IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v435y2022ics0096300322005471.html
   My bibliography  Save this article

Stability analysis of game models with fixed and stochastic delays

Author

Listed:
  • Hu, Limi
  • Qiu, Xiaoling

Abstract

In this paper, we combine evolutionary game with dynamics, and discuss two kinds of game models with time delay. First, based on continuous distributed (kernel function) stochastic delay, we give the asymptotic stability condition of general three-strategy game model. Second, we study the replicator dynamics of two-community three-strategy game model with two fixed time delays (i.e. τ1 within the community and τ2 between different communities). Based on Hopf bifurcation theory, by calculating the critical conditions for the existence of bifurcation, the influence of bifurcation on the stability of equilibrium points is analyzed. Finally, we take rock-paper-scissors game as an example to verify the correctness of the theoretical results, when the delay τ meets certain conditions or doesn’t exceed the critical value, the stability of the system will not change.

Suggested Citation

  • Hu, Limi & Qiu, Xiaoling, 2022. "Stability analysis of game models with fixed and stochastic delays," Applied Mathematics and Computation, Elsevier, vol. 435(C).
  • Handle: RePEc:eee:apmaco:v:435:y:2022:i:c:s0096300322005471
    DOI: 10.1016/j.amc.2022.127473
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322005471
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2022.127473?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. Minggang Wang & Hua Xu, 2012. "A Novel Four-Dimensional Energy-Saving and Emission-Reduction System and Its Linear Feedback Control," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, December.
    2. 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.
    3. Wettergren, Thomas A., 2021. "Replicator dynamics of an N-player snowdrift game with delayed payoffs," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    4. Wang, Jingnan & Shi, Hongbin & Xu, Li & Zang, Lu, 2022. "Hopf bifurcation and chaos of tumor-Lymphatic model with two time delays," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    5. 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.
    6. Zhang, Zizhen & Kundu, Soumen & Tripathi, Jai Prakash & Bugalia, Sarita, 2020. "Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    7. Xiaojie Chen & Attila Szolnoki, 2018. "Punishment and inspection for governing the commons in a feedback-evolving game," PLOS Computational Biology, Public Library of Science, vol. 14(7), pages 1-15, July.
    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. Wang, Yudi & Xiang, Pengcheng, 2024. "Evolutionary game and system dynamics for analysis on stakeholder strategies of regional high-speed rail project in investment decision stage," Technology in Society, Elsevier, vol. 77(C).
    2. Wettergren, Thomas A., 2023. "Replicator dynamics of evolutionary games with different delays on costs and benefits," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    3. Xiuling Li & Haotian Fan, 2024. "Bifurcation Analysis of a Class of Two-Delay Lotka–Volterra Predation Models with Coefficient-Dependent Delay," Mathematics, MDPI, vol. 12(10), pages 1-22, May.
    4. Tianjun Su & Linhai Wu & Jingxiang Zhang, 2024. "Evolutionary Game and Simulation Analysis of Food Safety Regulation under Time Delay Effect," Mathematics, MDPI, vol. 12(8), pages 1-23, April.
    5. Mengzhu Xu & Zixin Liu & Changjin Xu & Nengfa Wang, 2024. "Evolutionary Game Analysis of Digital Financial Enterprises and Regulators Based on Delayed Replication Dynamic Equation," Mathematics, MDPI, vol. 12(3), pages 1-18, January.

    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. Liu, Siyuan & Zhang, Chunyan & Li, Kun & Zhang, Jianlei, 2022. "Exploring the inducement for social dilemma and cooperation promotion mechanisms in structured populations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. 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).
    3. Arefin, Md. Rajib & Tanimoto, Jun, 2024. "Coupling injunctive social norms with evolutionary games," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    4. Li, Wen-Jing & Chen, Zhi & Jin, Ke-Zhong & Li, Lan & Yuan, Lin & Jiang, Luo-Luo & Perc, Matjaž & Kurths, Jürgen, 2022. "Eliminating poverty through social mobility promotes cooperation in social dilemmas," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    5. 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.
    6. Yan, Fang & Hou, Xiaorong & Tian, Tingting & Chen, Xiaojie, 2023. "Nonlinear model reference adaptive control approach for governance of the commons in a feedback-evolving game," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    7. Huang, Shaoxu & Liu, Xuesong & Hu, Yuhan & Fu, Xiao, 2023. "The influence of aggressive behavior on cooperation evolution in social dilemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    8. Zhijun Wu, 2020. "Why multilingual, and how to keep it—An evolutionary dynamics perspective," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-24, November.
    9. Cheng, Fei & Chen, Tong & Chen, Qiao, 2020. "Rewards based on public loyalty program promote cooperation in public goods game," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    10. Ullah, Mohammad Sharif & Higazy, M. & Kabir, K.M. Ariful, 2022. "Dynamic analysis of mean-field and fractional-order epidemic vaccination strategies by evolutionary game approach," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    11. Tetsushi Ohdaira, 2021. "Cooperation evolves by the payoff-difference-based probabilistic reward," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(11), pages 1-8, November.
    12. Qiang Wang & Linjie Liu & Xiaojie Chen, 2020. "Evolutionary Dynamics of Cooperation in the Public Goods Game with Individual Disguise and Peer Punishment," Dynamic Games and Applications, Springer, vol. 10(3), pages 764-782, September.
    13. Zhang, Liming & Li, Haihong & Dai, Qionglin & Yang, Junzhong, 2022. "Adaptive persistence based on environment comparison enhances cooperation in evolutionary games," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    14. Zhang, Lulu & Pan, Qiuhui & He, Mingfeng, 2022. "The influence of donation behavior on the evolution of cooperation in social dilemma," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    15. Li, Kun & Mao, Yizhou & Wei, Zhenlin & Cong, Rui, 2021. "Pool-rewarding in N-person snowdrift game," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    16. Ding, Rui & Wang, Xianjia & Liu, Yang & Zhao, Jinhua & Gu, Cuiling, 2023. "Evolutionary games with environmental feedbacks under an external incentive mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    17. Bai, Pengzhou & Qiang, Bingzhuang & Zou, Kuan & Huang, Changwei, 2024. "Preferential selection based on adaptive attractiveness induce by reinforcement learning promotes cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    18. Wang, Lichen & Liu, Yuyuan & Guo, Ruqiang & Zhang, Liang & Liu, Linjie & Hua, Shijia, 2024. "Cooperation and resource sustainability in coupling social-ecological systems with dynamic growth rates," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    19. Pi, Jinxiu & Yang, Guanghui & Yang, Hui, 2022. "Evolutionary dynamics of cooperation in N-person snowdrift games with peer punishment and individual disguise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).
    20. Ohdaira, Tetsushi, 2024. "The universal probabilistic reward based on the difference of payoff realizes the evolution of cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 182(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:eee:apmaco:v:435:y:2022:i:c:s0096300322005471. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.