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An improved two-step method for solving generalized Nash equilibrium problems

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  • Han, Deren
  • Zhang, Hongchao
  • Qian, Gang
  • Xu, Lingling

Abstract

The generalized Nash equilibrium problem (GNEP) is a noncooperative game in which the strategy set of each player, as well as his payoff function, depend on the rival players strategies. As a generalization of the standard Nash equilibrium problem (NEP), the GNEP has recently drawn much attention due to its capability of modeling a number of interesting conflict situations in, for example, an electricity market and an international pollution control. In this paper, we propose an improved two-step (a prediction step and a correction step) method for solving the quasi-variational inequality (QVI) formulation of the GNEP. Per iteration, we first do a projection onto the feasible set defined by the current iterate (prediction) to get a trial point; then, we perform another projection step (correction) to obtain the new iterate. Under certain assumptions, we prove the global convergence of the new algorithm. We also present some numerical results to illustrate the ability of our method, which indicate that our method outperforms the most recent projection-like methods of Zhang et al. (2010).

Suggested Citation

  • Han, Deren & Zhang, Hongchao & Qian, Gang & Xu, Lingling, 2012. "An improved two-step method for solving generalized Nash equilibrium problems," European Journal of Operational Research, Elsevier, vol. 216(3), pages 613-623.
    • Handle: RePEc:eee:ejores:v:216:y:2012:i:3:p:613-623
    DOI: 10.1016/j.ejor.2011.08.008
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    3. Axel Dreves & Francisco Facchinei & Andreas Fischer & Markus Herrich, 2014. "A new error bound result for Generalized Nash Equilibrium Problems and its algorithmic application," Computational Optimization and Applications, Springer, vol. 59(1), pages 63-84, October.
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    6. Ma, Jie & Xu, Min & Meng, Qiang & Cheng, Lin, 2020. "Ridesharing user equilibrium problem under OD-based surge pricing strategy," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 1-24.
    7. Axel Dreves, 2014. "Finding all solutions of affine generalized Nash equilibrium problems with one-dimensional strategy sets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(2), pages 139-159, October.
    8. Zheng Peng & Wenxing Zhu, 2013. "An Alternating Direction Method for Nash Equilibrium of Two-Person Games with Alternating Offers," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 533-551, May.
    9. Axel Dreves, 2016. "Improved error bound and a hybrid method for generalized Nash equilibrium problems," Computational Optimization and Applications, Springer, vol. 65(2), pages 431-448, November.
    10. Riccardi, R. & Bonenti, F. & Allevi, E. & Avanzi, C. & Gnudi, A., 2015. "The steel industry: A mathematical model under environmental regulations," European Journal of Operational Research, Elsevier, vol. 242(3), pages 1017-1027.
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