Nash Equilibrium Problems of Polynomials

Jiawang Nie, Xindong Tang

Research output: Contribution to journalJournal articlepeer-review


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 languageEnglish
Number of pages27
JournalMathematics of Operations Research
Publication statusE-pub ahead of print - 14 Jul 2023

User-Defined Keywords

  • Primary: 90C23, 90C33, 91A10, 65K05
  • Nash equilibrium
  • polynomial optimization
  • Moment-SOS relaxation
  • Lagrange multiplier expression
  • tight relaxation


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