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Minimax inequality equivalent to the Fan-Knaster-Kuratowski-Mazurkiewicz Theorem

Author

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  • Lin, Y. Joseph
  • Tian, Guoqiang

Abstract

The purpose of this note is to give further generalizations of the Ky Fan minimax inequality by relaxing the compactness and convexity of sets and the quasi-concavity of the functional and to show that our minimax inequalities are equivalent to the Fan-Knaster-Kuratowski-Mazurkiewicz (FKKM) theorem and a modified FKKM theorem given in this note.

Suggested Citation

  • Lin, Y. Joseph & Tian, Guoqiang, 1993. "Minimax inequality equivalent to the Fan-Knaster-Kuratowski-Mazurkiewicz Theorem," MPRA Paper 41220, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:41220
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    File URL: https://mpra.ub.uni-muenchen.de/41220/1/MPRA_paper_41220.pdf
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    References listed on IDEAS

    as
    1. Tian, Guoqiang, 1992. "Existence of equilibrium in abstract economies with discontinuous payoffs and non-compact choice spaces," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 379-388.
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    Cited by:

    1. Tian, Guoqiang, 2012. "A Full Characterization on Fixed-Point Theorem, Minimax Inequality, Saddle Point, and KKM Theorem," MPRA Paper 57929, University Library of Munich, Germany, revised Jul 2014.
    2. Tieying Huang & Jiuqiang Liu, 2022. "Fuzzy Strong Nash Equilibria in Generalized Fuzzy Games with Application in Urban Public-Sports Services," Mathematics, MDPI, vol. 10(20), pages 1-10, October.

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    More about this item

    Keywords

    The minimax inequality; Variational inequalities; The FKKM theorem; Noncompact and nonconvex sets; Equivalence;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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