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A New Theorem to Find Berge Equilibria

Author

Listed:
  • Olivier Musy

    () (EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

  • Antonin Pottier
  • Tarik Tazdaït

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Olivier Musy & Antonin Pottier & Tarik Tazdaït, 2012. "A New Theorem to Find Berge Equilibria," Post-Print hal-01385826, HAL.
  • Handle: RePEc:hal:journl:hal-01385826
    Note: View the original document on HAL open archive server: https://hal-univ-paris10.archives-ouvertes.fr/hal-01385826
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    References listed on IDEAS

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    1. 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, August.
    2. 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.
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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. Jarosław Pykacz & Paweł Bytner & Piotr Frąckiewicz, 2019. "Example of a Finite Game with No Berge Equilibria at All," Games, MDPI, Open Access Journal, vol. 10(1), pages 1-4, January.
    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. 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.
    5. 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.
    6. Bertrand Crettez, 2017. "A New Sufficient Condition for a Berge Equilibrium to be a Berge–Vaisman Equilibrium," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 15(3), pages 451-459, September.
    7. Bertrand Crettez, 2017. "On Sugden’s “mutually beneficial practice” and Berge equilibrium," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 64(4), pages 357-366, December.
    8. Schouten, Jop & Borm, Peter & Hendrickx, Ruud, 2018. "Unilateral Support Equilibria," Discussion Paper 2018-011, Tilburg University, Center for Economic Research.

    More about this item

    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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