IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v206y2025i2d10.1007_s10957-025-02695-4.html
   My bibliography  Save this article

Robust Soft-Constrained Nash Equilibria in the Multi-Player Discrete-Time Descriptor Dynamic Game

Author

Listed:
  • Muhammad Wakhid Musthofa

    (UIN Sunan Kalijaga Yogyakarta)

  • Jacob Engwerda

    (Retiree Tilburg University)

Abstract

This paper considers the design of robust control strategies for a discrete-time descriptor system influenced by multiple players with their own disturbance attenuation levels. Assuming players use linear feedback strategies, the Nash equilibrium strategies are derived for a non-cooperative setting. In a simulation study on water extraction from a common resource, it is demonstrated what the potential effects are if players use different attenuation levels. Also, the impact of the number of players and divergent preferences on results are investigated. To derive the equilibrium strategies, first, the solution of the zero-sum discrete-time dynamic game where one player is playing against nature is presented. Using this result, we present sufficient conditions for the existence of a soft-constrained linear feedback Nash equilibrium (SLFNE) for the multi-player soft-constrained linear quadratic regular dynamic game. From this result, we obtain then directly robust disturbance attenuation controllers for the system, where every player satisfies his own attenuation level.

Suggested Citation

  • Muhammad Wakhid Musthofa & Jacob Engwerda, 2025. "Robust Soft-Constrained Nash Equilibria in the Multi-Player Discrete-Time Descriptor Dynamic Game," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-29, August.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:2:d:10.1007_s10957-025-02695-4
    DOI: 10.1007/s10957-025-02695-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-025-02695-4
    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/s10957-025-02695-4?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.

    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:206:y:2025:i:2:d:10.1007_s10957-025-02695-4. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.