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Strong Berge and Pareto Equilibrium Existence for a Noncooperative Game

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  • Tarik Tazdaït

    (CIRED - centre international de recherche sur l'environnement et le développement - Cirad - Centre de Coopération Internationale en Recherche Agronomique pour le Développement - EHESS - École des hautes études en sciences sociales - AgroParisTech - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique)

  • Moussa Larbani
  • Rabia Nessah

    (UMR CNRS 8179 - Université de Lille, Sciences et Technologies - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper, we study the main properties of the strong Berge equilibrium which is also a Pareto efficient (SBPE) and the strong Nash equilibrium (SNE). We prove that any SBPE is also a SNE, we prove also existence theorem of SBPE based on the KyFan inequality. Finally, we also provide a method for computing SPBE.

Suggested Citation

  • Tarik Tazdaït & Moussa Larbani & Rabia Nessah, 2007. "Strong Berge and Pareto Equilibrium Existence for a Noncooperative Game," Working Papers halshs-00271464, HAL.
    • Handle: RePEc:hal:wpaper:halshs-00271464
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00271464
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    References listed on IDEAS

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    1. Michel Le Breton & Hideo Konishi & Shlomo Weber, 1996. "Equivalence of strong and coalition-proof Nash equilibria in games without spillovers (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 97-113.
    2. Hirai, Toshiyuki & Masuzawa, Takuya & Nakayama, Mikio, 2006. "Coalition-proof Nash equilibria and cores in a strategic pure exchange game of bads," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 162-170, March.
    3. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
    4. Tarik Tazdaït & Moussa Larbani & Rabia Nessah, 2007. "On Berge Equilibrium," CIRED Working Papers halshs-00271452, HAL.
    5. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Equilibria in a Model with Partial Rivalry," Journal of Economic Theory, Elsevier, vol. 72(1), pages 225-237, January.
    6. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
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