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Existence of $$\alpha $$ α -Robust Weak Nash Equilibria for Leader–Follower Population Games with Fuzzy Parameters

Author

Listed:
  • Guoling Wang

    (Guizhou University)

  • Miao Wang

    (Guizhou University)

  • Hui Yang

    (Guizhou University)

  • Guanghui Yang

    (Guizhou University)

  • Chun Wang

    (Guizhou Open University)

Abstract

This paper mainly studies the existence of $$\alpha $$ α -robust weak Nash equilibria for leader-follower population games with fuzzy parameters. First, $$\alpha $$ α -robust weak Nash equilibria for population games with fuzzy parameters are defined based on u-type set relations and their existence is proved by Fan-Glicksberg fixed theorem. Second, such equilibrium solutions are further proposed for leader-follower population games with fuzzy parameters and their existence is further shown. Finally, four examples are constructed to illustrate their feasibility, respectively. Our results are new and different from the existing ones.

Suggested Citation

  • Guoling Wang & Miao Wang & Hui Yang & Guanghui Yang & Chun Wang, 2024. "Existence of $$\alpha $$ α -Robust Weak Nash Equilibria for Leader–Follower Population Games with Fuzzy Parameters," Journal of Optimization Theory and Applications, Springer, vol. 203(3), pages 2739-2758, December.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:3:d:10.1007_s10957-024-02534-y
    DOI: 10.1007/s10957-024-02534-y
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    References listed on IDEAS

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    1. Tharakunnel, Kurian & Bhattacharyya, Siddhartha, 2009. "Single-leader-multiple-follower games with boundedly rational agents," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1593-1603, August.
    2. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    3. Giovanni P. Crespi & Daishi Kuroiwa & Matteo Rocca, 2020. "Robust Nash equilibria in vector-valued games with uncertainty," Annals of Operations Research, Springer, vol. 289(2), pages 185-193, June.
    4. Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, January.
    5. John R. Conlon, 2009. "Two New Conditions Supporting the First-Order Approach to Multisignal Principal-Agent Problems," Econometrica, Econometric Society, vol. 77(1), pages 249-278, January.
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