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Mutual support in games: Some properties of Berge equilibria

Author

Listed:
  • A.M. Colman

    (Department of Psychology [Leicester] - University of Leicester)

  • T.W. Körner

    (DPMMS - Department of Pure Mathematics and Mathematical Statistics - CMS - Faculty of mathematics Centre for Mathematical Sciences [Cambridge] - CAM - University of Cambridge [UK])

  • O. Musy

    (EconomiX - EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

  • T. 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)

Abstract

The Berge equilibrium concept formalizes mutual support among players motivated by the altruistic social value orientation in games. We prove some basic results for Berge equilibria and their relations to Nash equilibria, and we provide a straightforward method for finding Berge equilibria in n-player games. We explore some specific examples, and we explain how the Berge equilibrium provides a compelling model of cooperation in social dilemmas. We show that the Berge equilibrium also explains coordination in some common interest games and is partially successful in explaining the payoff dominance phenomenon, and we comment that the theory of team reasoning provides alternative solutions to these problems. © 2011 Elsevier Inc.

Suggested Citation

  • 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.
    • Handle: RePEc:hal:journl:hal-00716357
    DOI: 10.1016/j.jmp.2011.02.001
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    Citations

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    Cited by:

    1. 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.
    2. Jarosław Pykacz & Paweł Bytner & Piotr Frąckiewicz, 2019. "Example of a Finite Game with No Berge Equilibria at All," Games, MDPI, vol. 10(1), pages 1-4, January.
    3. Ahmad Nahhas & H. W. Corley, 2017. "A Nonlinear Programming Approach to Determine a Generalized Equilibrium for N-Person Normal Form Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-15, September.
    4. Schouten, Jop & Borm, Peter & Hendrickx, Ruud, 2018. "Unilateral Support Equilibria," Discussion Paper 2018-011, Tilburg University, Center for Economic Research.
    5. Sylvain Baumann, 2017. "Spying Solution In The Framework Of Terrorist Conflicts," Post-Print hal-02949086, HAL.
    6. Ünveren, Burak & Donduran, Murat & Barokas, Guy, 2023. "On self- and other-regarding cooperation: Kant versus Berge," Games and Economic Behavior, Elsevier, vol. 141(C), pages 1-20.
    7. Schouten, Jop, 2022. "Cooperation, allocation and strategy in interactive decision-making," Other publications TiSEM d5d41448-8033-4f6b-8ec0-c, Tilburg University, School of Economics and Management.
    8. 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.
    9. Briony D Pulford & Eva M Krockow & Andrew M Colman & Catherine L Lawrence, 2016. "Social Value Induction and Cooperation in the Centipede Game," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-21, March.
    10. Guilhem Lecouteux, 2018. "What does “we” want? Team Reasoning, Game Theory, and Unselfish Behaviours," Revue d'économie politique, Dalloz, vol. 128(3), pages 311-332.
    11. Bertrand Crettez, 2017. "On Hobbes’s state of nature and game theory," Theory and Decision, Springer, vol. 83(4), pages 499-511, December.
    12. 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.
    13. 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.
    14. Giannini Italino Alves Vieira & Leandro Chaves Rêgo, 2020. "Berge Solution Concepts in the Graph Model for Conflict Resolution," Group Decision and Negotiation, Springer, vol. 29(1), pages 103-125, February.
    15. Rodica Ioana Lung & Mihai Suciu & Noémi Gaskó & D Dumitrescu, 2015. "Characterization and Detection of ϵ-Berge-Zhukovskii Equilibria," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-15, July.
    16. Bertrand Crettez, 2017. "On Sugden’s “mutually beneficial practice” and Berge equilibrium," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 64(4), pages 357-366, December.
    17. Mehrdad Vahabi, 2012. "Avant-Propos," Revue d'économie politique, Dalloz, vol. 122(2), pages 135-151.

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