IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v191y2025ics0960077924013870.html

Synergy effect of strategy diversity and persistence promotes cooperation

Author

Listed:
  • Huang, Linya
  • Zhang, Liming
  • Huang, Changwei
  • Han, Wenchen

Abstract

Cooperation is a ubiquitous phenomenon in the real world, even in highly competitive environments, which seems to defy the principles of natural selection. The factors of strategic heterogeneity and persistence are crucial in fostering cooperation, and numerous studies have been devoted to unraveling their effects. However, the intricate interplay between these two elements has seldom been explored. In this research, we present a dual-mechanism framework that encompasses both the diversity of cooperation strategies and the adaptive persistence with which individuals adhere to their chosen strategies. Numerical simulations reveal that the synergistic effect of these dual mechanisms can significantly and stably increase the number of non-defective agents, particularly in situations where the temptation to defect is high. Moreover, despite being presented with a multitude of cooperation strategies, agents tend to converge on a single preferred strategy. When agents shift their preference from a high cooperation strategy to a low cooperation strategy, there is an increase in the number of non-defective agents, yet the global cooperation willingness remains unchanged.

Suggested Citation

  • Huang, Linya & Zhang, Liming & Huang, Changwei & Han, Wenchen, 2025. "Synergy effect of strategy diversity and persistence promotes cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924013870
    DOI: 10.1016/j.chaos.2024.115835
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924013870
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115835?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Xie, Kai & Liu, Tingjin, 2024. "The regulation of good and evi promotes cooperation in public goods game," Applied Mathematics and Computation, Elsevier, vol. 478(C).
    2. Xu, Zhixiong & Xu, Zhehang & Zhang, Wei & Han, Xiao-Pu & Meng, Fanyuan, 2024. "Memory-based spatial evolutionary prisoner’s dilemma," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    3. Liu, Yuanming & Huang, Changwei & Dai, Qionglin, 2018. "Preferential selection based on strategy persistence and memory promotes cooperation in evolutionary prisoner’s dilemma games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 481-489.
    4. Liu, Jinzhuo & Meng, Haoran & Wang, Wei & Xie, Zhongwen & Yu, Qian, 2019. "Evolution of cooperation on independent networks: The influence of asymmetric information sharing updating mechanism," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 234-241.
    5. Hu, Qi & Jin, Tao & Jiang, Yulian & Liu, Xingwen, 2024. "Reputation incentives with public supervision promote cooperation in evolutionary games," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    6. Hisashi Ohtsuki & Christoph Hauert & Erez Lieberman & Martin A. Nowak, 2006. "A simple rule for the evolution of cooperation on graphs and social networks," Nature, Nature, vol. 441(7092), pages 502-505, May.
    7. Valerio Capraro & Joseph Y. Halpern & Matjaž Perc, 2024. "From Outcome-Based to Language-Based Preferences," Journal of Economic Literature, American Economic Association, vol. 62(1), pages 115-154, March.
    8. Martin A. Nowak & Karl Sigmund, 1998. "Evolution of indirect reciprocity by image scoring," Nature, Nature, vol. 393(6685), pages 573-577, June.
    9. Charles Efferson & Helen Bernhard & Urs Fischbacher & Ernst Fehr, 2024. "Super-additive cooperation," Nature, Nature, vol. 626(8001), pages 1034-1041, February.
    10. M.A. Nowak & K. Sigmund, 1998. "Evolution of Indirect Reciprocity by Image Scoring/ The Dynamics of Indirect Reciprocity," Working Papers ir98040, International Institute for Applied Systems Analysis.
    11. Matjaž Perc & Zhen Wang, 2010. "Heterogeneous Aspirations Promote Cooperation in the Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 5(12), pages 1-8, December.
    12. Feng, Kehuan & Han, Songlin & Feng, Minyu & Szolnoki, Attila, 2024. "An evolutionary game with reputation-based imitation-mutation dynamics," Applied Mathematics and Computation, Elsevier, vol. 472(C).
    13. Aming Li & Lei Zhou & Qi Su & Sean P. Cornelius & Yang-Yu Liu & Long Wang & Simon A. Levin, 2020. "Evolution of cooperation on temporal networks," Nature Communications, Nature, vol. 11(1), pages 1-9, December.
    14. Martin A. Nowak & Karl Sigmund, 2005. "Evolution of indirect reciprocity," Nature, Nature, vol. 437(7063), pages 1291-1298, October.
    15. Christoph Hauert & Michael Doebeli, 2004. "Spatial structure often inhibits the evolution of cooperation in the snowdrift game," Nature, Nature, vol. 428(6983), pages 643-646, April.
    16. 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).
    17. Zhang, Lan & Xie, Yuan & Huang, Changwei & Li, Haihong & Dai, Qionglin, 2020. "Heterogeneous investments induced by historical payoffs promote cooperation in spatial public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    18. He, Jialu & Cui, Lei, 2024. "The persistence-based game transition resolves the social dilemma," Applied Mathematics and Computation, Elsevier, vol. 477(C).
    19. Zhang, Yali & Lu, Yikang & Jin, Haoyu & Dong, Yuting & Du, Chunpeng & Shi, Lei, 2024. "The impact of dynamic reward on cooperation in the spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    20. Han, Xu & Zhao, Xiaowei & Xia, Haoxiang, 2018. "Promotion of cooperation by adaptive interaction: The role of heterogeneity in neighborhoods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 483-491.
    21. Zou, Qingsong & Hu, Kaipeng, 2020. "Heterogeneous aspiration resolves social dilemma in structured populations," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    22. Han, Xu & Xia, Haoxiang & Zhao, Xiaowei, 2024. "Memory–based adaptive interaction willingness enhances cooperation in spatial prisoner's dilemma," Applied Mathematics and Computation, Elsevier, vol. 476(C).
    23. Qian, Jia-Li & Zhou, Yin-Xiang & Hao, Qing-Yi, 2024. "The emergence of cooperative behavior based on random payoff and heterogeneity of concerning social image," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    24. 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).
    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. Qiang, Shiru & Zhang, Hui, 2025. "Effect of adaptive migration with interaction intensity on the evolution of cooperation," Ecological Modelling, Elsevier, vol. 508(C).
    2. Li, Xiaopeng & Zhang, Xiuli & Wang, Zhonglin & Pang, Yicheng, 2025. "Dynamic asymmetric reflective decision-making supports the evolution of cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).

    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. Qiang, Shiru & Zhang, Hui, 2025. "Effect of adaptive migration with interaction intensity on the evolution of cooperation," Ecological Modelling, Elsevier, vol. 508(C).
    2. Yue, Hongyu & Xiong, Xiaojin & Feng, Minyu & Szolnoki, Attila, 2025. "Dynamic evolution of cooperation based on adaptive reputation threshold and game transition," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    3. Yao Meng & Sean P. Cornelius & Yang-Yu Liu & Aming Li, 2024. "Dynamics of collective cooperation under personalised strategy updates," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    4. Xie, Kai & Liu, Yaojun & Liu, Tingjin, 2024. "Unveiling the masks: Deception and reputation in spatial prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    5. Chengzhang Ma & Wei Cao & Wangheng Liu & Rong Gui & Ya Jia, 2013. "Direct Sum Matrix Game with Prisoner's Dilemma and Snowdrift Game," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-7, December.
    6. Li, Minlan & Wang, Chao & Han, Yanyan & Wang, Si-Yi & Wang, Ruiwu, 2025. "Environmental feedback promotes cooperation in a spatial prisoner's dilemma game with preferential selection," Applied Mathematics and Computation, Elsevier, vol. 495(C).
    7. Xie, Kai & Liu, Xingwen & Wang, Huazhang & Jiang, Yulian, 2023. "Multi-heterogeneity public goods evolutionary game on lattice," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    8. Du, Faqi & Fu, Feng, 2013. "Quantifying the impact of noise on macroscopic organization of cooperation in spatial games," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 35-44.
    9. Xie, Kai & Szolnoki, Attila, 2025. "Reputation in public goods cooperation under double Q-learning protocol," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    10. Swami Iyer & Timothy Killingback, 2020. "Evolution of Cooperation in Social Dilemmas with Assortative Interactions," Games, MDPI, vol. 11(4), pages 1-31, September.
    11. Wang, Yang & Lu, Shounan, 2025. "Environmental-feedback-driven time-varying reputation update solve social dilemmas," Applied Mathematics and Computation, Elsevier, vol. 507(C).
    12. Quan, Ji & Tao, Yufan & Wang, Xianjia, 2025. "Evolution of cooperation in spatial public goods games with resource-allocating leaders," Chaos, Solitons & Fractals, Elsevier, vol. 197(C).
    13. Ge, Xin & Yang, Jian & He, Xi & Liu, Yue & Zhao, YiXiang & Li, Lili, 2025. "Effects of third-order reputation mechanism on the dynamic evolution of cooperation in mixed-games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 660(C).
    14. Lv, Shaojie & Wang, Xianjia, 2020. "The impact of heterogeneous investments on the evolution of cooperation in public goods game with exclusion," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    15. Hu, Menglong & Wang, Juan & Kong, Lingcong & An, Kang & Bi, Tao & Guo, Baohong & Dong, Enzeng, 2015. "Incorporating the information from direct and indirect neighbors into fitness evaluation enhances the cooperation in the social dilemmas," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 47-52.
    16. Xiong, Xiaojin & Yao, Yichao & Feng, Minyu & Chica, Manuel, 2024. "Adaptive payoff-driven interaction in networked snowdrift games," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    17. 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.
    18. Hu, Qi & Jin, Tao & Jiang, Yulian & Liu, Xingwen, 2024. "Reputation incentives with public supervision promote cooperation in evolutionary games," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    19. Isamu Okada, 2020. "A Review of Theoretical Studies on Indirect Reciprocity," Games, MDPI, vol. 11(3), pages 1-17, July.
    20. Rezaei, Golriz & Kirley, Michael, 2012. "Dynamic social networks facilitate cooperation in the N-player Prisoner’s Dilemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6199-6211.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:191:y:2025:i:c:s0960077924013870. 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.