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An Intelligent Algorithm for Solving the Efficient Nash Equilibrium of a Single-Leader Multi-Follower Game

Author

Listed:
  • Lu-Ping Liu

    (School of Mathematics and Statistic, Guizhou University, Huaxidadao, Guiyang 550025, China
    These authors contributed equally to this work.)

  • Wen-Sheng Jia

    (School of Mathematics and Statistic, Guizhou University, Huaxidadao, Guiyang 550025, China
    These authors contributed equally to this work.)

Abstract

This aim of this paper is to provide the immune particle swarm optimization (IPSO) algorithm for solving the single-leader–multi-follower game (SLMFG). Through cooperating with the particle swarm optimization (PSO) algorithm and an immune memory mechanism, the IPSO algorithm is designed. Furthermore, we define the efficient Nash equilibrium from the perspective of mathematical economics, which maximizes social welfare and further refines the number of Nash equilibria. In the end, numerical experiments show that the IPSO algorithm has fast convergence speed and high effectiveness.

Suggested Citation

  • Lu-Ping Liu & Wen-Sheng Jia, 2021. "An Intelligent Algorithm for Solving the Efficient Nash Equilibrium of a Single-Leader Multi-Follower Game," Mathematics, MDPI, vol. 9(5), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:454-:d:504755
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    References listed on IDEAS

    as
    1. Julio B. Clempner & Alexander S. Poznyak, 2019. "Solving Transfer Pricing Involving Collaborative and Non-cooperative Equilibria in Nash and Stackelberg Games: Centralized–Decentralized Decision Making," Computational Economics, Springer;Society for Computational Economics, vol. 54(2), pages 477-505, August.
    2. Anthropelos, Michail & Boonen, Tim J., 2020. "Nash equilibria in optimal reinsurance bargaining," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 196-205.
    3. Alexey Izmailov & Mikhail Solodov, 2014. "On error bounds and Newton-type methods for generalized Nash equilibrium problems," Computational Optimization and Applications, Springer, vol. 59(1), pages 201-218, October.
    4. Bhatti, Bilal Ahmad & Broadwater, Robert, 2020. "Distributed Nash Equilibrium Seeking for a Dynamic Micro-grid Energy Trading Game with Non-quadratic Payoffs," Energy, Elsevier, vol. 202(C).
    Full references (including those not matched with items on IDEAS)

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