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Coevolution of consensus and cooperation in evolutionary Hegselmann–Krause dilemma with the cooperation cost

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  • Huang, Changwei
  • Hou, Yongzhao
  • Han, Wenchen

Abstract

In this work, we focus on the opinion consensus involved with evolutionary games based on Hegselmann–Krause model. Agents can choose to be defective, unwilling to change their opinions, or cooperative, willing to change opinions following the ordinary Hegselmann–Krause rule. The payoff of an agent is assumed as the local benefit, depicting the local consensus around this agent, paying the opinion variation cost, the effort to change the agent’s opinion. Increasing the cost hinders the preference of cooperation and suppresses forging consensus. On the contrary, increasing the bounded confidence, as well as the average degree, helps agents gain a higher benefit and reach consensus. The consensus is the tradeoff between supportive factors, a high confidence bound or a large average degree, and the drawback, a high variation cost. When these two competitive factors share a same strength, it costs the longest time for the population reaching consensus. It is verified by numerical simulations on not only scale-free networks but also Erdös-Rényi random networks.

Suggested Citation

  • Huang, Changwei & Hou, Yongzhao & Han, Wenchen, 2023. "Coevolution of consensus and cooperation in evolutionary Hegselmann–Krause dilemma with the cooperation cost," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923001169
    DOI: 10.1016/j.chaos.2023.113215
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    1. Han, Wenchen & Gao, Shun & Huang, Changwei & Yang, Junzhong, 2022. "Non-consensus states in circular opinion model with repulsive interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    2. Ren, Yizhi & Chen, Xiangyu & Wang, Zhen & Shi, Benyun & Cui, Guanghai & Wu, Ting & Choo, Kim-Kwang Raymond, 2018. "Neighbor-considered migration facilitates cooperation in prisoner’s dilemma games," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 95-105.
    3. Xi Chen & Xiao Zhang & Yong Xie & Wei Li, 2017. "Opinion Dynamics of Social-Similarity-Based Hegselmann–Krause Model," Complexity, Hindawi, vol. 2017, pages 1-12, December.
    4. Huang, Changwei & Dai, Qionglin & Han, Wenchen & Feng, Yuee & Cheng, Hongyan & Li, Haihong, 2018. "Effects of heterogeneous convergence rate on consensus in opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 428-435.
    5. Xinhao Yang & Sheng Xu & Ze Li, 2017. "Consensus Congestion Control in Multirouter Networks Based on Multiagent System," Complexity, Hindawi, vol. 2017, pages 1-10, June.
    6. Xi Chen & Zhan Wu & Hongwei Wang & Wei Li, 2017. "Impact of Heterogeneity on Opinion Dynamics: Heterogeneous Interaction Model," Complexity, Hindawi, vol. 2017, pages 1-10, April.
    7. Rainer Hegselmann & Ulrich Krause, 2002. "Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 5(3), pages 1-2.
    8. Guillaume Deffuant & David Neau & Frederic Amblard & Gérard Weisbuch, 2000. "Mixing beliefs among interacting agents," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 3(01n04), pages 87-98.
    9. Baumann, Fabian & Sokolov, Igor M. & Tyloo, Melvyn, 2020. "A Laplacian approach to stubborn agents and their role in opinion formation on influence networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    10. Pineda, M. & Buendía, G.M., 2015. "Mass media and heterogeneous bounds of confidence in continuous opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 420(C), pages 73-84.
    11. Fei Ding & Yun Liu & Yong Li, 2009. "Co-Evolution Of Opinion And Strategy In Persuasion Dynamics: An Evolutionary Game Theoretical Approach," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 479-490.
    12. Fu, Guiyuan & Zhang, Weidong & Li, Zhijun, 2015. "Opinion dynamics of modified Hegselmann–Krause model in a group-based population with heterogeneous bounded confidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 558-565.
    13. Han, Wenchen & Huang, Changwei & Yang, Junzhong, 2019. "Opinion clusters in a modified Hegselmann–Krause model with heterogeneous bounded confidences and stubbornness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    14. Quanbo Zha & Gang Kou & Hengjie Zhang & Haiming Liang & Xia Chen & Cong-Cong Li & Yucheng Dong, 2020. "Opinion dynamics in finance and business: a literature review and research opportunities," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-22, December.
    15. Shun Gao & Changwei Huang & Wenchen Han & Junzhong Yang, 2020. "General consensus with circular opinion under attractive and repulsive mechanisms," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-11, March.
    16. Alessandro Di Mare & Vito Latora, 2007. "Opinion Formation Models Based On Game Theory," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(09), pages 1377-1395.
    17. Han, Wenchen & Feng, Yuee & Qian, Xiaolan & Yang, Qihui & Huang, Changwei, 2020. "Clusters and the entropy in opinion dynamics on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
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