Nash Equilibrium Problems of Polynomials

Jiawang Nie () and Xindong Tang ()
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Jiawang Nie: Department of Mathematics, University of California San Diego, La Jolla, California 92093
Xindong Tang: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Mathematics of Operations Research, 2024, vol. 49, issue 2, 1065-1090

Abstract: 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.

Keywords: Primary: 90C23; 90C33; 91A10; 65K05; Nash equilibrium; polynomial optimization; Moment-SOS relaxation; Lagrange multiplier expression; tight relaxation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:49:y:2024:i:2:p:1065-1090

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