IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v401y2021ics0096300321001223.html
   My bibliography  Save this article

Environmental-based defensive promotes cooperation in the prisoner’s dilemma game

Author

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

Abstract

In real life, individuals tend to be self-interested. The defectors exploit the cooperators for high payoffs, and the cooperators take defensive measures to reduce their own losses. Since the defensive behavior of cooperators is affected by environmental factors, this paper proposes an environmental-based defensive game model in the well-mixed population. Theoretical analysis shows that when cooperators do not have the defensive awareness, all the individuals choose defection. When cooperators have defensive awareness, the cooperators can survive in the fierce competition, so as to realize the stable coexistence of cooperation and defection. If all the cooperators have defensive awareness, the system can reach an evolutionary stable state of full cooperation. Through abundant numerical calculations, it is found that when the temptation is small and the defensive probability is large, the cooperation fraction is significantly affected by the threshold. Furthermore, the stronger the defensive awareness, the higher the cooperation fraction. As long as there are cooperators in the population who take defensive measures, a state of full defection can be avoided. Reducing the defensive cost and increasing the defensive benefit as well as the defensive loss are conducive to enhance cooperation level. In a word, defensive behavior promotes cooperation, which provides a new perspective for understanding the emergence of cooperation.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:401:y:2021:i:c:s0096300321001223
    DOI: 10.1016/j.amc.2021.126074
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321001223
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126074?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, Qiuling & Du, Chunpeng, 2019. "Impact of expansion of priority range on cooperation in the prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 77-80.
    2. 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).
    3. 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).
    4. 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.
    5. Zhang, Boyu & An, Xinmiao & Dong, Yali, 2021. "Conditional cooperator enhances institutional punishment in public goods game," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    6. Luo-Luo Jiang & Matjaž Perc & Attila Szolnoki, 2013. "If Cooperation Is Likely Punish Mildly: Insights from Economic Experiments Based on the Snowdrift Game," PLOS ONE, Public Library of Science, vol. 8(5), pages 1-7, May.
    7. Li, Yumeng & Wang, Hanchen & Du, Wenbo & Perc, Matjaž & Cao, Xianbin & Zhang, Jun, 2019. "Resonance-like cooperation due to transaction costs in the prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 248-257.
    8. Niu, Xiaotong & Xu, Jiwei & Deng, Zhenghong, 2017. "Conditional punishment resolves social dilemma in spatial network," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 256-259.
    9. Wang, Jianwei & Wang, Rong & Yu, Fengyuan & Wang, Ziwei & Li, Qiaochu, 2020. "Learning continuous and consistent strategy promotes cooperation in prisoner’s dilemma game with mixed strategy," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    10. Liu, Run-Ran & Jia, Chun-Xiao & Rong, Zhihai, 2020. "Effects of strategy-updating cost on evolutionary spatial prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    11. 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).
    12. Yang, Xiqing & Zhang, Feng & Wang, Wanxiong, 2019. "Predation promotes cooperation in Prisoner’s dilemma games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 20-24.
    13. Gao, Jia & Li, Zhi & Cong, Rui & Wang, Long, 2012. "Tolerance-based punishment in continuous public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(16), pages 4111-4120.
    14. Wang, Zhen & Zhang, Geng-shun & Ding, Hong & Cui, Guang-Hai & Yao, Ye, 2019. "Strategy imitation behavior driven influence adjustment promotes cooperation in spatial prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    15. Ding, Hong & Zhang, Geng-shun & Wang, Shi-hao & Li, Juan & Wang, Zhen, 2019. "Q-learning boosts the evolution of cooperation in structured population by involving extortion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    16. Guanghai Cui & Zhen Wang & Ling Dong & Xiaoli Cao & Yue Liu & Zhiwang Zhang, 2019. "Influence of contribution-based resource allocation mechanism on individual resource sharing cooperation in social networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 30(12), pages 1-19, December.
    17. Li, Wen-Jing & Jiang, Luo-Luo & Perc, Matjaž, 2021. "A limited mobility of minorities facilitates cooperation in social dilemmas," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    18. Liu, Chengwei & Wang, Juan & Li, Xiaopeng & Xia, Chengyi, 2020. "The link weight adjustment considering historical strategy promotes the cooperation in the spatial prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    19. Feng Zhang & Cang Hui, 2011. "Eco-Evolutionary Feedback and the Invasion of Cooperation in Prisoner's Dilemma Games," PLOS ONE, Public Library of Science, vol. 6(11), pages 1-7, November.
    20. Li, Shulan & Hong, Lijun & Geng, Yini & Shen, Chen, 2020. "Popularity-driven fitness calculation promotes cooperation in spatial prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    21. Yang, Han-Xin & Chen, Xiaojie, 2018. "Promoting cooperation by punishing minority," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 460-466.
    22. Wang, Qiuling & Ren, Xiaobin & Gao, Bo & Wang, Jiaqian, 2020. "Heterogeneity reproductive ability promotes cooperation in spatial prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    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. Katarina Kostelić, 2023. "Implications of (un)awareness for decision-making in strategic interaction: another take on the Prisoner’s dilemma," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 50(2), pages 251-268, June.
    2. 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).

    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. 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).
    3. Mao, Yajun & Rong, Zhihai & Wu, Zhi-Xi, 2021. "Effect of collective influence on the evolution of cooperation in evolutionary prisoner’s dilemma games," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    4. 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).
    5. Lu, Shounan & Dai, Jianhua & Zhu, Ge & Guo, Li, 2023. "Investigating the effectiveness of interaction-efficiency-driven strategy updating under progressive-interaction for the evolution of the prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    6. Wang, Chaoqian & Huang, Chaochao & Pan, Qiuhui & He, Mingfeng, 2022. "Modeling the social dilemma of involution on a square lattice," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    7. Wang, Chaoqian & Huang, Chaochao, 2022. "Between local and global strategy updating in public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    8. Zhao, Shanshan & Pan, Qiuhui & Zhu, Wenqiang & He, Mingfeng, 2023. "How “punishing evil and promoting good” promotes cooperation in social dilemma," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    9. 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).
    10. Yang, Zhengzhi & Zheng, Lei & Perc, Matjaž & Li, Yumeng, 2024. "Interaction state Q-learning promotes cooperation in the spatial prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    11. Wang, Mie & Kang, HongWei & Shen, Yong & Sun, XingPing & Chen, QingYi, 2021. "The role of alliance cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    12. 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).
    13. Wang, Jianwei & Chen, Wei & Yu, Fengyuan & He, Jialu & Xu, Wenshu, 2022. "Wealth-based rule favors cooperation in costly public goods games when individual selection is inevitable," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    14. Zhang, Jing & Li, Zhao & Zhang, Jiqiang & Ma, Lin & Zheng, Guozhong & Chen, Li, 2023. "Emergence of oscillatory cooperation in a population with incomplete information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).
    15. Quan, Ji & Pu, Zhenjuan & Wang, Xianjia, 2021. "Comparison of social exclusion and punishment in promoting cooperation: Who should play the leading role?," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    16. Li, Xiaopeng & Hao, Gang & Zhang, Zhipeng & Xia, Chengyi, 2021. "Evolution of cooperation in heterogeneously stochastic interactions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    17. Quan, Ji & Yu, Junyu & Li, Xia & Wang, Xianjia, 2023. "Conditional switching between social excluders and loners promotes cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 169(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.
    19. Su, Lichen & Yang, Zhengzhi & Zhou, Bowen & Zhang, Naitian & Li, Yumeng, 2023. "Effects of interdependent network reciprocity on the evolution of public cooperation," Applied Mathematics and Computation, Elsevier, vol. 454(C).
    20. Pi, Jinxiu & Yang, Guanghui & Tang, Wei & Yang, Hui, 2022. "Stochastically stable equilibria for evolutionary snowdrift games with time costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(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:401:y:2021:i:c:s0096300321001223. 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.