEDINGS OF THE 41ST IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, 2002, : 3964 - 3969
[27] Efficient Strategy Computation in Zero-Sum Asymmetric Information Repeated Games
Li, Lichun
Shamma, Jeff S.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2020, 65 (07) : 2785 - 2800
[28] Pure strategy equilibria in symmetric two-player zero-sum games
Duersch, Peter
Oechssler, Joerg
Schipper, Burkhard C.
INTERNATIONAL JOURNAL OF GAME THEORY, 2012, 41 (03) : 553 - 564
[29] Information spillover in multiple zero-sum games
Pahl, Lucas
INTERNATIONAL JOURNAL OF GAME THEORY, 2024, 53 (01) : 71 - 104
[30] An undecidable statement regarding zero-sum games
Fey, Mark
GAMES AND ECONOMIC BEHAVIOR, 2024, 145 : 19 - 26

← 1 2 3 4 5 →