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Coupling static opinions with evolutionary games: Shaping cooperation in spatial social dilemmas

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  • Qin, Lijuan
  • Zhang, Yali
  • Du, Chunpeng
  • Duan, Xiaofang
  • Lu, Yikang

Abstract

A fundamental feature of most game-theoretic models coupling opinions is that individuals’ opinions can change during interactions. However, this study explores the impact of static opinions on the evolution of cooperation in the spatial Prisoner’s Dilemma Game (PDG). By coupling fixed opinions with strategy interactions on a square lattice, we examine how opinion benefits, the conformity parameter, and group dominance affect cooperative behavior. Simulation results show that higher opinion benefits significantly enhance cooperation by facilitating the formation of cooperator clusters. In addition, the conformity parameter α balances the effects of opinions and strategies. Notably, balanced initial opinion distributions promote stable cooperation, whereas polarized distributions suppress it. These findings highlight the critical role of static opinions in shaping cooperative behavior and offer new insights into the mechanisms of cooperation in structured populations.

Suggested Citation

  • Qin, Lijuan & Zhang, Yali & Du, Chunpeng & Duan, Xiaofang & Lu, Yikang, 2025. "Coupling static opinions with evolutionary games: Shaping cooperation in spatial social dilemmas," Chaos, Solitons & Fractals, Elsevier, vol. 199(P2).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p2:s0960077925007763
    DOI: 10.1016/j.chaos.2025.116763
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    1. Ding, Rui & Wang, Xianjia & Quan, Ji & Ma, Shuting & Zhao, Jinhua, 2025. "Evolutionary dynamics of spatial public goods games with insurance mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 195(C).
    2. Butz, Britta & Harbring, Christine, 2020. "Donations as an incentive for cooperation in public good games," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 85(C).
    3. Chen, Wei & Wang, Huafeng & Sheng, Yukun, 2025. "The role of emotional expression in the evolution of cooperation in spatial prisoner’s dilemma games," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    4. Martin A. Nowak & Karl Sigmund, 1998. "Evolution of indirect reciprocity by image scoring," Nature, Nature, vol. 393(6685), pages 573-577, June.
    5. Yang, Yizhou & Li, Haihong & Gao, Shun & Dai, Qionglin & Yang, Junzhong, 2025. "Interdependent evolutionary dynamics of opinion and strategy on two-layer networks," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    6. Wang, Lu & Ye, Shun-Qiang & Cheong, Kang Hao & Bao, Wei & Xie, Neng-gang, 2018. "The role of emotions in spatial prisoner’s dilemma game with voluntary participation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1396-1407.
    7. 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.
    8. Ding, Fei & Liu, Yun & Shen, Bo & Si, Xia-Meng, 2010. "An evolutionary game theory model of binary opinion formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1745-1752.
    9. 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).
    10. Geng, Yini & Lu, Yikang & Hong, Lijun & Shi, Lei, 2025. "Evolution of cooperation with asymmetric rewards," Applied Mathematics and Computation, Elsevier, vol. 487(C).
    11. Zhang, Zhipeng & Yang, Chen & Han, Weiwei & Xia, Chengyi, 2025. "Co-evolutionary dynamics of threshold PGGs with collective-risk environment feedback," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 658(C).
    12. Lu, Yikang & de Miguel-Arribas, Alfonso & Shi, Lei, 2025. "Influence of social peers on vaccine hesitancy under imperfect vaccination," Applied Mathematics and Computation, Elsevier, vol. 491(C).
    13. Quan, Ji & Tao, Leyao & Wang, Xianjia, 2025. "Cooperation dynamics of social dilemmas on an opinion-dependent weighted network," Applied Mathematics and Computation, Elsevier, vol. 502(C).
    14. 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).
    15. 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).
    16. Ding, Rui & Wang, Xianjia & Zhao, Jinhua & Gu, Cuiling, 2025. "Effects of punishment driven by inequity aversion on promoting cooperation in public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    17. Andrew M. Colman, 2006. "The puzzle of cooperation," Nature, Nature, vol. 440(7085), pages 744-745, April.
    18. Zhu, Zhewen & Dong, Yuting & Lu, Yikang & Shi, Lei, 2021. "Information exchange promotes and jeopardizes cooperation on interdependent networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 569(C).
    19. Unai Alvarez-Rodriguez & Federico Battiston & Guilherme Ferraz Arruda & Yamir Moreno & Matjaž Perc & Vito Latora, 2021. "Evolutionary dynamics of higher-order interactions in social networks," Nature Human Behaviour, Nature, vol. 5(5), pages 586-595, May.
    20. Floriana Gargiulo & José J Ramasco, 2012. "Influence of Opinion Dynamics on the Evolution of Games," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-7, November.
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