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The Stability of Set of Solutions for Symmetric Vector Quasi-Equilibrium Problems

Author

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  • J. C. Chen

    (Nanchang University)

  • X. H. Gong

    (Nanchang University)

Abstract

In this paper, the stability of the set of solutions for symmetric vector quasi-equilibrium problems is discussed. Then, we prove a generic stability theorem and give an existence theorem for essentially connected components of the set of solutions for symmetric vector quasi-equilibrium problems. Finally, we apply these results to vector weak saddle point problems with constraints.

Suggested Citation

  • J. C. Chen & X. H. Gong, 2008. "The Stability of Set of Solutions for Symmetric Vector Quasi-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 359-374, March.
    • Handle: RePEc:spr:joptap:v:136:y:2008:i:3:d:10.1007_s10957-007-9309-7
    DOI: 10.1007/s10957-007-9309-7
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    References listed on IDEAS

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    1. Hillas, John, 1990. "On the Definition of the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 58(6), pages 1365-1390, November.
    2. Z. Lin, 2005. "Essential Components of the Set of Weakly Pareto-Nash Equilibrium Points for Multiobjective Generalized Games in Two Different Topological Spaces," Journal of Optimization Theory and Applications, Springer, vol. 124(2), pages 387-405, February.
    3. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
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    Cited by:

    1. Zaiyun Peng & Ziyuan Wang & Xinmin Yang, 2020. "Connectedness of Solution Sets for Weak Generalized Symmetric Ky Fan Inequality Problems via Addition-Invariant Sets," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 188-206, April.
    2. 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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