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

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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.

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Acknowledgements

The authors sincerely thank the anonymous referees for their careful reading, and constructive comments that improved the earlier version of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Yekini Shehu & Xiaolong Qin

  2. College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Lulu Liu & Qiao-Li Dong

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  1. Yekini Shehu
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  2. Lulu Liu
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  3. Xiaolong Qin
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  4. Qiao-Li Dong
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Correspondence to Xiaolong Qin.

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Shehu, Y., Liu, L., Qin, X. et al. Reflected Iterative Method for Non-Monotone Equilibrium Problems with Applications to Nash-Cournot Equilibrium Models. Netw Spat Econ 22, 153–180 (2022). https://doi.org/10.1007/s11067-022-09562-z

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