IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v8y2018i4d10.1007_s13235-017-0225-7.html
   My bibliography  Save this article

Discrete and Continuous Distributed Delays in Replicator Dynamics

Author

Listed:
  • Nesrine Ben-Khalifa

    (University of Avignon)

  • Rachid El-Azouzi

    (University of Avignon)

  • Yezekael Hayel

    (University of Avignon)

Abstract

In this paper, we study evolutionary games and we examine the stability of the evolutionarily stable strategy (ESS) in the continuous-time replicator dynamics with distributed time delays. In many examples, the interactions between individuals take place instantaneously, but their impacts are not immediate and take a certain amount of time which is usually random. In this paper, we study the consequences of distributed delays on the stability of the replicator dynamics. The main results are that (i) under the exponential delay distribution, the ESS is asymptotically stable for any value of the rate parameter; (ii) the necessary and sufficient conditions for the asymptotic stability of the ESS under uniform and Erlang distributions; and (iii) for the discrete distributed delays, we derive a necessary and sufficient delay-independent stability conditions. We illustrate our results with numerical examples from the Hawk–Dove game.

Suggested Citation

  • Nesrine Ben-Khalifa & Rachid El-Azouzi & Yezekael Hayel, 2018. "Discrete and Continuous Distributed Delays in Replicator Dynamics," Dynamic Games and Applications, Springer, vol. 8(4), pages 713-732, December.
    • Handle: RePEc:spr:dyngam:v:8:y:2018:i:4:d:10.1007_s13235-017-0225-7
    DOI: 10.1007/s13235-017-0225-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-017-0225-7
    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/s13235-017-0225-7?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. Iijima, Ryota, 2011. "Heterogeneous information lags and evolutionary stability," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 83-85, March.
    2. Hiroshi Oaku, 2002. "Evolution with Delay," The Japanese Economic Review, Japanese Economic Association, vol. 53(1), pages 114-133, March.
    3. Elizabeth Wesson & Richard Rand, 2016. "Hopf Bifurcations in Delayed Rock–Paper–Scissors Replicator Dynamics," Dynamic Games and Applications, Springer, vol. 6(1), pages 139-156, March.
    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. Takahara, Akihiro & Sakiyama, Tomoko, 2023. "Twisted strategy may enhance the evolution of cooperation in spatial prisoner’s dilemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 629(C).
    2. Hu, Limi & Qiu, Xiaoling, 2022. "Stability analysis of game models with fixed and stochastic delays," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    3. Marek Bodnar & Jacek Miȩkisz & Raffi Vardanyan, 2020. "Three-Player Games with Strategy-Dependent Time Delays," Dynamic Games and Applications, Springer, vol. 10(3), pages 664-675, September.
    4. Chongyi Zhong & Hui Yang & Zixin Liu & Juanyong Wu, 2020. "Stability of Replicator Dynamics with Bounded Continuously Distributed Time Delay," Mathematics, MDPI, vol. 8(3), pages 1-12, March.

    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. Jacek Miȩkisz & Michał Matuszak & Jan Poleszczuk, 2014. "Stochastic Stability in Three-Player Games with Time Delays," Dynamic Games and Applications, Springer, vol. 4(4), pages 489-498, December.
    2. Marek Bodnar & Jacek Miȩkisz & Raffi Vardanyan, 2020. "Three-Player Games with Strategy-Dependent Time Delays," Dynamic Games and Applications, Springer, vol. 10(3), pages 664-675, September.
    3. Jinxiu Pi & Hui Yang & Yadong Shu & Chongyi Zhong & Guanghui Yang, 2020. "The Stability of Two-Community Replicator Dynamics with Discrete Multi-Delays," Mathematics, MDPI, vol. 8(12), pages 1-17, November.
    4. Iijima, Ryota, 2011. "Heterogeneous information lags and evolutionary stability," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 83-85, March.
    5. Hu, Wenjun & Zhang, Gang & Tian, Haiyan, 2019. "The stability of imitation dynamics with discrete distributed delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 218-224.
    6. Hu, Limi & Qiu, Xiaoling, 2022. "Stability analysis of game models with fixed and stochastic delays," Applied Mathematics and Computation, Elsevier, vol. 435(C).

    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:8:y:2018:i:4:d:10.1007_s13235-017-0225-7. 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.