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The finite intersection property for equilibrium problems

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  • John Cotrina

    (Universidad del Pacífico)

  • Anton Svensson

    (Universidad de O’Higgins)

Abstract

The “finite intersection property” for bifunctions is introduced and its relationship with generalized monotonicity properties is studied. Some characterizations are considered involving the Minty equilibrium problem. Also, some results concerning existence of equilibria and quasi-equilibria are established recovering several results in the literature. Furthermore, we give an existence result for generalized Nash equilibrium problems and variational inequality problems.

Suggested Citation

  • John Cotrina & Anton Svensson, 2021. "The finite intersection property for equilibrium problems," Journal of Global Optimization, Springer, vol. 79(4), pages 941-957, April.
    • Handle: RePEc:spr:jglopt:v:79:y:2021:i:4:d:10.1007_s10898-020-00961-5
    DOI: 10.1007/s10898-020-00961-5
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    References listed on IDEAS

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    1. 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.
    2. Rabia Nessah & Guoqiang Tian, 2016. "On the existence of Nash equilibrium in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 515-540, March.
    3. O. Chaldi & Z. Chbani & H. Riahi, 2000. "Equilibrium Problems with Generalized Monotone Bifunctions and Applications to Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 105(2), pages 299-323, May.
    4. D. Aussel & N. Hadjisavvas, 2004. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 445-450, May.
    5. D. Aussel & J. Cotrina, 2013. "Quasimonotone Quasivariational Inequalities: Existence Results and Applications," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 637-652, September.
    6. M. Bianchi & R. Pini, 2005. "Coercivity Conditions for Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 79-92, January.
    7. M. Castellani & M. Giuli, 2013. "Refinements of existence results for relaxed quasimonotone equilibrium problems," Journal of Global Optimization, Springer, vol. 57(4), pages 1213-1227, December.
    8. 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. F. Fakhar & H. R. Hajisharifi & Z. Soltani, 2023. "Noncoercive and noncontinuous equilibrium problems: existence theorem in infinite-dimensional spaces," Journal of Global Optimization, Springer, vol. 86(4), pages 989-1003, August.
    2. Mircea Balaj, 2022. "Scalar and vector equilibrium problems with pairs of bifunctions," Journal of Global Optimization, Springer, vol. 84(3), pages 739-753, November.
    3. Mircea Balaj & Marco Castellani & Massimiliano Giuli, 2023. "New criteria for existence of solutions for equilibrium problems," Computational Management Science, Springer, vol. 20(1), pages 1-16, December.
    4. Nguyen Xuan Hai & Nguyen Hong Quan & Vo Viet Tri, 2023. "Some saddle-point theorems for vector-valued functions," Journal of Global Optimization, Springer, vol. 86(1), pages 141-161, May.

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