Nash Equilibrium Problems of Polynomials

• 成果类型: Article; Early Access
• 署名作者: Nie, Jiawang; Tang, Xindong
• 署名单位: University of California System; University of California San Diego; Hong Kong Polytechnic University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.0334
• 发表日期: 2023
• 关键词: moment-sos hierarchy; relaxation algorithms; optimization; squares; computation; tssos; sums

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.