IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v15y2025i2d10.1007_s13235-024-00594-3.html
   My bibliography  Save this article

Rate of Convergence for First-Order Singular Perturbation Problems: Hamilton–Jacobi–Isaacs Equations and Mean Field Games of Acceleration

Author

Listed:
  • Piermarco Cannarsa

    (Universitá degli Studi di Roma Tor Vergata)

  • Cristian Mendico

    (Universitá degli Studi di Roma Tor Vergata)

Abstract

This work focuses on the rate of convergence for singular perturbation problems for first-order Hamilton–Jacobi equations. We use the nonlinear adjoint method to analyze how the Hamiltonian’s regularizing effect on the initial data influences the convergence rate. As an application we derive the rate of convergence for singularly perturbed two-players zero-sum deterministic differential games (i.e., leading to Hamilton–Jacobi–Isaacs equations) and, subsequently, in case of singularly perturbed mean field games of acceleration. Namely, we show that in both the models the rate of convergence is $$\varepsilon $$ ε .

Suggested Citation

  • Piermarco Cannarsa & Cristian Mendico, 2025. "Rate of Convergence for First-Order Singular Perturbation Problems: Hamilton–Jacobi–Isaacs Equations and Mean Field Games of Acceleration," Dynamic Games and Applications, Springer, vol. 15(2), pages 592-609, May.
    • Handle: RePEc:spr:dyngam:v:15:y:2025:i:2:d:10.1007_s13235-024-00594-3
    DOI: 10.1007/s13235-024-00594-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-024-00594-3
    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/s13235-024-00594-3?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:dyngam:v:15:y:2025:i:2:d:10.1007_s13235-024-00594-3. 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.