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Existence and computation of Berge equilibrium and of two refinements

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  • Courtois, Pierre
  • Nessah, Rabia
  • Tazdaït, Tarik

Abstract

This paper presents existence conditions as well as computation methods for Berge equilibrium and two refinements: Berge–Vaisman equilibrium and Berge–Nash equilibrium. Each equilibrium concept is interpreted and illustrated on the basis of relevant examples and general existence conditions satisfying weak continuity and quasi-concavity conditions are provided.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:mateco:v:72:y:2017:i:c:p:7-15
    DOI: 10.1016/j.jmateco.2017.04.004
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    References listed on IDEAS

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    1. R. Nessah & M. Larbani, 2007. "New Sufficient Conditions for the g-maximum Inequality," Post-Print hal-00257307, HAL.
    2. Michael R. Baye & Guoqiang Tian & Jianxin Zhou, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," Review of Economic Studies, Oxford University Press, vol. 60(4), pages 935-948.
    3. R. Nessah & M. Larbani & T. Tazdait, 2007. "A note on Berge equilibrium," Post-Print hal-00204224, HAL.
    4. 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.
    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. R. Nessah & G. Tian, 2013. "Existence of solution of minimax inequalities, equilibria in games and fixed points without convexity and compactness assumptions," Post-Print hal-00785017, HAL.
    7. 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.
    8. Nessah, Rabia & Tazdaı¨t, Tarik, 2013. "Absolute optimal solution for a compact and convex game," European Journal of Operational Research, Elsevier, vol. 224(2), pages 353-361.
    9. 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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    Cited by:

    1. Schouten, Jop & Borm, Peter & Hendrickx, Ruud, 2018. "Unilateral Support Equilibria," Discussion Paper 2018-011, Tilburg University, Center for Economic Research.

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