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A Modified Michael’s Selection Theorem with Application to Generalized Nash Equilibrium Problem

Author

Listed:
  • Marco Castellani

    (University of L’Aquila)

  • Massimiliano Giuli

    (University of L’Aquila)

Abstract

This paper provides a sufficient condition for the existence of solutions for generalized Nash equilibrium problems in the infinite-dimensional setting and with a countable (possibly infinite) number of players. The result has been achieved as a consequence of a modified version of Michael’s selection theorem that works even when the range space is not metrizable and the set-valued map has not closed values.

Suggested Citation

  • Marco Castellani & Massimiliano Giuli, 2023. "A Modified Michael’s Selection Theorem with Application to Generalized Nash Equilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 199-211, January.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:1:d:10.1007_s10957-022-02090-3
    DOI: 10.1007/s10957-022-02090-3
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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. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
    3. Paolo Cubiotti & Jen-Chih Yao, 2010. "Nash equilibria of generalized games in normed spaces without upper semicontinuity," Journal of Global Optimization, Springer, vol. 46(4), pages 509-519, April.
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