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Existence of Equilibrium Solution for Multi-Leader–Follower Games with Fuzzy Goals and Parameters

Author

Listed:
  • Zhenli Liu

    (Guizhou University)

  • Guoling Wang

    (Guizhou University)

  • Guanghui Yang

    (Guizhou University)

Abstract

In this paper, we first propose the model of multi-leader–follower games with fuzzy goals involving fuzzy parameters and introduce its $$\alpha $$ α -FNS equilibrium. Next, we shift our attention to the existence of $$\alpha $$ α -FNS equilibrium and prove it by Kakutani’s fixed point theorem. Finally, we illustrate an example to show that the equilibrium existence result is valid.

Suggested Citation

  • Zhenli Liu & Guoling Wang & Guanghui Yang, 2024. "Existence of Equilibrium Solution for Multi-Leader–Follower Games with Fuzzy Goals and Parameters," Journal of Optimization Theory and Applications, Springer, vol. 200(2), pages 585-601, February.
    • Handle: RePEc:spr:joptap:v:200:y:2024:i:2:d:10.1007_s10957-023-02340-y
    DOI: 10.1007/s10957-023-02340-y
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    References listed on IDEAS

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    1. Julien, Ludovic A., 2017. "On noncooperative oligopoly equilibrium in the multiple leader–follower game," European Journal of Operational Research, Elsevier, vol. 256(2), pages 650-662.
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    3. Xie Ding, 2012. "Equilibrium existence theorems for multi-leader-follower generalized multiobjective games in FC-spaces," Journal of Global Optimization, Springer, vol. 53(3), pages 381-390, July.
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    5. Vijay, V. & Chandra, S. & Bector, C.R., 2005. "Matrix games with fuzzy goals and fuzzy payoffs," Omega, Elsevier, vol. 33(5), pages 425-429, October.
    6. Fatiha Kacher & Moussa Larbani, 2006. "Solution Concept For A Non-Cooperative Game With Fuzzy Parameters," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 489-498.
    7. ZHAO, Jingang, 1991. "The equilibria of a multiple objective game," LIDAM Reprints CORE 987, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Zhe Yang & Yan Ju, 2016. "Existence and generic stability of cooperative equilibria for multi-leader-multi-follower games," Journal of Global Optimization, Springer, vol. 65(3), pages 563-573, July.
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