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Nash Equilibrium Problems of Polynomials

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jiawang Nie & Xindong Tang, 2024. "Nash Equilibrium Problems of Polynomials," Mathematics of Operations Research, INFORMS, vol. 49(2), pages 1065-1090, May.
    • Handle: RePEc:inm:ormoor:v:49:y:2024:i:2:p:1065-1090
    DOI: 10.1287/moor.2022.0334
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