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On Berge Equilibrium

Author

Listed:
  • Tarik Tazdaït

    (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)

  • Moussa Larbani
  • Rabia Nessah

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

Abstract

Based on the notion of equilibrium of a coalition P relatively to a coalition K, of Berge, Zhukovskii has introduced Berge equilibrium as an alternative solution to Nash equilibrium for non cooperative games in normal form. The essential advantage of this equilibrium is that it does not require negotiation of any player with the remaining players, which is not the case when a game has more than one Nashequilibrium. The problem of existence of Berge equilibrium is more difficult (compared to that of Nash). This paper is a contribution to the problem of existence and computation of Berge equilibrium of a non cooperative game. Indeed, using the g-maximum equality, we establish the existence of a Berge equilibrium of a non-cooperative game in normal form. In addition, we give sufficient conditions for theexistence of a Berge equilibrium which is also a Nash equilibrium. This allows us to get equilibria enjoying the properties of both concepts of solution. Finally, using these results, we provide two methods for the computation of Berge equilibria: the first one computes Berge equilibria; the second one computes Berge equilibria which are also Nash equilibria.

Suggested Citation

  • Tarik Tazdaït & Moussa Larbani & Rabia Nessah, 2007. "On Berge Equilibrium," Working Papers halshs-00271452, HAL.
  • Handle: RePEc:hal:wpaper:halshs-00271452
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00271452
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    References listed on IDEAS

    as
    1. R. Nessah & M. Larbani & T. Tazdait, 2007. "A note on Berge equilibrium," Post-Print hal-00716706, HAL.
    2. Tarik Tazdaït & Moussa Larbani & Rabia Nessah, 2007. "On Berge Equilibrium," CIRED Working Papers halshs-00271452, HAL.
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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. Tarik Tazdaït & Moussa Larbani & Rabia Nessah, 2007. "On Berge Equilibrium," Working Papers halshs-00271452, HAL.
    3. Tarik Tazdaït & Moussa Larbani & Rabia Nessah, 2007. "Strong Berge and Pareto Equilibrium Existence for a Noncooperative Game," Working Papers halshs-00271464, HAL.
    4. 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.
    5. 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.
    6. 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.
    7. Schouten, Jop & Borm, Peter & Hendrickx, Ruud, 2018. "Unilateral Support Equilibria," Discussion Paper 2018-011, Tilburg University, Center for Economic Research.
    8. Rabia Nessah & Raluca Parvulescu, 2017. "On the Existence of Pareto Efficient Nash Equilibria in Discontinuous Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-13, September.
    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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    2. 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.
    3. 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.
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