IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v155y2022ics0960077921010171.html
   My bibliography  Save this article

Advanced defensive cooperators promote cooperation in the prisoner’s dilemma game

Author

Listed:
  • Gao, Liyan
  • Pan, Qiuhui
  • He, Mingfeng

Abstract

There are four strategies in the population, including primary defensive cooperation, advanced defensive cooperation, anti-defensive defection and common defection. The primary defensive cooperators take defensive measures when they interact with the common defectors. To pursue higher payoffs, anti-defensive defectors disguise identity to get rid of the defense of the primary defensive cooperators. Nevertheless, they cannot escape from the defense of the advanced defensive cooperators, and will be punished. By undertaking a screening cost, the advanced defensive cooperators play a defensive role against the anti-defensive defectors and common defectors simultaneously. The effect of defense is reflected in the increase of the cooperator’s benefit and the decrease of the defector’s benefit. We use replication dynamics to study the evolution process of the strategies in the well-mixed population. It is found that the advanced defensive cooperators can effectively promote cooperation. The common defectors disappear at low temptation values. However, the fraction of common defectors is non-monotonic about defensive benefit at high temptation values. Interestingly, when the defensive loss is small, the increase in the fraction of anti-defensive defectors stimulates the prosperity of advanced defensive cooperators, which in turn inhibits the evolution of anti-defensive defectors. This process is called negative feedback. Primary defensive cooperators are effectively free-riding on advanced defensive cooperators under larger defensive loss and fine. In addition, reducing the screening cost can improve the cooperation level.

Suggested Citation

  • Gao, Liyan & Pan, Qiuhui & He, Mingfeng, 2022. "Advanced defensive cooperators promote cooperation in the prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010171
    DOI: 10.1016/j.chaos.2021.111663
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921010171
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111663?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. Wang, Zhen & Chen, Tianyi & Wang, Xingpu & Jin, Jiuwu & Li, Mingchu, 2013. "Evolution of co-operation among mobile agents with different influence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4655-4662.
    2. Song, Qun & Cao, Zhaoheng & Tao, Rui & Jiang, Wei & Liu, Chen & Liu, Jinzhuo, 2020. "Conditional neutral punishment promotes cooperation in the spatial prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    3. Xie, Yunya & Zhang, Shuhua & Zhang, Zhipeng & Bu, Hongyu, 2020. "Impact of binary social status with hierarchical punishment on the evolution of cooperation in the spatial prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. Zhang, Lan & Huang, Changwei & Li, Haihong & Dai, Qionglin & Yang, Junzhong, 2021. "Effects of directional migration for pursuit of profitable circumstances in evolutionary games," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Han, Xu & Zhao, Xiaowei & Xia, Haoxiang, 2021. "Evolution of cooperation through aspiration-based adjustment of interaction range in spatial prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    6. Cheng-Yi Xia & Xiao-Kun Meng & Zhen Wang, 2015. "Heterogeneous Coupling between Interdependent Lattices Promotes the Cooperation in the Prisoner’s Dilemma Game," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-13, June.
    7. Hongyan Cheng & Qionglin Dai & Haihong Li & Xiaolan Qian & Mei Zhang & Junzhong Yang, 2013. "Effects of directional migration on prisoner’s dilemma game in a square domain," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(4), pages 1-6, April.
    8. Geng, Yini & Shen, Chen & Hu, Kaipeng & Shi, Lei, 2018. "Impact of punishment on the evolution of cooperation in spatial prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 540-545.
    9. Miyaji, Kohei & Tanimoto, Jun, 2021. "A co-evolutionary model combined mixed-strategy and network adaptation by severing disassortative neighbors promotes cooperation in prisoner’s dilemma games," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    10. Zhu, Peican & Wang, Xiaoyu & Jia, Danyang & Guo, Yangming & Li, Shudong & Chu, Chen, 2020. "Investigating the co-evolution of node reputation and edge-strategy in prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    11. Dong, Yukun & Xu, Hedong & Fan, Suohai, 2019. "Memory-based stag hunt game on regular lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 519(C), pages 247-255.
    12. Zhang, Liming & Huang, Changwei & Li, Haihong & Dai, Qionglin & Yang, Junzhong, 2021. "Cooperation guided by imitation, aspiration and conformity-driven dynamics in evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    13. Chu, Chen & Zhai, Yao & Mu, Chunjiang & Hu, Die & Li, Tong & Shi, Lei, 2019. "Reputation-based popularity promotes cooperation in the spatial prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    14. Tanimoto, Jun, 2015. "The impact of initial cooperation fraction on the evolutionary fate in a spatial prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 171-188.
    15. Wang, Qiuling & Meng, Haoran & Gao, Bo, 2019. "Spontaneous punishment promotes cooperation in public good game," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 183-187.
    16. Gao, Liyan & Pan, Qiuhui & He, Mingfeng, 2021. "Effects of defensive cooperation strategy on the evolution of cooperation in social dilemma," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    17. Jian, Qing & Li, Xiaopeng & Wang, Juan & Xia, Chengyi, 2021. "Impact of reputation assortment on tag-mediated altruistic behaviors in the spatial lattice," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    18. Shu, Feng & Liu, Yaojun & Liu, Xingwen & Zhou, Xiaobing, 2019. "Memory-based conformity enhances cooperation in social dilemmas," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 480-490.
    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. Chen, Qin & Pan, Qiuhui & He, Mingfeng, 2022. "The influence of quasi-cooperative strategy on social dilemma evolution," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Hao, Weijuan & Hu, Yuhan, 2024. "The implications of deep cooperation strategy for the evolution of cooperation in social dilemmas," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    3. Zhu, Wenqiang & Pan, Qiuhui & Song, Sha & He, Mingfeng, 2023. "Effects of exposure-based reward and punishment on the evolution of cooperation in prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    4. Wang, Xianjia & Yang, Zhipeng & Liu, Yanli & Chen, Guici, 2023. "A reinforcement learning-based strategy updating model for the cooperative evolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    5. Li, Wen-Jing & Chen, Zhi & Wang, Jun & Jiang, Luo-Luo & Perc, Matjaž, 2023. "Social mobility and network reciprocity shape cooperation in collaborative networks," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    6. 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).
    7. Xie, Yunya & Bai, Yu & Zhang, Yankun & Peng, Zhengyin, 2024. "Trust-induced cooperation under the complex interaction of networks and emotions," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

    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. Chen, Qin & Pan, Qiuhui & He, Mingfeng, 2022. "The influence of quasi-cooperative strategy on social dilemma evolution," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Pi, Bin & Li, Yuhan & Feng, Minyu, 2022. "An evolutionary game with conformists and profiteers regarding the memory mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    3. Huang, Chaochao & Wang, Chaoqian, 2024. "Memory-based involution dilemma on square lattices," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    4. Zu, Jinjing & Xu, Fanxin & Jin, Tao & Xiang, Wei, 2022. "Reward and Punishment Mechanism with weighting enhances cooperation in evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    5. Zhang, Lan & Pan, Jianchen & Huang, Changwei, 2023. "Effect of mixed random and directional migration on cooperation in the spatial prisoner’s dilemma," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    6. Locodi, A.M. & O’Riordan, C., 2023. "The effects of varying game payoffs and lattice dimensionality on Prisoner’s Dilemma games," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    7. Gao, Liyan & Pan, Qiuhui & He, Mingfeng, 2021. "Environmental-based defensive promotes cooperation in the prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    8. Sun, Chengbin & Luo, Chao, 2020. "Co-evolution of influence-based preferential selection and limited resource with multi-games on interdependent networks," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    9. Wang, Zi-Ren & Deng, Zheng-Hong & Wang, Huan-Bo & Qu, Yun, 2021. "Moderate irrational sentiment-driven fitness can promote cooperation in the prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
    10. 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).
    11. Zhu, Jiabao & Liu, Xingwen, 2021. "The number of strategy changes can be used to promote cooperation in spatial snowdrift game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 575(C).
    12. Li, Xiaopeng & Han, Weiwei & Yang, Wenjun & Wang, Juan & Xia, Chengyi & Li, Hui-jia & Shi, Yong, 2022. "Impact of resource-based conditional interaction on cooperation in spatial social dilemmas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 594(C).
    13. Lu, Shounan & Zhu, Ge & Dai, Jianhua, 2023. "Promoting effect of adaptive interaction based on random neighbors to cooperation in the spatial prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    14. Gao, Hongyu & Wang, Juan & Zhang, Fan & Li, Xiaopeng & Xia, Chengyi, 2021. "Cooperation dynamics based on reputation in the mixed population with two species of strategists," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    15. Bi, Yan & Yang, Hui, 2023. "Based on reputation consistent strategy times promotes cooperation in spatial prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    16. Geng, Yini & Liu, Yifan & Lu, Yikang & Shen, Chen & Shi, Lei, 2022. "Reinforcement learning explains various conditional cooperation," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    17. Feng, Sinan & Liu, Xuesong, 2024. "Effects of three-faced strategy on the evolution of cooperation in social dilemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 639(C).
    18. Wang, Chaoqian & Lin, Zongzhe & Rothman, Dale S., 2022. "Public goods game on coevolving networks driven by the similarity and difference of payoff," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    19. Shilin Xiao & Liming Zhang & Haihong Li & Qionglin Dai & Junzhong Yang, 2022. "Environment-driven migration enhances cooperation in evolutionary public goods games," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(4), pages 1-9, April.
    20. Deng, Yunsheng & Zhang, Jihui, 2021. "Memory-based prisoner's dilemma game with history optimal strategy learning promotes cooperation on interdependent networks," Applied Mathematics and Computation, Elsevier, vol. 390(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:chsofr:v:155:y:2022:i:c:s0960077921010171. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.