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Existence of Projected Solutions for Generalized Nash Equilibrium Problems

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  • Orestes Bueno

    (Universidad del Pacífico)

  • John Cotrina

    (Universidad del Pacífico)

Abstract

We study the existence of projected solutions for generalized Nash equilibrium problems defined in Banach spaces, under mild convexity assumptions for each loss function and without lower semicontinuity assumptions on the constraint maps. Our approach is based on Himmelberg’s fixed point theorem. As a consequence, we also obtain existence of projected solutions for quasi-equilibrium problems and quasi-variational inequalities. Finally, we show the existence of projected solutions for Single-Leader–Multi-Follower games.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:191:y:2021:i:1:d:10.1007_s10957-021-01941-9
    DOI: 10.1007/s10957-021-01941-9
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    References listed on IDEAS

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    7. Didier Aussel & Rachana Gupta & Aparna Mehra, 2016. "Evolutionary Variational Inequality Formulation of the Generalized Nash Equilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 74-90, April.
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    9. Didier Aussel & Anton Svensson, 2020. "A Short State of the Art on Multi-Leader-Follower Games," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 53-76, Springer.
    10. John Cotrina & Javier Zúñiga, 2018. "Time-Dependent Generalized Nash Equilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 1054-1064, December.
    11. 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.
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    Cited by:

    1. 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.

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