Rare but severe concerted punishment that favors cooperation |
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Authors: | Deng Kuiying Li Zhuozheng Kurokawa Shun Chu Tianguang |
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Institution: | a State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, Chinab Department of Biological Sciences, The University of Tokyo, Bunkyoku, Tokyo 113-0033, Japanc Key Laboratory of Machine Perception (Ministry of Education), Peking University, Beijing 100871, China |
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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. |
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Keywords: | Finite population Fixation probability Evolutionarily stable strategy Public Goods game |
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