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Methods for Solving Generalized Nash Equilibrium

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  • Biao Qu
  • Jing Zhao

Abstract

The generalized Nash equilibrium problem (GNEP) is an extension of the standard Nash equilibrium problem (NEP), in which each player′s strategy set may depend on the rival player′s strategies. In this paper, we present two descent type methods. The algorithms are based on a reformulation of the generalized Nash equilibrium using Nikaido‐Isoda function as unconstrained optimization. We prove that our algorithms are globally convergent and the convergence analysis is not based on conditions guaranteeing that every stationary point of the optimization problem is a solution of the GNEP.

Suggested Citation

  • Biao Qu & Jing Zhao, 2013. "Methods for Solving Generalized Nash Equilibrium," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:762165
    DOI: 10.1155/2013/762165
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    References listed on IDEAS

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    1. Anna Heusinger & Christian Kanzow, 2009. "Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions," Computational Optimization and Applications, Springer, vol. 43(3), pages 353-377, July.
    2. S.D. Flam & A. Ruszczynski, 1994. "Noncooperative Convex Games: Computing Equilibrium By Partial Regularization," Working Papers wp94042, International Institute for Applied Systems Analysis.
    3. Axel Dreves & Christian Kanzow, 2011. "Nonsmooth optimization reformulations characterizing all solutions of jointly convex generalized Nash equilibrium problems," Computational Optimization and Applications, Springer, vol. 50(1), pages 23-48, September.
    4. Harker, Patrick T., 1991. "Generalized Nash games and quasi-variational inequalities," European Journal of Operational Research, Elsevier, vol. 54(1), pages 81-94, September.
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    Cited by:

    1. Biao Qu & Jing Zhao, 2020. "Corrigendum to “Methods for Solving Generalized Nash Equilibrium”," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).

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