合作行为普遍存在于人类社会，定量理解个体和群体合作行为的传播因而成为物理、生物和管理等学科的热点研究问题之一。近年来，惩罚、声望和空间效应等合作机制被相继发现。我们研究了惩罚效率对合作行为的影响。

在雪堆博弈中，参与者可以选择合作或者背叛策略。当合作者与合作者进行博弈时，两者的收益均为1；当合作者与背叛者进行博弈的时候，合作者的收益为1-r，而背叛者的收益为1+r；当背叛者和背叛者进行博弈的时候，两者的收益均为0。参数r刻画成本效益比，0<r<1。通过招募志愿者进行雪堆博弈实验，我们发现，体系的合作者所占比例和平均收益均随着成本效益比r的增加而减少。这说明r较小的时候，合作易于维持；而r较大的时候，合作难于维持。接着，我们考察了在这两种情形下，惩罚的效率。我们发现当r=0.2,时，重罚和轻罚在统计意义上的效率是相同的；而当r=0.8时，重罚的效率明显优于轻罚。这就说明了。当合作易于维持的时候，轻罚就能收到很好的效果，而在合作难于维持的时候，重罚能够收到好的效果。谓之，盛世施仁政，乱世用重典。

If Cooperation Is Likely Punish Mildly: Insights from Economic ExperimentsBased on the Snowdrift Game

Punishment may deter antisocial behavior. Yet to punishis costly, and the costs often do not offset the gains that are due to elevatedlevels of cooperation. However, the effectiveness of punishment depends notonly on how costly it is, but also on the circumstances defining the socialdilemma. Using the snowdrift game as the basis, we have conducted a series of economicexperiments to determine whether severe punishment is more effective than mildpunishment. We have observed that severe punishment is not necessarily more effective,even if the cost of punishment is identical in both cases. The benefits ofsevere punishment become evident only under extremely adverse conditions, whento cooperate is highly improbable in the absence of sanctions. If cooperationis likely, mild punishment is not less effective and leads to higher averagepayoffs, and is thus the much preferred alternative. Presented results suggestthat the positive effects of punishment stem not only from imposed fines, butmay also have a psychological background. Small fines can do wonders inmotivating us to chose cooperation over defection, but without the paralyzingeffect that may be brought about by large fines. The later should be utilizedonly when absolutely necessary.

论文链接：http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0064677

论文下载：If Cooperation Is Likely Punish Mildly.pdf