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Tolerance-based punishment in continuous public goods game

Author

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  • Gao, Jia
  • Li, Zhi
  • Cong, Rui
  • Wang, Long

Abstract

Altruistic punishment for defectors is considered as a key motive for the explanation of cooperation. However, there is no clear border between the cooperative and defective behaviors in a continuous strategy game. We propose a model to study the effect of punishment on the evolution of cooperation in continuous public goods game, wherein individuals have the traits to punish the co-players based on social tolerance. We show that a reasonable punishment with a uniform tolerance can spur individuals to make more investments. Additionally, for a fixed punishment cost and a fixed fine, a moderate value of tolerance can result in the best promotion of cooperation. Furthermore, we investigate the coevolutionary dynamics of investment and tolerance. We find that the population splits into two branches: high-tolerance individuals who make high investments and low-tolerance individuals who make low investments. A dynamic equilibrium is achieved between these two types of individuals. Our work extends punishment to continuous cooperative behaviors and the results may enhance the understanding of altruistic punishment in the evolution of human cooperation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:16:p:4111-4120
    DOI: 10.1016/j.physa.2012.03.027
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    Cited by:

    1. 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).
    2. 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).
    3. Chen, Qiao & Chen, Tong & Wang, Yongjie, 2016. "How the expanded crowd-funding mechanism of some southern rural areas in China affects cooperative behaviors in threshold public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 649-655.
    4. Hajime Shimao & Mayuko Nakamaru, 2013. "Strict or Graduated Punishment? Effect of Punishment Strictness on the Evolution of Cooperation in Continuous Public Goods Games," PLOS ONE, Public Library of Science, vol. 8(3), pages 1-10, March.
    5. Quan, Ji & Yang, Wenjun & Li, Xia & Wang, Xianjia & Yang, Jian-Bo, 2020. "Social exclusion with dynamic cost on the evolution of cooperation in spatial public goods games," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    6. Lu, Peng, 2015. "Learn good from bad: Effects of good and bad neighbors in spatial prisoners’ dilemma games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 351-358.
    7. Liu, Yandi & Zheng, Tainian & Li, Yonghui & Dai, Yu, 2020. "Does the conformity save us when information advantage fails?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    8. Lu, Peng, 2015. "Individual choice and reputation distribution of cooperative behaviors among heterogeneous groups," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 39-46.
    9. Lu, Peng & Wang, Fang, 2015. "Heterogeneity of inferring reputation probability in cooperative behaviors for the spatial prisoners’ dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 367-378.
    10. Lu, Peng, 2015. "Imitating winner or sympathizing loser? Quadratic effects on cooperative behavior in prisoners’ dilemma games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 327-337.
    11. Quan, Ji & Yang, Xiukang & Wang, Xianjia, 2018. "Spatial public goods game with continuous contributions based on Particle Swarm Optimization learning and the evolution of cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 973-983.
    12. 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).
    13. Zhang, Shuhua & Zhang, Zhipeng & Wu, Yu’e & Yan, Ming & Xie, Yunya, 2018. "Tolerance-based punishment and cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 267-272.
    14. Peng Lu & Xiaoping Zheng, 2015. "Social Stratification and Cooperative Behavior in Spatial Prisoners' Dilemma Games," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-16, July.

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