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Rare but severe concerted punishment that favors cooperation

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  • Deng, Kuiying
  • Li, Zhuozheng
  • Kurokawa, Shun
  • Chu, Tianguang

Abstract

As one of the mechanisms that are supposed to explain the evolution of cooperation among unrelated individuals, costly punishment, in which altruistic individuals privately bear the cost to punish defection, suffers from such drawbacks as decreasing individuals’ welfare, inducing second-order free riding, the difficulty of catching defection, and the possibility of triggering retaliation. To improve this promising mechanism, here we propose an extended Public Goods game with rare but severe concerted punishment, in which once a defector is caught punishment is triggered and the cost of punishment is equally shared among the remainder of the group. Analytical results show that, when the probability for concerted punishment is above a threshold, cooperating is, while defecting is not, an evolutionarily stable strategy in finite populations, and that this way of punishment can considerably decrease the total cost of inhibiting defection, especially in large populations.

Suggested Citation

  • Deng, Kuiying & Li, Zhuozheng & Kurokawa, Shun & Chu, Tianguang, 2012. "Rare but severe concerted punishment that favors cooperation," Theoretical Population Biology, Elsevier, vol. 81(4), pages 284-291.
    • Handle: RePEc:eee:thpobi:v:81:y:2012:i:4:p:284-291
    DOI: 10.1016/j.tpb.2012.02.005
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    Cited by:

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    2. Shi, Zhenyu & Wei, Wei & Zheng, Hongwei & Zheng, Zhiming, 2023. "Bidirectional supervision: An effective method to suppress corruption and defection under the third party punishment mechanism of donation games," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    3. Shun Kurokawa & Joe Yuichiro Wakano & Yasuo Ihara, 2018. "Evolution of Groupwise Cooperation: Generosity, Paradoxical Behavior, and Non-Linear Payoff Functions," Games, MDPI, vol. 9(4), pages 1-24, December.
    4. Fukutomi, Masao & Kurokawa, Shun, 2018. "How much cost should reciprocators pay in order to distinguish the opponent's cooperation from the opponent's defection?," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 301-314.
    5. Luo-Luo Jiang & Matjaž Perc & Attila Szolnoki, 2013. "If Cooperation Is Likely Punish Mildly: Insights from Economic Experiments Based on the Snowdrift Game," PLOS ONE, Public Library of Science, vol. 8(5), pages 1-7, May.
    6. Kurokawa, Shun, 2019. "How memory cost, switching cost, and payoff non-linearity affect the evolution of persistence," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 174-192.

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