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On the existence of Berge's strong equilibrium

Author

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  • Messaoud Deghdak

    (Laboratoire de Mathématiques Appliquées et Modélisation - Département de Mathématiques)

  • Monique Florenzano

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper, we establish the existence of Berge's strong equilibrium for games with n persons in infinite dimensional strategy spaces in the case where the payoff function of each player is quasi-concave. Moreover, we study the continuity of Berge's strong equilibrium correspondence and prove that most of Berge's strong games are essential.

Suggested Citation

  • Messaoud Deghdak & Monique Florenzano, 2011. "On the existence of Berge's strong equilibrium," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00611851, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00611851
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00611851
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    References listed on IDEAS

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    1. 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.
    2. Monique Florenzano, 2007. "General equilibrium," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00250167, HAL.
    3. Borglin, Anders & Keiding, Hans, 1976. "Existence of equilibrium actions and of equilibrium : A note on the `new' existence theorems," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 313-316, December.
    4. R. Nessah & M. Larbani & T. Tazdait, 2007. "A note on Berge equilibrium," Post-Print hal-00716706, HAL.
    5. Tarik Tazdaït & Moussa Larbani & Rabia Nessah, 2007. "On Berge Equilibrium," CIRED Working Papers halshs-00271452, HAL.
    6. Yu, Jian, 1999. "Essential equilibria of n-person noncooperative games," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 361-372, April.
    7. Yong-Hui Zhou & Jian Yu & Shu-Wen Xiang, 2007. "Essential stability in games with infinitely many pure strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 493-503, April.
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    More about this item

    Keywords

    Nash equilibrium; strong Berge equilibrium; fixed point; essential games.; Equilibre de Nash; équilibre fort de Berge; point fixe; jeux essentiels.;
    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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