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Mercenary punishment in structured populations

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  • Lee, Hsuan-Wei
  • Cleveland, Colin
  • Szolnoki, Attila

Abstract

Punishing those who refuse to participate in common efforts is a known and intensively studied way to maintain cooperation among self-interested agents. But this act is costly, hence punishers who are generally also engaged in the original joint venture, become vulnerable, which jeopardizes the effectiveness of this incentive. As an alternative, we may hire special players, whose only duty is to watch the population and punish defectors. Such a policelike or mercenary punishment can be maintained by a tax-based fund. If this tax is negligible, a cyclic dominance may emerge among different strategies. When this tax is relevant then this solution disappears. In the latter case, the fine level becomes a significant factor that determines whether punisher players coexist with cooperators or alternatively with defectors. The maximal average outcome can be reached at an intermediate cost value of punishment. Our observations highlight that we should take special care when such kind of punishment and accompanying tax are introduced to reach a collective goal.

Suggested Citation

  • Lee, Hsuan-Wei & Cleveland, Colin & Szolnoki, Attila, 2022. "Mercenary punishment in structured populations," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    • Handle: RePEc:eee:apmaco:v:417:y:2022:i:c:s0096300321008791
    DOI: 10.1016/j.amc.2021.126797
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    1. Fu, Mingjian & Wang, Jingbin & Cheng, Linlin & Chen, Lijuan, 2021. "Promotion of cooperation with loyalty-based reward in the spatial prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    2. Mark Broom & Igor V. Erovenko & Jan Rychtář, 2021. "Modelling Evolution in Structured Populations Involving Multiplayer Interactions," Dynamic Games and Applications, Springer, vol. 11(2), pages 270-293, June.
    3. Xu, Liang & Cao, Xianbin & Du, Wenbo & Li, Yumeng, 2018. "Effects of taxation on the evolution of cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 63-68.
    4. Filippo Palombi & Stefano Ferriani & Simona Toti, 2020. "Coevolutionary dynamics of a variant of the cyclic Lotka–Volterra model with three-agent interactions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(10), pages 1-18, October.
    5. 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).
    6. Lee, Hsuan-Wei & Cleveland, Colin & Szolnoki, Attila, 2021. "Small fraction of selective cooperators can elevate general wellbeing significantly," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    7. Cheng, Fei & Chen, Tong & Chen, Qiao, 2019. "Matching donations based on social capital in Internet crowdfunding can promote cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    8. He, Nanrong & Chen, Xiaojie & Szolnoki, Attila, 2019. "Central governance based on monitoring and reporting solves the collective-risk social dilemma," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 334-341.
    9. Shannon R. Serrao & Uwe C. Täuber, 2021. "Stabilizing spiral structures and population diversity in the asymmetric May–Leonard model through immigration," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(8), pages 1-15, August.
    10. Lv, Shaojie & Song, Feifei, 2022. "Particle swarm intelligence and the evolution of cooperation in the spatial public goods game with punishment," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    11. Qian Zhao & Yajun Mao & Zhihai Rong, 2020. "The evolution of extortion strategy in the kagome lattice," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(11), pages 1-10, November.
    12. Liu, Run-Ran & Jia, Chun-Xiao & Rong, Zhihai, 2019. "Effects of enhancement level on evolutionary public goods game with payoff aspirations," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 242-248.
    13. Dirk Helbing & Attila Szolnoki & Matjaž Perc & György Szabó, 2010. "Evolutionary Establishment of Moral and Double Moral Standards through Spatial Interactions," PLOS Computational Biology, Public Library of Science, vol. 6(4), pages 1-9, April.
    14. Nagatani, Takashi, 2019. "Infection promotes species coexistence: Rock–paper–scissors game with epidemic on graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    15. Cheng, Fei & Chen, Tong & Chen, Qiao, 2020. "Rewards based on public loyalty program promote cooperation in public goods game," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    16. Szolnoki, Attila & Chen, Xiaojie, 2020. "Strategy dependent learning activity in cyclic dominant systems," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    17. Xiaojie Chen & Attila Szolnoki, 2018. "Punishment and inspection for governing the commons in a feedback-evolving game," PLOS Computational Biology, Public Library of Science, vol. 14(7), pages 1-15, July.
    18. Liu, Jinzhuo & Li, Tong & Wang, Wei & Zhao, Na & Hang, Feilu, 2018. "Impact of strategy-neutral rewarding on the evolution of cooperative behavior," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 76-79.
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    6. Shuo Wang & Zhuang Li & Weidong Li & Hua Jiang, 2022. "Continuous Spatial Public Goods Game Based on Particle Swarm Optimization with Memory Stability," Mathematics, MDPI, vol. 10(23), pages 1-16, December.
    7. Sun, Xingping & Li, Mingyuan & Kang, Hongwei & Shen, Yong & Chen, Qingyi, 2023. "Combined effect of pure punishment and reward in the public goods game," Applied Mathematics and Computation, Elsevier, vol. 445(C).
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    15. Zhang, Huizhen & An, Tianbo & Yan, Pingping & Hu, Kaipeng & An, Jinjin & Shi, Lijuan & Zhao, Jian & Wang, Jingrui, 2024. "Exploring cooperative evolution with tunable payoff’s loners using reinforcement learning," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    16. Shen, Yong & Lei, Wei & Kang, Hongwei & Li, Mingyuan & Sun, Xingping & Chen, Qingyi, 2023. "Evolutionary dynamics of public goods game with tax-based rewarding cooperators," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    17. Zhang, Yao & Hao, Qing-Yi & Qian, Jia-Li & Wu, Chao-Yun & Bi, Yan, 2024. "The influence of the heterogeneities of social institutions and individuals’ tendency to establish social institutions on cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
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    22. Jun Qian & Tongda Zhang & Xiao Sun & Yueting Chai, 2023. "The coordination of collective and individual solutions in risk-resistant scenarios," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(2), pages 1-15, February.

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