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Stability of Replicator Dynamics with Bounded Continuously Distributed Time Delay

Author

Listed:
  • Chongyi Zhong

    (School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China)

  • Hui Yang

    (School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China)

  • Zixin Liu

    (School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China)

  • Juanyong Wu

    (School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China)

Abstract

In this paper, we consider evolutionary games and construct a model of replicator dynamics with bounded continuously distributed time delay. In many circumstances, players interact simultaneously while impacts of their choices take place after some time, which implies a time delay exists. We consider the time delay as bounded continuously distributed other than some given constant. Then, we investigate the stability of the evolutionarily stable strategy in the replicator dynamics with bounded continuously distributed time delay in two-player game contexts. Some stability conditions of the unique interior Nash equilibrium are obtained. Finally, the simple but important Hawk–Dove game is used to verify our results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:431-:d:333215
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    References listed on IDEAS

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    7. James Burridge & Yu Gao & Yong Mao, 2017. "Delayed response in the Hawk Dove game," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(1), pages 1-6, January.
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    Cited by:

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    2. Yuan, Hairui & Meng, Xinzhu, 2022. "Replicator dynamics of division of labor games with delayed payoffs in infinite populations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

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