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Existence and Stability of Fuzzy Slightly Altruistic Equilibrium for a Class of Generalized Multiobjective Fuzzy Games

Author

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  • Jian-ping Tian

    (Guizhou University
    Guizhou Provincial Key Laboratory of Games Decision Making and Control Systems)

  • Wen-sheng Jia

    (Guizhou University
    Guizhou Provincial Key Laboratory of Games Decision Making and Control Systems)

  • Li Zhou

    (Guizhou University
    Guizhou Provincial Key Laboratory of Games Decision Making and Control Systems)

Abstract

We mainly study the existence, structural stability and robustness of fuzzy slightly altruistic equilibria for a class of generalized multiobjective fuzzy games which are expressed as $$\varpi $$ ϖ . Firstly, we introduce the concept of fuzzy slightly altruistic equilibrium and prove the existence of equilibrium for the $$\varpi $$ ϖ by Fan–Glicksberg fixed point theorem. Secondly, the connections between $$\varpi $$ ϖ and bounded rationality are discussed by an abstract rationality functions. Moreover, we construct the problem space of $$\varpi $$ ϖ which is represented by $$\varLambda $$ Λ and show that most $$\varpi \in \varLambda $$ ϖ ∈ Λ are structurally stable and robust to $$\varepsilon $$ ε -equilibrium on the meaning of Baire category. These results are new and extend some existing results in recent literature.

Suggested Citation

  • Jian-ping Tian & Wen-sheng Jia & Li Zhou, 2024. "Existence and Stability of Fuzzy Slightly Altruistic Equilibrium for a Class of Generalized Multiobjective Fuzzy Games," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 111-125, October.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:1:d:10.1007_s10957-024-02471-w
    DOI: 10.1007/s10957-024-02471-w
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