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A New Theorem To Find Berge Equilibria

Author

Listed:
  • OLIVIER MUSY

    (Economix, Université Paris Ouest Nanterre La Défense, 200 Avenue de la République, 92001 Nanterre Cedex, France)

  • ANTONIN POTTIER

    (CIRED-CNRS-EHESS-Ecole des Ponts ParisTech, Campus du Jardin Tropical, 45 bis, Avenue de la Belle Gabrielle, 94736 Nogent Sur Marne Cedex, France)

  • TARIK TAZDAIT

    (CIRED-CNRS-EHESS-Ecole des Ponts ParisTech, Campus du Jardin Tropical, 45 bis, Avenue de la Belle Gabrielle, 94736 Nogent Sur Marne Cedex, France)

Abstract

This paper examines the existence of Berge equilibrium. Colmanet al.provide a theorem on the existence of this type of equilibrium in the paper [Colman, A. M., Körner, T. W., Musy, O. and Tazdaït, T. [2011] Mutual support in games: Some properties of Berge equilibria,J. Math. Psychol.55, 166–175]. This theorem has been demonstrated on the basis of a correspondence with Nash equilibrium. We propose to restate this theorem without using Nash equilibrium, and deduce a method for the computation of Berge equilibria.

Suggested Citation

  • Olivier Musy & Antonin Pottier & Tarik Tazdait, 2012. "A New Theorem To Find Berge Equilibria," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1-10.
    • Handle: RePEc:wsi:igtrxx:v:14:y:2012:i:01:n:s0219198912500053
    DOI: 10.1142/S0219198912500053
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    References listed on IDEAS

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    1. Courtois, Pierre & Nessah, Rabia & Tazdaït, Tarik, 2015. "How To Play Games? Nash Versus Berge Behaviour Rules," Economics and Philosophy, Cambridge University Press, vol. 31(1), pages 123-139, March.
    2. Ken Binmore, 1994. "Game Theory and the Social Contract, Volume 1: Playing Fair," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262023636, December.
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    Citations

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    Cited by:

    1. Bertrand Crettez, 2019. "Unilateral Support Equilibrium, Berge Equilibrium, and Team Problems Solutions," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 17(4), pages 727-739, December.
    2. Mehrdad Vahabi, 2012. "Political Economy of Conflict Foreword," Revue d'économie politique, Dalloz, vol. 122(2), pages 153-169.
    3. 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.
    4. 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.
    5. 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.
    6. Rabia Nessah & Moussa Larbani, 2014. "Berge–Zhukovskii Equilibria: Existence And Characterization," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-11.

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    More about this item

    Keywords

    Berge equilibrium; Nash equilibrium; mutual support; C72;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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