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A note on Berge equilibrium

Author

Listed:
  • R. Nessah

    (LEM - Lille - Economie et Management - Université de Lille, Sciences et Technologies - CNRS - Centre National de la Recherche Scientifique)

  • M. Larbani

    (Department of Business Administration, Faculty of Economics and Management Sciences, IIUM University Jalan Gombak, 53100 Kuala Lumpur - affiliation inconnue)

  • T. Tazdait

    (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 work is a contribution on the problem of the existence of Berge equilibrium. Abalo and Kostreva give an existence theorem for this equilibrium that appears in the papers [K.Y. Abalo, M.M. Kostreva, Berge equilibrium: Some recent results from fixed-point theorems, Appl. Math. Comput. 169 (2005) 624-638; K.Y. Abalo, M.M. Kostreva, Some existence theorems of Nash and Berge equilibria, Appl. Math. Lett. 17 (2004) 569-573]. We found that the assumptions of these theorems are not sufficient for the existence of Berge equilibrium. Indeed, we construct a game that verifies Abalo and Kostreva's assumptions, but has no Berge equilibrium. Then we provide a condition that overcomes the problem in these theorems. Our conclusion is also valid for Radjef's theorem, which is the basic reference for [K.Y. Abalo, M.M. Kostreva, Berge equilibrium: Some recent results from fixed-point theorems, Appl. Math. Comput. 169 (2005) 624-638; K.Y. Abalo, M.M. Kostreva, Some existence theorems of Nash and Berge equilibria, Appl. Math. Lett. 17 (2004) 569-573; K.Y. Abalo, M.M. Kostreva, Fixed points, Nash games and their organizations, Topol. Methods Nonlinear Anal. 8 (1996) 205-215; K.Y. Abalo, M.M. Kostreva, Equi-well-posed games, J. Optim. Theory Appl. 89 (1996) 89-99]. © 2007 Elsevier Ltd. All rights reserved.

Suggested Citation

  • R. Nessah & M. Larbani & T. Tazdait, 2007. "A note on Berge equilibrium," Post-Print hal-00716706, HAL.
    • Handle: RePEc:hal:journl:hal-00716706
    DOI: 10.1016/j.aml.2006.09.005
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    Cited by:

    1. Courtois, Pierre & Nessah, Rabia & Tazdaït, Tarik, 2017. "Existence and computation of Berge equilibrium and of two refinements," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 7-15.
    2. Larbani, Moussa & Nessah, Rabia, 2008. "A note on the existence of Berge and Berge-Nash equilibria," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 258-271, March.
    3. Ahmad Nahhas & H. W. Corley, 2017. "A Nonlinear Programming Approach to Determine a Generalized Equilibrium for N-Person Normal Form Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-15, September.
    4. Schouten, Jop & Borm, Peter & Hendrickx, Ruud, 2018. "Unilateral Support Equilibria," Discussion Paper 2018-011, Tilburg University, Center for Economic Research.
    5. Messaoud Deghdak & Monique Florenzano, 2011. "On The Existence Of Berge'S Strong Equilibrium," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 325-340.
    6. Tarik Tazdaït & Moussa Larbani & Rabia Nessah, 2007. "On Berge Equilibrium," CIRED Working Papers halshs-00271452, HAL.
    7. Ünveren, Burak & Donduran, Murat & Barokas, Guy, 2023. "On self- and other-regarding cooperation: Kant versus Berge," Games and Economic Behavior, Elsevier, vol. 141(C), pages 1-20.
    8. Schouten, Jop, 2022. "Cooperation, allocation and strategy in interactive decision-making," Other publications TiSEM d5d41448-8033-4f6b-8ec0-c, Tilburg University, School of Economics and Management.
    9. Antonin Pottier & Rabia Nessah, 2014. "Berge–Vaisman And Nash Equilibria: Transformation Of Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-8.

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