IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v9y2019i3d10.1007_s13235-018-0282-6.html
   My bibliography  Save this article

Krasovskii–Subbotin Approach to Mean Field Type Differential Games

Author

Listed:
  • Yurii Averboukh

    (Krasovskii Institute of Mathematics and Mechanics UrB RAS
    Ural Federal University)

Abstract

A mean field type differential game is a mathematical model of a large system of identical agents under mean field interaction controlled by two players with opposite purposes. We study the case when the dynamics of each agent is given by ODE and the players can observe the distribution of the agents. We construct suboptimal strategies and prove the existence of the value function.

Suggested Citation

  • Yurii Averboukh, 2019. "Krasovskii–Subbotin Approach to Mean Field Type Differential Games," Dynamic Games and Applications, Springer, vol. 9(3), pages 573-593, September.
  • Handle: RePEc:spr:dyngam:v:9:y:2019:i:3:d:10.1007_s13235-018-0282-6
    DOI: 10.1007/s13235-018-0282-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-018-0282-6
    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/s13235-018-0282-6?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. P. Cardaliaguet & M. Quincampoix, 2008. "Deterministic Differential Games Under Probability Knowledge Of Initial Condition," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 1-16.
    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. Olga Yufereva, 2022. "Approximate Capture in Gromov–Hausdorff Close Spaces," Dynamic Games and Applications, Springer, vol. 12(4), pages 1376-1387, December.
    2. Yurii Averboukh & Antonio Marigonda & Marc Quincampoix, 2021. "Extremal Shift Rule and Viability Property for Mean Field-Type Control Systems," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 244-270, April.

    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. Xiaochi Wu, 2022. "Existence of value for a differential game with asymmetric information and signal revealing," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(1), pages 213-247, March.
    2. Xiaochi Wu, 2021. "Differential Games with Incomplete Information and with Signal Revealing: The Symmetric Case," Dynamic Games and Applications, Springer, vol. 11(4), pages 863-891, December.
    3. Rainer Buckdahn & Juan Li & Marc Quincampoix, 2013. "Value function of differential games without Isaacs conditions. An approach with nonanticipative mixed strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 989-1020, November.
    4. Sylvain Sorin, 2011. "Zero-Sum Repeated Games: Recent Advances and New Links with Differential Games," Dynamic Games and Applications, Springer, vol. 1(1), pages 172-207, March.
    5. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    6. Chloe Jimenez & Marc Quincampoix & Yuhong Xu, 2016. "Differential Games with Incomplete Information on a Continuum of Initial Positions and without Isaacs Condition," Dynamic Games and Applications, Springer, vol. 6(1), pages 82-96, March.
    7. R. Buckdahn & P. Cardaliaguet & M. Quincampoix, 2011. "Some Recent Aspects of Differential Game Theory," Dynamic Games and Applications, Springer, vol. 1(1), pages 74-114, March.
    8. Jun Moon, 2022. "State and Control Path-Dependent Stochastic Zero-Sum Differential Games: Viscosity Solutions of Path-Dependent Hamilton–Jacobi–Isaacs Equations," Mathematics, MDPI, vol. 10(10), pages 1-32, May.
    9. Alberto Bressan & Deling Wei, 2013. "Stackelberg Solutions of Feedback Type for Differential Games with Random Initial Data," Dynamic Games and Applications, Springer, vol. 3(3), pages 341-358, September.
    10. Yurii Averboukh & Antonio Marigonda & Marc Quincampoix, 2021. "Extremal Shift Rule and Viability Property for Mean Field-Type Control Systems," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 244-270, April.
    11. Sylvain Sorin, 2018. "Limit Value of Dynamic Zero-Sum Games with Vanishing Stage Duration," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 51-63, February.
    12. Xiaochi Wu, 2019. "Infinite Horizon Differential Games with Asymmetric Information," Dynamic Games and Applications, Springer, vol. 9(3), pages 858-880, September.
    13. Valerii Patsko & Marc Quincampoix, 2019. "Preface: DGAA Special Issue on Pursuit-Evasion Games and Differential Games with Incomplete Information," Dynamic Games and Applications, Springer, vol. 9(3), pages 569-572, September.
    14. Miquel Oliu-Barton, 2015. "Differential Games with Asymmetric and Correlated Information," Dynamic Games and Applications, Springer, vol. 5(3), pages 378-396, September.
    15. Vianney Perchet & Marc Quincampoix, 2015. "On a Unified Framework for Approachability with Full or Partial Monitoring," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 596-610, March.
    16. Alós-Ferrer, Carlos & Kern, Johannes, 2015. "Repeated games in continuous time as extensive form games," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 34-57.

    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:9:y:2019:i:3:d:10.1007_s13235-018-0282-6. 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.