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.
Original language | English |
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Pages (from-to) | 1065–1090 |
Number of pages | 26 |
Journal | Mathematics of Operations Research |
Volume | 49 |
Issue number | 2 |
Early online date | 14 Jul 2023 |
DOIs | |
Publication status | Published - May 2024 |
Scopus Subject Areas
- Mathematics(all)
- Computer Science Applications
- Management Science and Operations Research
User-Defined Keywords
- Lagrange multiplier expression
- Moment-SOS relaxation
- Nash equilibrium
- Primary: 90C23, 90C33, 91A10, 65K05
- polynomial optimization
- tight relaxation