Center for Systems and Control, College of Engineering, Peking University, Beijing, 100871, China.
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China.
Sci Rep. 2018 Jan 11;8(1):528. doi: 10.1038/s41598-017-18727-7.
Punishment is widely recognized as an effective approach for averting from exploitation by free-riders in human society. However, punishment is costly, and thus rational individuals are unwilling to take the punishing action, resulting in the second-order free-rider problem. Recent experimental study evidences that individuals prefer conditional punishment, and their punishing decision depends on other members' punishing decisions. In this work, we thus propose a theoretical model for conditional punishment and investigate how such conditional punishment influences cooperation in the public goods game. Considering conditional punishers only take the punishing action when the number of unconditional punishers exceeds a threshold number, we demonstrate that such conditional punishment induces the effect of a double-edged sword on the evolution of cooperation both in well-mixed and structured populations. Specifically, when it is relatively easy for conditional punishers to engage in the punishment activity corresponding to a low threshold value, cooperation can be promoted in comparison with the case without conditional punishment. Whereas when it is relatively difficult for conditional punishers to engage in the punishment activity corresponding to a high threshold value, cooperation is inhibited in comparison with the case without conditional punishment. Moreover, we verify that such double-edged sword effect exists in a wide range of model parameters and can be still observed in other different punishment regimes.
惩罚被广泛认为是人类社会中防止搭便车行为的有效方法。然而，惩罚是有代价的，因此理性个体不愿意采取惩罚行为，从而导致了二阶搭便车问题。最近的实验研究表明，个体更喜欢条件性惩罚，并且他们的惩罚决策取决于其他成员的惩罚决策。在这项工作中，我们提出了一个条件性惩罚的理论模型，并研究了这种条件性惩罚如何影响公共物品博弈中的合作。考虑到条件惩罚者只有在无条件惩罚者的数量超过一个阈值时才会采取惩罚行为，我们证明了这种条件性惩罚在均匀混合和结构种群中对合作的进化都有双重作用。具体来说，当条件惩罚者相对容易参与对应于低阈值的惩罚活动时，与没有条件惩罚的情况相比，合作可以得到促进。而当条件惩罚者相对难以参与对应于高阈值的惩罚活动时，与没有条件惩罚的情况相比，合作受到抑制。此外，我们验证了这种双刃剑效应存在于广泛的模型参数范围内，并且在其他不同的惩罚制度中仍然可以观察到。
