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Reflected Iterative Method for Non-Monotone Equilibrium Problems with Applications to Nash-Cournot Equilibrium Models

Author

Listed:
  • Yekini Shehu

    (Zhejiang Normal University)

  • Lulu Liu

    (Civil Aviation University of China)

  • Xiaolong Qin

    (Zhejiang Normal University)

  • Qiao-Li Dong

    (Civil Aviation University of China)

Abstract

In this paper, we introduce a numerical iterative algorithm with a reflected step to solve the equilibrium problem, which involves non-monotone bifunctions, in real Hilbert spaces. We give weak convergence analysis when the bifunctions are convex and jointly weakly continuous alongside the associated Minty equilibrium problem with a solution. The assumptions in this paper are weaker than the pseudo-monotonicity Lipschitz-type continuity assumptions used recently on equilibrium problems in the literature. Numerical results on Nash-Cournot equilibrium models show that our algorithm is competitive and efficient.

Suggested Citation

  • Yekini Shehu & Lulu Liu & Xiaolong Qin & Qiao-Li Dong, 2022. "Reflected Iterative Method for Non-Monotone Equilibrium Problems with Applications to Nash-Cournot Equilibrium Models," Networks and Spatial Economics, Springer, vol. 22(1), pages 153-180, March.
    • Handle: RePEc:kap:netspa:v:22:y:2022:i:1:d:10.1007_s11067-022-09562-z
    DOI: 10.1007/s11067-022-09562-z
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    References listed on IDEAS

    as
    1. Yekini Shehu, 2012. "Iterative method for fixed point problem, variational inequality and generalized mixed equilibrium problems with applications," Journal of Global Optimization, Springer, vol. 52(1), pages 57-77, January.
    2. Zhaomiao Guo & Yueyue Fan, 2017. "A Stochastic Multi-agent Optimization Model for Energy Infrastructure Planning under Uncertainty in An Oligopolistic Market," Networks and Spatial Economics, Springer, vol. 17(2), pages 581-609, June.
    3. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
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    6. M. Castellani & M. Giuli, 2013. "Refinements of existence results for relaxed quasimonotone equilibrium problems," Journal of Global Optimization, Springer, vol. 57(4), pages 1213-1227, December.
    7. Giancarlo Bigi & Mauro Passacantando, 2016. "Gap functions for quasi-equilibria," Journal of Global Optimization, Springer, vol. 66(4), pages 791-810, December.
    8. Jean Strodiot & Thi Nguyen & Van Nguyen, 2013. "A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems," Journal of Global Optimization, Springer, vol. 56(2), pages 373-397, June.
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