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Inverse Maximum Theorems and Their Relations with Equilibrium and Fixed Point Theorems

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  • John Cotrina

    (Universidad del Pacífico)

  • Raúl Fierro

    (Pontificia Universidad Católica de Valparaíso)

Abstract

This work is devoted to inverse maximum theorems and is motivated by the ones given by Komiya and Yamauchi. Also, we show that the results by Arrow and Debreu, on the existence of solutions for generalized Nash games, and the Kakutani–Fan–Glicksberg fixed point theorem can be derived from the Debreu–Fan–Glicksberg theorem, for classical Nash games.

Suggested Citation

  • John Cotrina & Raúl Fierro, 2023. "Inverse Maximum Theorems and Their Relations with Equilibrium and Fixed Point Theorems," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1118-1129, September.
    • Handle: RePEc:spr:joptap:v:198:y:2023:i:3:d:10.1007_s10957-023-02279-0
    DOI: 10.1007/s10957-023-02279-0
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    References listed on IDEAS

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    1. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
    2. Morgan, Jacqueline & Scalzo, Vincenzo, 2007. "Pseudocontinuous functions and existence of Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 174-183, February.
    3. Tian, Guoqiang & Zhou, Jianxin, 1995. "Transfer continuities, generalizations of the Weierstrass and maximum theorems: A full characterization," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 281-303.
    4. Hidetoshi Komiya, 1997. "Inverse of the Berge maximum theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 371-375.
    5. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    6. Orestes Bueno & John Cotrina, 2021. "Existence of Projected Solutions for Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 344-362, October.
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