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- Title
Nash Equilibrium Problems of Polynomials.
- Authors
Nie, Jiawang; Tang, Xindong
- 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. Funding: J. Nie was supported by the National Science Foundation [Grant DMS-2110780].
- Subjects
NATIONAL Science Foundation (U.S.); NASH equilibrium; POLYNOMIALS; LAGRANGE multiplier
- Publication
Mathematics of Operations Research, 2024, Vol 49, Issue 2, p1065
- ISSN
0364-765X
- Publication type
Article
- DOI
10.1287/moor.2022.0334