IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i24p3158-d697190.html
   My bibliography  Save this article

Existence and Generic Stability of Strong Noncooperative Equilibria of Vector-Valued Games

Author

Listed:
  • Yu Zhang

    (College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China)

  • Shih-Sen Chang

    (Center for General Education, China Medical University, Taichung 40402, Taiwan)

  • Tao Chen

    (School of Fundamental Sciences, Yunnan Open University, Kunming 650223, China)

Abstract

In this paper, we obtain an existence theorem of general strong noncooperative equilibrium point of vector-valued games, in which every player maximizes all goals. We also obtain an existence theorem of strong equilibrium point of vector-valued games with single-leader–multi-follower framework by using the upper semicontinuous of parametric strong noncooperative equilibrium point set of the followers. Moreover, we obtain some results on the generic stability of general strong noncooperative equilibrium point vector-valued games.

Suggested Citation

  • Yu Zhang & Shih-Sen Chang & Tao Chen, 2021. "Existence and Generic Stability of Strong Noncooperative Equilibria of Vector-Valued Games," Mathematics, MDPI, vol. 9(24), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3158-:d:697190
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/24/3158/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/24/3158/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zhe Yang & Yong Pu, 2012. "Existence and stability of minimax regret equilibria," Journal of Global Optimization, Springer, vol. 54(1), pages 17-26, September.
    2. Mark Voorneveld & Sofia Grahn & Martin Dufwenberg, 2000. "Ideal equilibria in noncooperative multicriteria games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(1), pages 65-77, September.
    3. M.S. Radjef & K. Fahem, 2008. "A note on ideal Nash equilibrium in multicriteria games," Post-Print hal-00716317, HAL.
    4. Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, January.
    5. Xie Ding, 2012. "Equilibrium existence theorems for multi-leader-follower generalized multiobjective games in FC-spaces," Journal of Global Optimization, Springer, vol. 53(3), pages 381-390, July.
    6. Yu, Jian, 1999. "Essential equilibria of n-person noncooperative games," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 361-372, April.
    7. Zhe Yang & Yan Ju, 2016. "Existence and generic stability of cooperative equilibria for multi-leader-multi-follower games," Journal of Global Optimization, Springer, vol. 65(3), pages 563-573, July.
    Full references (including those not matched with items on IDEAS)

    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. Zhe Yang & Yan Ju, 2016. "Existence and generic stability of cooperative equilibria for multi-leader-multi-follower games," Journal of Global Optimization, Springer, vol. 65(3), pages 563-573, July.
    2. Naouel Yousfi-Halimi & Mohammed Said Radjef & Hachem Slimani, 2018. "Refinement of pure Pareto Nash equilibria in finite multicriteria games using preference relations," Annals of Operations Research, Springer, vol. 267(1), pages 607-628, August.
    3. Maria Carmela Ceparano & Jacqueline Morgan, 2017. "Equilibrium selection in multi-leader-follower games with vertical information," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 526-543, October.
    4. Karima Fahem & Mohammed Radjef, 2015. "Properly efficient Nash equilibrium in multicriteria noncooperative games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(2), pages 175-193, October.
    5. Axel Dreves & Christian Kanzow, 2011. "Nonsmooth optimization reformulations characterizing all solutions of jointly convex generalized Nash equilibrium problems," Computational Optimization and Applications, Springer, vol. 50(1), pages 23-48, September.
    6. Flam, Sjur & Ruszczynski, A., 2006. "Computing Normalized Equilibria in Convex-Concave Games," Working Papers 2006:9, Lund University, Department of Economics.
    7. Giorgia Oggioni & Yves Smeers & Elisabetta Allevi & Siegfried Schaible, 2012. "A Generalized Nash Equilibrium Model of Market Coupling in the European Power System," Networks and Spatial Economics, Springer, vol. 12(4), pages 503-560, December.
    8. Alejandro Jofré & R. Terry Rockafellar & Roger J-B. Wets, 2007. "Variational Inequalities and Economic Equilibrium," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 32-50, February.
    9. Ciarcià, Carla & Daniele, Patrizia, 2016. "New existence theorems for quasi-variational inequalities and applications to financial models," European Journal of Operational Research, Elsevier, vol. 251(1), pages 288-299.
    10. Oriol Carbonell-Nicolau & Richard McLean, 2013. "Approximation results for discontinuous games with an application to equilibrium refinement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 1-26, September.
    11. Contreras, Javier & Krawczyk, Jacek & Zuccollo, James, 2008. "The invisible polluter: Can regulators save consumer surplus?," MPRA Paper 9890, University Library of Munich, Germany.
    12. Jiang, Zhoutong & Lei, Chao & Ouyang, Yanfeng, 2020. "Optimal investment and management of shared bikes in a competitive market," Transportation Research Part B: Methodological, Elsevier, vol. 135(C), pages 143-155.
    13. Anna Rettieva, 2017. "Equilibria in Dynamic Multicriteria Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-21, March.
    14. Hadi Charkhgard & Martin Savelsbergh & Masoud Talebian, 2018. "Nondominated Nash points: application of biobjective mixed integer programming," 4OR, Springer, vol. 16(2), pages 151-171, June.
    15. Alexey Izmailov & Mikhail Solodov, 2014. "On error bounds and Newton-type methods for generalized Nash equilibrium problems," Computational Optimization and Applications, Springer, vol. 59(1), pages 201-218, October.
    16. J. Contreras & J. B. Krawczyk & J. Zuccollo, 2016. "Economics of collective monitoring: a study of environmentally constrained electricity generators," Computational Management Science, Springer, vol. 13(3), pages 349-369, July.
    17. Benjamin F. Hobbs & J. S. Pang, 2007. "Nash-Cournot Equilibria in Electric Power Markets with Piecewise Linear Demand Functions and Joint Constraints," Operations Research, INFORMS, vol. 55(1), pages 113-127, February.
    18. Julien, Ludovic A., 2017. "On noncooperative oligopoly equilibrium in the multiple leader–follower game," European Journal of Operational Research, Elsevier, vol. 256(2), pages 650-662.
    19. Ludovic A. Julien, 2021. "Noncooperative oligopoly equilibrium in markets with hierarchical competition," EconomiX Working Papers 2021-14, University of Paris Nanterre, EconomiX.
    20. Contreras, Javier & Krawczyk, Jacek & Zuccollo, James, 2008. "Can planners control competitive generators?," MPRA Paper 10395, University Library of Munich, Germany.

    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:gam:jmathe:v:9:y:2021:i:24:p:3158-:d:697190. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.