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Ky Fan Inequalities and Nash Equilibrium Points without Semicontinuity and Compactness

Author

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  • M. B. Lignola

    (Dipartimento di Matematica e Applicazioni “R. Caccioppoli,”)

Abstract

In this paper, a Ky Fan inequality without compactness and semicontinuity assumptions is proved. The inequality is next applied in order to obtain existence results for Nash equilibrium points for two-person games in topological vector spaces and in reflexive Banach spaces.

Suggested Citation

  • M. B. Lignola, 1997. "Ky Fan Inequalities and Nash Equilibrium Points without Semicontinuity and Compactness," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 137-145, July.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:1:d:10.1023_a:1022611820107
    DOI: 10.1023/A:1022611820107
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    Citations

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    Cited by:

    1. Brânzei, R. & Morgan, J. & Scalzo, V. & Tijs, S.H., 2002. "Approximate Fixed Point Theorems in Banach Spaces with Applications in Game Theory," Other publications TiSEM 72176fe7-80c2-4a99-a9e4-d, Tilburg University, School of Economics and Management.
    2. C. Pensevalle & G. Pieri, 2000. "On Existence of Nash Equilibria of Games with Constraints on Multistrategies," Journal of Optimization Theory and Applications, Springer, vol. 107(3), pages 601-613, December.
    3. Rabia Nessah & Guoqiang Tian, 2013. "Existence of Solution of Minimax Inequalities, Equilibria in Games and Fixed Points Without Convexity and Compactness Assumptions," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 75-95, April.
    4. 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.
    5. Rabia Nessah & Kristiaan Kerstens, 2008. "Characterizations of the Existence of Nash Equilibria with Non-convex Strategy Sets," Working Papers 2008-ECO-13, IESEG School of Management.
    6. A. Ziad, 2001. "A Counterexample to 0-Diagonal Quasiconcavity in a Minimax Inequality," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 457-462, May.
    7. Rabia Nessah & Guoqiang Tian, 2008. "Existence of Equilibrium in Minimax Inequalities, Saddle Points, Fixed Points, and Games without Convexity Sets," Working Papers 2008-ECO-15, IESEG School of Management, revised Nov 2010.
    8. Francesco Ciardiello, 2007. "Convexity on Nash Equilibria without Linear Structure," Quaderni DSEMS 15-2007, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia.
    9. Xinyu Zhang & Chunyan Yang & Renjie Han & Shiqing Zhang, 2024. "Nash’s Existence Theorem for Non-Compact Strategy Sets," Mathematics, MDPI, vol. 12(13), pages 1-10, June.
    10. Francesco Ciardiello, 2007. "Some Examples and Counterexamples about Continuity on Equilibrium Problems," Quaderni DSEMS 16-2007, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia.

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