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A note on ideal Nash equilibrium in multicriteria games

Author

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  • M.S. Radjef

    (Unité de recherche LaMOS = Research unit LaMOS - Unité de recherche Laboratoire de Modélisation et Optimisation des Systèmes [Université de Béjaïa] - UB - Université Abderrahmane Mira [Université de Béjaïa] = University Abderrahmane Mira [University of Béjaïa])

  • K. Fahem

    (UMMTO - Université Mouloud Mammeri [Tizi Ouzou], CIRED - centre international de recherche sur l'environnement et le développement - Cirad - Centre de Coopération Internationale en Recherche Agronomique pour le Développement - EHESS - École des hautes études en sciences sociales - AgroParisTech - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper is a contribution to the problem of existence of ideal Nash equilibrium in noncooperative multicriteria games in strategic form. We give an existence theorem by using the maximal element theorem due to Deguire et al. [P. Deguire, K.K. Tan, G.X.-Z. Yuan, The study of maximal elements, fixed points for Ls-majorized mappings and their applications to minimax and variational inequalities in product topological spaces, Nonlinear Anal. TMA 37 (1999) 933-951] and the characterization provided by Voorneveld et al. [M. Voorneveld, S. Grahn, M. Dufwenberg, Ideal equilibria in non cooperative multicriteria games, Math. Methods Oper. Res. 52 (2000) 65-77]. © 2008 Elsevier Ltd. All rights reserved.

Suggested Citation

  • M.S. Radjef & K. Fahem, 2008. "A note on ideal Nash equilibrium in multicriteria games," Post-Print hal-00716317, HAL.
    • Handle: RePEc:hal:journl:hal-00716317
    DOI: 10.1016/j.aml.2007.12.009
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    Cited by:

    1. Yu Zhang & Shih-Sen Chang & Tao Chen, 2021. "Existence and Generic Stability of Strong Noncooperative Equilibria of Vector-Valued Games," Mathematics, MDPI, vol. 9(24), pages 1-13, December.
    2. Karima Fahem & Mohammed Radjef, 2015. "Properly efficient Nash equilibrium in multicriteria noncooperative games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(2), pages 175-193, October.
    3. Naouel Yousfi-Halimi & Mohammed Said Radjef & Hachem Slimani, 2018. "Refinement of pure Pareto Nash equilibria in finite multicriteria games using preference relations," Annals of Operations Research, Springer, vol. 267(1), pages 607-628, August.

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