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On The Strong Hybrid Solution Of An N-Person Game

Author

Listed:
  • Bertrand Crettez

    (CRED - Centre de Recherche en Economie et Droit - Université Paris-Panthéon-Assas)

  • Rabia Nessah

    (LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - Université de Lille - CNRS - Centre National de la Recherche Scientifique)

  • 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 - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique)

Abstract

We propose a new notion of coalitional equilibrium, the strong hybrid solution, which is a refinement of Zhao's hybrid solution. It is well suited to study situations where people cooperate within coalitions but where coalitions compete with one another. In the strong hybrid solution, as opposed to the hybrid solution, the strategy profile assigned to each coalition is strongly Pareto optimal. We show that there exists a strong hybrid solution whenever preferences are partially quasi-transferable.

Suggested Citation

  • Bertrand Crettez & Rabia Nessah & Tarik Tazdaït, 2022. "On The Strong Hybrid Solution Of An N-Person Game," Post-Print hal-03875293, HAL.
    • Handle: RePEc:hal:journl:hal-03875293
    DOI: 10.1016/j.mathsocsci.2021.07.006
    Note: View the original document on HAL open archive server: https://hal.science/hal-03875293
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    References listed on IDEAS

    as
    1. Parkash Chander, 2007. "The gamma-core and coalition formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 539-556, April.
    2. Scarf, Herbert E., 1971. "On the existence of a coopertive solution for a general class of N-person games," Journal of Economic Theory, Elsevier, vol. 3(2), pages 169-181, June.
    3. Zhao, Jingang, 1999. "A [beta]-Core Existence Result and Its Application to Oligopoly Markets," Games and Economic Behavior, Elsevier, vol. 27(1), pages 153-168, April.
    4. Borm, P.E.M. & Tijs, S.H. & van den Aarssen, J.C.M., 1988. "Pareto equilibria in multiobjective games," Other publications TiSEM a02573c0-8c7e-409d-bc75-0, Tilburg University, School of Economics and Management.
    5. Zhao, Jingang, 1992. "The hybrid solutions of an N-person game," Games and Economic Behavior, Elsevier, vol. 4(1), pages 145-160, January.
    6. 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.
    7. Rader, Trout, 1972. "Theory of General Economic Equilibrium," Elsevier Monographs, Elsevier, edition 1, number 9780125750400.
    8. Yang, Zhe & Yuan, George Xianzhi, 2019. "Some generalizations of Zhao’s theorem: Hybrid solutions and weak hybrid solutions for games with nonordered preferences," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 94-100.
    9. Lan Di & George X. Yuan & Tu Zeng, 2021. "The consensus equilibria of mining gap games related to the stability of Blockchain Ecosystems," The European Journal of Finance, Taylor & Francis Journals, vol. 27(4-5), pages 419-440, March.
    10. Yano, Makoto, 1990. "A Local Theory of Cooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(3), pages 301-324.
    11. Ichiishi, Tatsuro, 1981. "A Social Coalitional Equilibrium Existence Lemma," Econometrica, Econometric Society, vol. 49(2), pages 369-377, March.
    12. Noguchi, Mitsunori, 2018. "Alpha cores of games with nonatomic asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 1-12.
    13. Simon Wilkie & Dimitrios Diamantaras, 1996. "On the set of Pareto efficient allocations in economies with public goods (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 371-379.
    14. Zhao, Jingang, 1996. "The hybrid equilibria and core selection in exchange economies with externalities," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 387-407.
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    Cited by:

    1. Wang, Lei & Zhao, Jingang, 2024. "The core in an N-firm dynamic Cournot oligopoly," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 20-26.

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