Nash Equilibrium Problems of Polynomials

Jiawang Nie, Xindong Tang

Research output: Contribution to journalJournal articlepeer-review

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)1065–1090
Number of pages26
JournalMathematics of Operations Research
Volume49
Issue number2
Early online date14 Jul 2023
DOIs
Publication statusPublished - 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

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