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Berge–Vaisman And Nash Equilibria: Transformation Of Games

Author

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  • ANTONIN POTTIER

    () (Centre International de Recherche pour l'Environnement, et le Développement CIRED-CNRS (UMR 8568), 45 bis, Avenue de la Belle Gabrielle, 94736 Nogent-sur-Marne Cedex, France)

  • RABIA NESSAH

    () (IESEG School of Management CNRS-LEM (UMR 8179), 3 rue de la Digue, 59000 Lille, France)

Abstract

In this paper, we reconsider the concept of Berge equilibrium. In a recent work, Colmanet al.[(2011)J. Math. Psych.55, 166–175] proposed a correspondence for two-player games between Berge and Nash equilibria by permutation of the utility functions. We define here more general transformations of games that lead to a correspondence with Berge and Nash equilibria and characterize all such transformations.

Suggested Citation

  • 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.
  • Handle: RePEc:wsi:igtrxx:v:16:y:2014:i:04:n:s0219198914500091
    DOI: 10.1142/S0219198914500091
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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-00204224, HAL.
    2. A.M. Colman & T.W. Körner & O. Musy & T. Tazdaït, 2011. "Mutual support in games: Some properties of Berge equilibria," Post-Print hal-00716357, HAL.
    3. 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.
    4. 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.
    5. 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, 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.
    2. 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.

    More about this item

    Keywords

    Berge equilibrium; Nash equilibrium; C72;

    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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