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The evolution of cooperation shaped by asymmetric link-weight integration capabilities

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  • Li, Xiaopeng
  • Guo, Shiyao
  • Li, Dongdong
  • Lin, Zhimin

Abstract

Previous studies have demonstrated that incorporating the dynamic adjustment link-weight into fitness calculations can significantly enhance the evolution of cooperation. However, the asymmetry of such capabilities has been largely overlooked. This study examines the role of asymmetric link-weight integration capabilities in the evolution of cooperation by categorizing players into two distinct types. Specifically, players with a proportion of β possess the ability to integrate link-weight when computing the fitness, while those with a proportion of 1−β lack this capacity. Meanwhile, the link-weight between players adaptively and dynamically adjust during the evolutionary process. Extensive Monte Carlo simulations reveal at the macro level that, the evolution of cooperation in the system exhibits a pronounced positive correlation with β. In particular, the simulation results show remarkable agreement with the theoretical predictions derived from the generalized mean-field analysis. Then, through time series, strategy patterns and strategy transitions, the microscopic mechanism of evolutionary dynamics is deeply analyzed, and it is confirmed that cooperators with the capabilities to integrate link-weight play a leading role in promoting the evolution of cooperation. Finally, robustness verification demonstrates that the asymmetric link-weight integration capabilities in promoting the evolution of cooperation is also applicable to other strategy update mode and social dilemmas. Our findings aim to shed light on the dynamics of cooperation in spatial social dilemmas, providing fresh insights for future investigations.

Suggested Citation

  • Li, Xiaopeng & Guo, Shiyao & Li, Dongdong & Lin, Zhimin, 2026. "The evolution of cooperation shaped by asymmetric link-weight integration capabilities," Chaos, Solitons & Fractals, Elsevier, vol. 202(P2).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925016005
    DOI: 10.1016/j.chaos.2025.117587
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    1. Hu, Liwen & He, Nanrong & Weng, Qifeng & Chen, Xiaojie & Perc, Matjaž, 2020. "Rewarding endowments lead to a win-win in the evolution of public cooperation and the accumulation of common resources," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Pereira, F.B. & Ferreira, R.S. & Alencar, D.S.M. & Alves, T.F.A. & Alves, G.A. & Lima, F.W.S. & Macedo-Filho, A., 2024. "Social dilemmas, network reciprocity, and small-world property," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 655(C).
    3. Liu, Chen & Shi, Juan & Li, Tong & Liu, Jinzhuo, 2019. "Aspiration driven coevolution resolves social dilemmas in networks," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 247-254.
    4. K. Sigmund, 1998. "Complex Adaptive Systems and the Evolution of Reciprocation," Working Papers ir98100, International Institute for Applied Systems Analysis.
    5. Liu, Chengyan & Lv, Wangyong & Cheng, Xinzexu & Wen, Yihao & Yang, Xiaofeng, 2024. "Evolution of strategies in evolution games on small-world networks and applications," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    6. 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.
    7. 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.
    8. Zhi-Qin Ma & Cheng-Yi Xia & Shi-Wen Sun & Li Wang & Huai-Bin Wang & Juan Wang, 2011. "Heterogeneous Link Weight Promotes The Cooperation In Spatial Prisoner'S Dilemma," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 22(11), pages 1257-1268.
    9. Xie, Yunya & Li, Jianbiao & Zhang, Yankun & Wang, Yue, 2025. "Ephemeral connections, persistent effects: Cooperation dynamics in temporal networks with historical interactions," Chaos, Solitons & Fractals, Elsevier, vol. 199(P3).
    10. Lu, Shounan & Wang, Yang, 2025. "Experience-driven learning and interactive rules under link weight adjustment promote cooperation in spatial prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 497(C).
    11. Guo, Tian & Du, Chunpeng & Shi, Lei, 2024. "Evolution of cooperation on interdependent networks: The impact of asymmetric punishment," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    12. Zhang, Gui & Xiong, Xiaojin & Pi, Bin & Feng, Minyu & Perc, Matjaž, 2025. "Spatial public goods games with queueing and reputation," Applied Mathematics and Computation, Elsevier, vol. 505(C).
    13. Xia, Cheng-yi & Ma, Zhi-qin & Wang, Yi-ling & Wang, Jin-song & Chen, Zeng-qiang, 2011. "Enhancement of cooperation in prisoner’s dilemma game on weighted lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4602-4609.
    14. Li, Xiaopeng & Sun, Shiwen & Xia, Chengyi, 2019. "Reputation-based adaptive adjustment of link weight among individuals promotes the cooperation in spatial social dilemmas," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 810-820.
    15. Ernst Fehr & Urs Fischbacher, 2003. "The nature of human altruism," Nature, Nature, vol. 425(6960), pages 785-791, October.
    16. Gao, Shun & Zhang, Wei & Zhang, Liming & Li Richter, Xiang-Yi & Zhang, Yi-Cheng & Dai, Qionglin, 2025. "Modified particle swarm strategies in spatial public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 200(P3).
    17. Chen, Hao & Cui, Weicheng, 2026. "Intergroup-based public goods games in complex networks with leader-driven other-regarding preferences," Applied Mathematics and Computation, Elsevier, vol. 508(C).
    18. Cardinot, Marcos & Griffith, Josephine & O’Riordan, Colm, 2018. "A further analysis of the role of heterogeneity in coevolutionary spatial games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 116-124.
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