IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i5p454-d504755.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/5/454/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/5/454/
    Download Restriction: no
    ---><---

    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. 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).
    3. Anthropelos, Michail & Boonen, Tim J., 2020. "Nash equilibria in optimal reinsurance bargaining," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 196-205.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Yanhong & Cheung, Ka Chun & Zhang, Yiying, 2024. "Bowley solution under the reinsurer's default risk," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 36-61.
    2. Leonardo Galli & Christian Kanzow & Marco Sciandrone, 2018. "A nonmonotone trust-region method for generalized Nash equilibrium and related problems with strong convergence properties," Computational Optimization and Applications, Springer, vol. 69(3), pages 629-652, April.
    3. Simone Sagratella, 2017. "Algorithms for generalized potential games with mixed-integer variables," Computational Optimization and Applications, Springer, vol. 68(3), pages 689-717, December.
    4. Pfeifer, Antun & Feijoo, Felipe & Duić, Neven, 2023. "Fast energy transition as a best strategy for all? The nash equilibrium of long-term energy planning strategies in coupled power markets," Energy, Elsevier, vol. 284(C).
    5. Dai, Shuangfeng & Mansouri, Seyed Amir & Huang, Shoujun & Alharthi, Yahya Z. & Wu, Yongfei & Bagherzadeh, Leila, 2024. "A multi-stage techno-economic model for harnessing flexibility from IoT-enabled appliances and smart charging systems: Developing a competitive local flexibility market using Stackelberg game theory," Applied Energy, Elsevier, vol. 373(C).
    6. Boonen, Tim J. & Ghossoub, Mario, 2023. "Bowley vs. Pareto optima in reinsurance contracting," European Journal of Operational Research, Elsevier, vol. 307(1), pages 382-391.
    7. Wu, Chuantao & Zhou, Dezhi & Lin, Xiangning & Sui, Quan & Wei, Fanrong & Li, Zhengtian, 2022. "A novel energy cooperation framework for multi-island microgrids based on marine mobile energy storage systems," Energy, Elsevier, vol. 252(C).
    8. Wang, Tonghe & Guo, Jian & Ai, Songpu & Cao, Junwei, 2021. "RBT: A distributed reputation system for blockchain-based peer-to-peer energy trading with fairness consideration," Applied Energy, Elsevier, vol. 295(C).
    9. Yan, Zhongzhen & Zhu, Xinyuan & Chang, Yiming & Wang, Xianglong & Ye, Zhiwei & Xu, Zhigang & Fars, Ashk, 2023. "Renewable energy effects on energy management based on demand response in microgrids environment," Renewable Energy, Elsevier, vol. 213(C), pages 205-217.
    10. Yang, Jie & Ma, Tieding & Ma, Kai & Yang, Bo & Guerrero, Josep M. & Liu, Zhixin, 2021. "Trading mechanism and pricing strategy of integrated energy systems based on credit rating and Bayesian game," Energy, Elsevier, vol. 232(C).
    11. Giancarlo Bigi & Mauro Passacantando, 2016. "Gap functions for quasi-equilibria," Journal of Global Optimization, Springer, vol. 66(4), pages 791-810, December.
    12. Wang, Hao-ran & Feng, Tian-tian & Xiong, Wei, 2022. "How can the dynamic game be integrated into blockchain-based distributed energy resources multi-agent transactions for decision-making?," Energy, Elsevier, vol. 254(PB).
    13. Christos Alexakis & Michael Dowling & Konstantinos Eleftheriou & Michael Polemis, 2021. "Textual Machine Learning: An Application to Computational Economics Research," Computational Economics, Springer;Society for Computational Economics, vol. 57(1), pages 369-385, January.
    14. Li, Zhengmao & Wu, Lei & Xu, Yan & Wang, Luhao & Yang, Nan, 2023. "Distributed tri-layer risk-averse stochastic game approach for energy trading among multi-energy microgrids," Applied Energy, Elsevier, vol. 331(C).
    15. Soares, João & Lezama, Fernando & Faia, Ricardo & Limmer, Steffen & Dietrich, Manuel & Rodemann, Tobias & Ramos, Sergio & Vale, Zita, 2024. "Review on fairness in local energy systems," Applied Energy, Elsevier, vol. 374(C).
    16. Luciana Marques & Wadaed Uturbey & Miguel Heleno, 2021. "An Integer Non-Cooperative Game Approach for the Transactive Control of Thermal Appliances in Energy Communities," Energies, MDPI, vol. 14(21), pages 1-22, October.
    17. María de los Ángeles Martínez & Damián Fernández, 2019. "On the Local and Superlinear Convergence of a Secant Modified Linear-Programming-Newton Method," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 993-1010, March.
    18. Axel Dreves & Simone Sagratella, 2020. "Nonsingularity and Stationarity Results for Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 711-743, June.
    19. Andreas Fischer & Markus Herrich & Alexey Izmailov & Mikhail Solodov, 2016. "Convergence conditions for Newton-type methods applied to complementarity systems with nonisolated solutions," Computational Optimization and Applications, Springer, vol. 63(2), pages 425-459, March.
    20. Axel Dreves, 2017. "Computing all solutions of linear generalized Nash equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(2), pages 207-221, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:454-:d:504755. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.