IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v203y2024i3d10.1007_s10957-024-02534-y.html
   My bibliography  Save this article

Existence of $$\alpha $$ α -Robust Weak Nash Equilibria for Leader–Follower Population Games with Fuzzy Parameters

Author

Listed:
  • Guoling Wang

    (Guizhou University)

  • Miao Wang

    (Guizhou University)

  • Hui Yang

    (Guizhou University)

  • Guanghui Yang

    (Guizhou University)

  • Chun Wang

    (Guizhou Open University)

Abstract

This paper mainly studies the existence of $$\alpha $$ α -robust weak Nash equilibria for leader-follower population games with fuzzy parameters. First, $$\alpha $$ α -robust weak Nash equilibria for population games with fuzzy parameters are defined based on u-type set relations and their existence is proved by Fan-Glicksberg fixed theorem. Second, such equilibrium solutions are further proposed for leader-follower population games with fuzzy parameters and their existence is further shown. Finally, four examples are constructed to illustrate their feasibility, respectively. Our results are new and different from the existing ones.

Suggested Citation

  • Guoling Wang & Miao Wang & Hui Yang & Guanghui Yang & Chun Wang, 2024. "Existence of $$\alpha $$ α -Robust Weak Nash Equilibria for Leader–Follower Population Games with Fuzzy Parameters," Journal of Optimization Theory and Applications, Springer, vol. 203(3), pages 2739-2758, December.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:3:d:10.1007_s10957-024-02534-y
    DOI: 10.1007/s10957-024-02534-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-024-02534-y
    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/s10957-024-02534-y?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. Tharakunnel, Kurian & Bhattacharyya, Siddhartha, 2009. "Single-leader-multiple-follower games with boundedly rational agents," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1593-1603, August.
    2. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    3. Giovanni P. Crespi & Daishi Kuroiwa & Matteo Rocca, 2020. "Robust Nash equilibria in vector-valued games with uncertainty," Annals of Operations Research, Springer, vol. 289(2), pages 185-193, June.
    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. John R. Conlon, 2009. "Two New Conditions Supporting the First-Order Approach to Multisignal Principal-Agent Problems," Econometrica, Econometric Society, vol. 77(1), pages 249-278, January.
    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. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
    2. Stefan Mišković, 2017. "A VNS-LP algorithm for the robust dynamic maximal covering location problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1011-1033, October.
    3. Chuong, T.D. & Jeyakumar, V., 2017. "Convergent hierarchy of SDP relaxations for a class of semi-infinite convex polynomial programs and applications," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 381-399.
    4. Chassein, André & Dokka, Trivikram & Goerigk, Marc, 2019. "Algorithms and uncertainty sets for data-driven robust shortest path problems," European Journal of Operational Research, Elsevier, vol. 274(2), pages 671-686.
    5. Dranichak, Garrett M. & Wiecek, Margaret M., 2019. "On highly robust efficient solutions to uncertain multiobjective linear programs," European Journal of Operational Research, Elsevier, vol. 273(1), pages 20-30.
    6. Clausen, Andrew, 2013. "Moral Hazard with Counterfeit Signals," SIRE Discussion Papers 2013-13, Scottish Institute for Research in Economics (SIRE).
    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. J. Behnamian & Z. Gharabaghli, 2023. "Multi-objective outpatient scheduling in health centers considering resource constraints and service quality: a robust optimization approach," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-35, March.
    9. Cai, W. & Singham, D.I., 2018. "A principal–agent problem with heterogeneous demand distributions for a carbon capture and storage system," European Journal of Operational Research, Elsevier, vol. 264(1), pages 239-256.
    10. Ohad Kadan & Philip J. Reny & Jeroen M. Swinkels, 2017. "Existence of Optimal Mechanisms in Principal‐Agent Problems," Econometrica, Econometric Society, vol. 85, pages 769-823, May.
    11. 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.
    12. Huang, Pidong, 2013. "Optimal Unemployment Insurance With Different Types of Job," MPRA Paper 46626, University Library of Munich, Germany.
    13. Kang, Yan-li & Tian, Jing-Song & Chen, Chen & Zhao, Gui-Yu & Li, Yuan-fu & Wei, Yu, 2021. "Entropy based robust portfolio," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    14. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    15. Antonio G. Martín & Manuel Díaz-Madroñero & Josefa Mula, 2020. "Master production schedule using robust optimization approaches in an automobile second-tier supplier," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 143-166, March.
    16. Hanif, Sarmad & Alam, M.J.E. & Roshan, Kini & Bhatti, Bilal A. & Bedoya, Juan C., 2022. "Multi-service battery energy storage system optimization and control," Applied Energy, Elsevier, vol. 311(C).
    17. Hamed Mamani & Shima Nassiri & Michael R. Wagner, 2017. "Closed-Form Solutions for Robust Inventory Management," Management Science, INFORMS, vol. 63(5), pages 1625-1643, May.
    18. Martijn G. de Jong & Jan-Benedict E. M. Steenkamp & Bernard P. Veldkamp, 2009. "A Model for the Construction of Country-Specific Yet Internationally Comparable Short-Form Marketing Scales," Marketing Science, INFORMS, vol. 28(4), pages 674-689, 07-08.
    19. Sturm, J.F. & Zhang, S., 2001. "On Cones of Nonnegative Quadratic Functions," Discussion Paper 2001-26, Tilburg University, Center for Economic Research.
    20. Contreras, Javier & Krawczyk, Jacek & Zuccollo, James, 2008. "The invisible polluter: Can regulators save consumer surplus?," MPRA Paper 9890, 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:spr:joptap:v:203:y:2024:i:3:d:10.1007_s10957-024-02534-y. 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.