IDEAS home Printed from https://ideas.repec.org/a/spr/jqecon/v17y2019i4d10.1007_s40953-019-00168-w.html
   My bibliography  Save this article

Unilateral Support Equilibrium, Berge Equilibrium, and Team Problems Solutions

Author

Listed:
  • Bertrand Crettez

    (Université Panthéon-Assas, Paris II, CRED, EA 7321)

Abstract

We compare two notions of equilibrium for other-regarding agents, namely Berge and unilateral support equilibria. A Berge equilibrium is a strategy profile such that the teammates of each agent choose their strategies in order to maximize his utility. A unilateral support equilibrium is a strategy profile such that the teammates of each agent non-cooperatively choose their strategies to maximize his utility. By definition the level of cooperation in a unilateral support equilibrium is no higher than in a Berge equilibrium. Yet, relying on ideas from Team theory, we provide conditions under which a unilateral support equilibrium is also a Berge equilibrium. We also provide conditions under which a unilateral support equilibrium is a Berge–Vaisman equilibrium, i.e., a strategy profile which is a Berge equilibrium and such that the payoff of each player is no lower than his maximin value.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jqecon:v:17:y:2019:i:4:d:10.1007_s40953-019-00168-w
    DOI: 10.1007/s40953-019-00168-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40953-019-00168-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s40953-019-00168-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    6. Schouten, Jop & Borm, Peter & Hendrickx, Ruud, 2018. "Unilateral Support Equilibria," Other publications TiSEM 02dd1da8-0dad-48f8-8fe1-6, Tilburg University, School of Economics and Management.
    7. Olivier Musy & Antonin Pottier & Tarik Tazdait, 2012. "A New Theorem To Find Berge Equilibria," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1-10.
    8. 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.
    9. 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.
    10. J. Marschak, 1955. "Elements for a Theory of Teams," Management Science, INFORMS, vol. 1(2), pages 127-137, January.
    11. Guala, Francesco & Mittone, Luigi & Ploner, Matteo, 2013. "Group membership, team preferences, and expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 86(C), pages 183-190.
    12. Olivier Musy & Antonin Pottier & Tarik Tazdait, 2012. "A New Theorem To Find Berge Equilibria," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1-10.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Crettez, Bertrand & Nessah, Rabia, 2020. "On the existence of unilateral support equilibrium," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 41-47.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Schouten, Jop & Borm, Peter & Hendrickx, Ruud, 2018. "Unilateral Support Equilibria," Discussion Paper 2018-011, Tilburg University, Center for Economic Research.
    2. 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.
    3. 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.
    4. 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.
    5. Schouten, Jop & Borm, Peter & Hendrickx, Ruud, 2018. "Unilateral Support Equilibria," Other publications TiSEM 02dd1da8-0dad-48f8-8fe1-6, Tilburg University, School of Economics and Management.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Crettez, Bertrand & Nessah, Rabia, 2020. "On the existence of unilateral support equilibrium," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 41-47.
    11. 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.
    12. 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.
    13. Rabia Nessah & Moussa Larbani, 2014. "Berge–Zhukovskii Equilibria: Existence And Characterization," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-11.
    14. Gonzalo Cisternas & Aaron Kolb, 2020. "Signaling with Private Monitoring," Papers 2007.15514, arXiv.org.
    15. 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.
    16. 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.
    17. Bertrand Crettez, 2017. "On Hobbes’s state of nature and game theory," Theory and Decision, Springer, vol. 83(4), pages 499-511, December.
    18. Mehrdad Vahabi, 2012. "Political Economy of Conflict Foreword," Revue d'économie politique, Dalloz, vol. 122(2), pages 153-169.
    19. Sylvain Baumann, 2017. "Spying Solution In The Framework Of Terrorist Conflicts," Post-Print hal-02949086, HAL.
    20. Alan Beggs, 2021. "Afriat and arbitrage," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 167-176, October.

    More about this item

    Keywords

    Berge equilibrium; Berge–Vaisman equilibrium; Berge–Nash equilibrium; Unilateral support equilibrium; Team optimal solution; Person-by-person optimal solution; Mutually beneficial practice;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D - Microeconomics

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jqecon:v:17:y:2019:i:4:d:10.1007_s40953-019-00168-w. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.