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Essential Stability of Solutions for Maximal Element Theorem with Applications

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  • Z. Yang

    (Chong Qing University)

  • Y. J. Pu

    (Chong Qing University)

Abstract

In this paper, we prove that most of problems in maximal element theorem (in the sense of Baire category) are essential and that, for any problem in maximal element theorem, there exists at least one essential component of its solution set. As applications, we deduce the existence of essential components of the set of Ky Fan’s points based on Ky Fan Minimax Inequality, the existence of essential components of the set of Nash equilibrium points for general n-person non-cooperative games and the existence of essential components of the set of solutions of vector Ky Fan Minimax Inequality.

Suggested Citation

  • Z. Yang & Y. J. Pu, 2011. "Essential Stability of Solutions for Maximal Element Theorem with Applications," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 284-297, August.
    • Handle: RePEc:spr:joptap:v:150:y:2011:i:2:d:10.1007_s10957-011-9812-8
    DOI: 10.1007/s10957-011-9812-8
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    References listed on IDEAS

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    3. Tarafdar, E., 1991. "A fixed point theorem and equilibrium point of an abstract economy," Journal of Mathematical Economics, Elsevier, vol. 20(2), pages 211-218.
    4. Hillas, John, 1990. "On the Definition of the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 58(6), pages 1365-1390, November.
    5. Toussaint, Sabine, 1984. "On the existence of equilibria in economies with infinitely many commodities and without ordered preferences," Journal of Economic Theory, Elsevier, vol. 33(1), pages 98-115, June.
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    Cited by:

    1. 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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