IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v16y2014i04ns0219198914500121.html
   My bibliography  Save this article

Berge–Zhukovskii Equilibria: Existence And Characterization

Author

Listed:
  • RABIA NESSAH

    (IESEG School of Management, CNRS-LEM (UMR 8179), 3 rue de la Digue, 59000 Lille, France)

  • MOUSSA LARBANI

    (Department of Business Administration, IIUM University, Jalan Gombak 53100, Kuala Lumpur, Malaysia)

Abstract

In this paper, we investigate the existence of Berge–Zhukovskii equilibrium in general normal form games. We characterize its existence via the existence of a symmetric Nash equilibrium of somen-person subgame derived of the initial game. The significance of the obtained results is illustrated by two applications. One in economy with environmental externalities and the other in oligopoly markets.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:igtrxx:v:16:y:2014:i:04:n:s0219198914500121
    DOI: 10.1142/S0219198914500121
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219198914500121
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219198914500121?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. 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.
    2. 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.
    3. 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.
    4. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, April.
    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. 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. Crettez, Bertrand & Nessah, Rabia, 2020. "On the existence of unilateral support equilibrium," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 41-47.
    3. 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.
    4. 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.
    5. 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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    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. Crettez, Bertrand & Nessah, Rabia, 2020. "On the existence of unilateral support equilibrium," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 41-47.
    9. Mehrdad Vahabi, 2012. "Political Economy of Conflict Foreword," Revue d'économie politique, Dalloz, vol. 122(2), pages 153-169.
    10. Campi, Luciano & Zabaljauregui, Diego, 2020. "Optimal market making under partial information with general intensities," LSE Research Online Documents on Economics 104612, London School of Economics and Political Science, LSE Library.
    11. Kaido, Hiroaki, 2017. "Asymptotically Efficient Estimation Of Weighted Average Derivatives With An Interval Censored Variable," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1218-1241, October.
    12. Andrea Attar & Thomas Mariotti & François Salanié, 2021. "Entry-Proofness and Discriminatory Pricing under Adverse Selection," American Economic Review, American Economic Association, vol. 111(8), pages 2623-2659, August.
    13. Askoura, Youcef & Billot, Antoine, 2021. "Social decision for a measure society," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    14. Xiaohong Chen & Andres Santos, 2018. "Overidentification in Regular Models," Econometrica, Econometric Society, vol. 86(5), pages 1771-1817, September.
    15. He, Wei & Sun, Yeneng, 2013. "Stationary Markov Perfect Equilibria in Discounted Stochastic Games," MPRA Paper 51274, University Library of Munich, Germany.
    16. Duggan, John, 2011. "General conditions for the existence of maximal elements via the uncovered set," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 755-759.
    17. Eduardo Perez & Delphine Prady, 2012. "Complicating to Persuade?," Working Papers hal-03583827, HAL.
    18. Romain Blanchard & Laurence Carassus & Miklós Rásonyi, 2018. "No-arbitrage and optimal investment with possibly non-concave utilities: a measure theoretical approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 241-281, October.
    19. René Aïd & Matteo Basei & Giorgia Callegaro & Luciano Campi & Tiziano Vargiolu, 2020. "Nonzero-Sum Stochastic Differential Games with Impulse Controls: A Verification Theorem with Applications," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 205-232, February.
    20. He, Wei & Yannelis, Nicholas C., 2015. "Equilibrium theory under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 86-95.

    More about this item

    Keywords

    Berge–Zhukovskii equilibrium; Nash equilibrium; mutual support; fixed point; oligopoly markets; C72;
    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

    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:wsi:igtrxx:v:16:y:2014:i:04:n:s0219198914500121. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/igtr/igtr.shtml .

    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.