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Costly punishment and cooperation in the evolutionary snowdrift game

Author

Listed:
  • Xu, C.
  • Ji, M.
  • Yap, Yee Jiun
  • Zheng, Da-Fang
  • Hui, P.M.

Abstract

The role of punishments in promoting cooperation is an important issue. We incorporate costly punishments into the snowdrift game (SG) by introducing a third punishing (P) character, and study the effects. The punishers, who carry basically a cooperative (C) character, are willing to pay a cost α so as to punish a non-cooperative (D) opponent by β. Depending on the initial fractions of the characters, α, β, and the cost-to-benefit ratio r in the SG, the three-character system evolves into a steady state consisting either only of C and P characters or only of C and D characters, in a well-mixed population. The former situation represents an enhancement in cooperation relative to the SG, while the latter is similar to the SG. The dynamics in approaching these different steady states are found to be different. Analytically, the key features in the dynamics and the steady states observed in simulations are captured by a set of differential equations. The sensitivity to the initial distribution of characters is studied by depicting the flow in a phase portrait and analyzing the nature of fixed points. The analysis also shows the role of P-character agents in preventing a system from invasion by D-character agents. Starting from a population consisting only of C and P agents, a D-character agent intended to invade the system cannot survive when the initial fraction of P agents is greater than r/β. Our model, defined intentionally as a simulation algorithm, can be readily generalized to incorporate many interesting effects, such as those in a networked population.

Suggested Citation

  • Xu, C. & Ji, M. & Yap, Yee Jiun & Zheng, Da-Fang & Hui, P.M., 2011. "Costly punishment and cooperation in the evolutionary snowdrift game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1607-1614.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:9:p:1607-1614
    DOI: 10.1016/j.physa.2010.12.044
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    Citations

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    Cited by:

    1. André Barreira Da Silva Rocha, 2017. "Cooperation In The Well-Mixed Two-Population Snowdrift Game With Punishment Enforced Through Different Mechanisms," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 20(04n05), pages 1-21, June.
    2. repec:ehu:ikerla:6608 is not listed on IDEAS
    3. Barreira da Silva Rocha, André & Laruelle, Annick, 2012. "Evolution of Cooperation in the Snowdrift Game with Incomplete Information and Heterogeneous Population," IKERLANAK 2012-62, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    4. Chen Shen & Chen Chu & Yini Geng & Jiahua Jin & Fei Chen & Lei Shi, 2018. "Cooperation enhanced by the coevolution of teaching activity in evolutionary prisoner's dilemma games with voluntary participation," PLOS ONE, Public Library of Science, vol. 13(2), pages 1-8, February.
    5. Zhong, Li-Xin & Xu, Wen-Juan & He, Yun-Xin & Zhong, Chen-Yang & Chen, Rong-Da & Qiu, Tian & Shi, Yong-Dong & Ren, Fei, 2017. "A generalized public goods game with coupling of individual ability and project benefit," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 73-80.
    6. repec:ehu:ikerla:8914 is not listed on IDEAS
    7. Wang, Mengyao & Pan, Qiuhui & He, Mingfeng, 2020. "The effect of individual attitude on cooperation in social dilemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    8. Silveira, Douglas & Vasconcelos, Silvinha, 2020. "Essays on duopoly competition with asymmetric firms: Is profit maximization always an evolutionary stable strategy?," International Journal of Production Economics, Elsevier, vol. 225(C).
    9. André Barreira da Silva Rocha & Annick Laruelle & Peio Zuazo, 2012. "Replicator Dynamics and Evolutionary Stable Strategies in Heterogeneous Games," Discussion Papers in Economics 11/54, Division of Economics, School of Business, University of Leicester.
    10. Li-Xin Zhong & Wen-Juan Xu & Yun-Xin He & Chen-Yang Zhong & Rong-Da Chen & Tian Qiu & Yong-Dong Shi & Fei Ren, 2017. "A generalized public goods game with coupling of individual ability and project benefit," Papers 1702.07423, arXiv.org, revised May 2017.

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