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Reformulations for Projected Solutions of Generalized Games

Author

Listed:
  • Carlos Calderón

    (Instituto de Matemática y Ciencias Afines)

  • Marco Castellani

    (University of L’Aquila)

  • John Cotrina

    (Universidad del Pacífico)

  • Massimiliano Giuli

    (University of L’Aquila)

Abstract

We show that projected solutions of a generalized game correspond to classical ones of an auxiliary generalized game obtained by doubling the number of players. Based on this reformulation and using known results for the existence of classical solutions, we deduce some new existence results for projected solutions of generalized Nash equilibrium problems and quasivariational inequalities.

Suggested Citation

  • Carlos Calderón & Marco Castellani & John Cotrina & Massimiliano Giuli, 2025. "Reformulations for Projected Solutions of Generalized Games," Journal of Optimization Theory and Applications, Springer, vol. 204(1), pages 1-13, January.
    • Handle: RePEc:spr:joptap:v:204:y:2025:i:1:d:10.1007_s10957-024-02591-3
    DOI: 10.1007/s10957-024-02591-3
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    References listed on IDEAS

    as
    1. Morgan, Jacqueline & Scalzo, Vincenzo, 2007. "Pseudocontinuous functions and existence of Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 174-183, February.
    2. Didier Aussel & Asrifa Sultana & Vellaichamy Vetrivel, 2016. "On the Existence of Projected Solutions of Quasi-Variational Inequalities and Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 818-837, September.
    3. 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.
    4. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    5. 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.
    6. Marco Castellani & Massimiliano Giuli & Sara Latini, 2023. "Projected solutions for finite-dimensional quasiequilibrium problems," Computational Management Science, Springer, vol. 20(1), pages 1-14, December.
    7. John Cotrina & Javier Zúñiga, 2019. "Quasi-equilibrium problems with non-self constraint map," Journal of Global Optimization, Springer, vol. 75(1), pages 177-197, September.
    8. 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.
    Full references (including those not matched with items on IDEAS)

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