Nash Equilibrium Problems of Polynomials

被引：4

作者：

Nie, Jiawang ^{[1
]}

Tang, Xindong ^{[2
]}

机构：

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[2] Hong Kong Polytech Univ, Dept Appl Math, Hung Hom, Kowloon, Hong Kong, Peoples R China

来源：

MATHEMATICS OF OPERATIONS RESEARCH | 2023年 / 49卷 / 02期

基金：

美国国家科学基金会;

关键词：

Nash equilibrium; polynomial optimization; Moment-SOS relaxation; Lagrange multiplier expression; tight relaxation; MOMENT-SOS HIERARCHY; RELAXATION ALGORITHMS; OPTIMIZATION; SQUARES; COMPUTATION; TSSOS; SUMS;

D O I：

10.1287/moor.2022.0334

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：

This paper studies Nash equilibrium problems that are given by polynomial functions. We formulate efficient polynomial optimization problems for computing Nash equilibria. The Moment-sum-of-squares relaxations are used to solve them. Under generic assumptions, the method can find a Nash equilibrium, if there is one. Moreover, it can find all Nash equilibria if there are finitely many ones of them. The method can also detect nonexistence if there is no Nash equilibrium.

引用

页码：1 / 26

页数：27

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