IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v167y2015i1d10.1007_s10957-014-0691-7.html
   My bibliography  Save this article

Invariant Solutions of Differential Games with Measures: A Discontinuous Time Reparameterization Approach

Author

Listed:
  • Elena Goncharova

    (Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences)

  • Maxim Staritsyn

    (Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences)

Abstract

The paper is devoted to bilevel qualitative games with impulsive dynamics described by a measure differential equation. We study games with fixed impulses, and games with impulsive control in the hands of the lower level player, provided that the upper level player aims to ensure the existence of invariant solutions to a measure differential equation under any admissible answer of the opponent. We give sufficient conditions for weak invariance of time-varying domains with respect to the impulsive dynamical games.

Suggested Citation

  • Elena Goncharova & Maxim Staritsyn, 2015. "Invariant Solutions of Differential Games with Measures: A Discontinuous Time Reparameterization Approach," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 382-400, October.
  • Handle: RePEc:spr:joptap:v:167:y:2015:i:1:d:10.1007_s10957-014-0691-7
    DOI: 10.1007/s10957-014-0691-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-014-0691-7
    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/s10957-014-0691-7?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. repec:dau:papers:123456789/5561 is not listed on IDEAS
    2. G. J. Olsder, 2009. "Phenomena in Inverse Stackelberg Games, Part 2: Dynamic Problems," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 601-618, December.
    3. Jean-Pierre Aubin & Nicolas Seube, 2005. "Conditional Viability for Impulse Differential Games," Annals of Operations Research, Springer, vol. 137(1), pages 269-297, July.
    4. Josef Shinar & Valery Y. Glizer & Vladimir Turetsky, 2012. "Complete Solution Of A Pursuit–Evasion Differential Game With Hybrid Evader Dynamics," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 1-31.
    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. Noortje Groot & Bart Schutter & Hans Hellendoorn, 2016. "Optimal Affine Leader Functions in Reverse Stackelberg Games," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 348-374, January.
    2. Engwerda, J.C., 2012. "Prospects of Tools from Differential Games in the Study Of Macroeconomics of Climate Change," Other publications TiSEM cac36d07-227b-4cf2-83cb-7, Tilburg University, School of Economics and Management.
    3. Yurii Averboukh, 2018. "Inverse Stackelberg Solutions for Games with Many Followers," Mathematics, MDPI, vol. 6(9), pages 1-9, August.
    4. Yifen Mu, 2014. "Inverse Stackelberg Public Goods Game with Multiple Hierarchies Under Global and Local Information Structures," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 332-350, October.
    5. G. J. Olsder, 2009. "Phenomena in Inverse Stackelberg Games, Part 1: Static Problems," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 589-600, December.
    6. Grigory Belyavsky & Natalya Danilova & Guennady Ougolnitsky, 2018. "A Markovian Mechanism of Proportional Resource Allocation in the Incentive Model as a Dynamic Stochastic Inverse Stackelberg Game," Mathematics, MDPI, vol. 6(8), pages 1-10, July.
    7. Olga Gorbaneva & Guennady Ougolnitsky, 2022. "Sustainability of Intertwined Supply Networks: A Game-Theoretic Approach," Games, MDPI, vol. 13(3), pages 1-21, April.
    8. Guennady Ougolnitsky & Anatoly Usov, 2019. "Spatially Distributed Differential Game Theoretic Model of Fisheries," Mathematics, MDPI, vol. 7(8), pages 1-13, August.
    9. Babajanyan, S.G. & Melkikh, A.V. & Allahverdyan, A.E., 2020. "Leadership scenarios in prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    10. Yurii Averboukh & Artem Baklanov, 2014. "Stackelberg Solutions of Differential Games in the Class of Nonanticipative Strategies," Dynamic Games and Applications, Springer, vol. 4(1), pages 1-9, March.
    11. Guennady Ougolnitsky & Anatoly Usov, 2023. "Differential Game-Theoretic Models of Cournot Oligopoly with Consideration of the Green Effect," Games, MDPI, vol. 14(1), pages 1-18, January.

    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:167:y:2015:i:1:d:10.1007_s10957-014-0691-7. 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.