IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i12p2120-d451840.html
   My bibliography  Save this article

The Stability of Two-Community Replicator Dynamics with Discrete Multi-Delays

Author

Listed:
  • Jinxiu Pi

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

  • Hui Yang

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

  • Yadong Shu

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

  • Chongyi Zhong

    (School of Mathematics and Big data, Guizhou Education University, Guiyang 550018, China)

  • Guanghui Yang

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

Abstract

This article investigates the stability of evolutionarily stable strategy in replicator dynamics of two-community with multi-delays. In the real environment, players interact simultaneously while the return of their choices may not be observed immediately, which implies one or more time-delays exists. In addition to using the method of classic characteristic equations, we also apply linear matrix inequality (i.e., LMI) to discuss the stability of the mixed evolutionarily stable strategy in replicator dynamics of two-community with multi-delays. We derive a delay-dependent stability and a delay-independent stability sufficient conditions of the evolutionarily stable strategy in the two-community replicator dynamics with two delays, and manage to extend the sufficient condition to n time delays. Lastly, numerical trials of the Hawk–Dove game are given to verify the effectiveness of the theoretical consequences.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2120-:d:451840
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/12/2120/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/12/2120/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-666, May.
    2. Hiroshi Oaku, 2002. "Evolution with Delay," The Japanese Economic Review, Japanese Economic Association, vol. 53(1), pages 114-133, March.
    3. Gau, R.S. & Lien, C.H. & Hsieh, J.G., 2007. "Global exponential stability for uncertain cellular neural networks with multiple time-varying delays via LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1258-1267.
    4. 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.
    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. Qianru Chen & Hualin Xie & Qunli Zhai, 2022. "Management Policy of Farmers’ Cultivated Land Abandonment Behavior Based on Evolutionary Game and Simulation Analysis," Land, MDPI, vol. 11(3), pages 1-23, February.
    2. Lichi Zhang & Yanyan Jiang & Junmin Wu, 2022. "Evolutionary Game Analysis of Government and Residents’ Participation in Waste Separation Based on Cumulative Prospect Theory," IJERPH, MDPI, vol. 19(21), pages 1-16, November.
    3. Gu, Tianqi & Xu, Weiping & Liang, Hua & He, Qing & Zheng, Nan, 2024. "School bus transport service strategies’ policy-making mechanism – An evolutionary game approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 182(C).
    4. Wang Mingbao & Du Zhiping & Duan Hong, 2017. "Study on Participant Behavior Game of Electronic Products Reverse Supply Chain Based on ECP," Journal of Systems Science and Information, De Gruyter, vol. 5(5), pages 411-434, October.
    5. Sun, Yong & Liu, Baoyin & Sun, Zhongrui & Yang, Ruijia, 2023. "Inter-regional cooperation in the transfers of energy-intensive industry: An evolutionary game approach," Energy, Elsevier, vol. 282(C).
    6. Jialu Li & Meiying Yang & Wei Xing & Xuan Zhao, 2018. "Information Acquisition Behavior: An Evolutionary Game Theory Perspective," Dynamic Games and Applications, Springer, vol. 8(2), pages 434-455, June.
    7. Hongxia Sun & Yao Wan & Huirong Lv, 2020. "System Dynamics Model for the Evolutionary Behaviour of Government Enterprises and Consumers in China’s New Energy Vehicle Market," Sustainability, MDPI, vol. 12(4), pages 1-21, February.
    8. Song Yang & Jincai Zhuang & Aifeng Wang & Yancai Zhang, 2019. "Evolutionary Game Analysis of Chinese Food Quality considering Effort Levels," Complexity, Hindawi, vol. 2019, pages 1-13, November.
    9. Bergstrom, Theodore C & Stark, Oded, 1993. "How Altruism Can Prevail in an Evolutionary Environment," American Economic Review, American Economic Association, vol. 83(2), pages 149-155, May.
    10. Hopkins, Ed, 1999. "Learning, Matching, and Aggregation," Games and Economic Behavior, Elsevier, vol. 26(1), pages 79-110, January.
    11. Guohui Song & Yongbin Wang, 2021. "Mainstream Value Information Push Strategy on Chinese Aggregation News Platform: Evolution, Modelling and Analysis," Sustainability, MDPI, vol. 13(19), pages 1-17, October.
    12. Sandholm,W.H., 2003. "Excess payoff dynamics, potential dynamics, and stable games," Working papers 5, Wisconsin Madison - Social Systems.
    13. Jin, Tao & Jiang, Yulian & Liu, Xingwen, 2023. "Evolutionary game analysis of the impact of dynamic dual credit policy on new energy vehicles after subsidy cancellation," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    14. Viossat, Yannick, 2008. "Evolutionary dynamics may eliminate all strategies used in correlated equilibrium," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 27-43, July.
    15. Guanqiao Pan & Hongchao Jiang & Qianhui Jin & Tianyi Zhao & Jiajun Wang & Li Wang, 2021. "Study on the Sharing Transportation Based on Game Theory," Sustainability, MDPI, vol. 13(16), pages 1-28, August.
    16. Hui Yu & Wei Wang & Baohua Yang & Cunfang Li, 2019. "Evolutionary Game Analysis of the Stress Effect of Cross-Regional Transfer of Resource-Exhausted Enterprises," Complexity, Hindawi, vol. 2019, pages 1-16, November.
    17. Xiongwei Quan & Gaoshan Zuo & Helin Sun, 2022. "Risk Perception Thresholds and Their Impact on the Behavior of Nearby Residents in Waste to Energy Project Conflict: An Evolutionary Game Analysis," Sustainability, MDPI, vol. 14(9), pages 1-20, May.
    18. Aaron Foote & Maryam Gooyabadi & Nikhil Addleman, 2023. "Factors in Learning Dynamics Influencing Relative Strengths of Strategies in Poker Simulation," Games, MDPI, vol. 14(6), pages 1-16, November.
    19. Takatoshi Tabuchi & Dao‐Zhi Zeng, 2004. "Stability of Spatial Equilibrium," Journal of Regional Science, Wiley Blackwell, vol. 44(4), pages 641-660, November.
    20. Xiaoyang Zhao, 2019. "Patenting Or Secret? The Interaction Between Leading Firms And Following Firms Based On Evolutionary Game Theory And Multi-Agent Simulation," International Journal of Innovation Management (ijim), World Scientific Publishing Co. Pte. Ltd., vol. 23(07), pages 1-22, October.

    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:gam:jmathe:v:8:y:2020:i:12:p:2120-:d:451840. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.