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Variational Analysis of Generalized Ordinal Nash Games on Banach Spaces

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  • Shivani Valecha

    (Indian Institute of Technology Bhilai)

  • Asrifa Sultana

    (Indian Institute of Technology Bhilai)

Abstract

We study the generalized ordinal Nash games defined over Banach spaces by employing variational techniques. To reformulate these games in terms of quasi-variational inequality problems, we will first form a suitable principal operator and study some significant properties of this operator. Then, we deduce the sufficient conditions to obtain an equilibrium for the proposed game by solving an auxiliary quasi-variational inequality. Based on this quasi-variational reformulation, we derive the existence of equilibrium for generalized ordinal Nash games with mid-point continuous preference maps. We apply the derived results to ensure the presence of Pareto equilibrium for multi-objective games and dynamic electricity markets.

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  • Shivani Valecha & Asrifa Sultana, 2026. "Variational Analysis of Generalized Ordinal Nash Games on Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 208(1), pages 1-25, January.
    • Handle: RePEc:spr:joptap:v:208:y:2026:i:1:d:10.1007_s10957-025-02838-7
    DOI: 10.1007/s10957-025-02838-7
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    References listed on IDEAS

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    1. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    2. Marco Castellani & Massimiliano Giuli, 2024. "A Continuity Result for the Adjusted Normal Cone Operator," Journal of Optimization Theory and Applications, Springer, vol. 200(2), pages 858-873, February.
    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. Giuseppe De Marco & Jacqueline Morgan, 2007. "A Refinement Concept For Equilibria In Multicriteria Games Via Stable Scalarizations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 169-181.
    5. Juho Kokkala & Kimmo Berg & Kai Virtanen & Jirka Poropudas, 2019. "Rationalizable strategies in games with incomplete preferences," Theory and Decision, Springer, vol. 86(2), pages 185-204, March.
    6. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    7. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    8. 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.
    9. Monica Milasi & Domenico Scopelliti, 2021. "A Variational Approach to the Maximization of Preferences Without Numerical Representation," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 879-893, September.
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