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A New Sufficient Condition for a Berge Equilibrium to be a Berge–Vaisman Equilibrium

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  • Bertrand Crettez

    (Université Panthéon-Assas, Paris II, CRED, EA 7321)

Abstract

In a Berge equilibrium each player is supported by his teammates in the sense that all the other players maximize his utility. A Berge equilibrium in which each player’s payoff is no lower than his maximin gain is called a Berge–Vaisman equilibrium. We propose and study a new sufficient condition for Berge equilibrium to be a Berge–Vaisman equilibrium. A Berge equilibrium is a Berge–Vaisman equilibrium if no individual equilibrium strategy is strongly dominated. We also give a necessary and sufficient condition for a Berge equilibrium to be a Berge–Vaisman equilibrium in two-player-two-action games.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jqecon:v:15:y:2017:i:3:d:10.1007_s40953-016-0066-z
    DOI: 10.1007/s40953-016-0066-z
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    References listed on IDEAS

    as
    1. Antonin Pottier & R Nessah, 2014. "Vaisman and Nash Equilibria: Transformation of Games," Post-Print hal-01523019, HAL.
    2. 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.
    3. 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.
    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.
    6. 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.
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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.

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    More about this item

    Keywords

    Berge equilibrium; Berge–Vaisman equilibrium; Sufficient Condition;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D - Microeconomics

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