Abstract The role of incentive institutions on promoting cooperation in public goods game (PGG) has attracted much attention. Theoretical studies based on Nash equilibrium analysis predict that the punishment effect is often stronger than the reward effect. Although this result is confirmed by empirical studies, subjects do not always play these rational strategies. Recent experiments indicate that most subjects in PGGs are conditional cooperators who tend to contribute the group average. In this paper, we consider PGGs with three types of subjects, namely, cooperators, defectors, and conditional cooperators. Evolutionary game method is applied to investigate how conditional cooperators affect the effectiveness of different types of incentives. Overall, having conditional cooperators cannot lead to a higher contribution level in the standard PGG or the PGG with institutional rewards. However, they can enhance the effectiveness of institutional punishment, where a high contribution level can be maintained even for small punishments. As a consequence, in PGGs with conditional cooperators, punishment always leads to a higher contribution rate than do rewards. Numerical analysis indicates that this result is robust to errors in decision making.

中文翻译：

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有条件的合作者在公共产品博弈中加强制度惩罚

摘要 激励机制在促进公共产品博弈（PGG）合作中的作用备受关注。基于纳什均衡分析的理论研究预测，惩罚效应往往强于奖励效应。尽管这一结果得到了实证研究的证实，但受试者并不总是采取这些理性策略。最近的实验表明，PGG 中的大多数受试者都是有条件的合作者，他们倾向于贡献群体平均值。在本文中，我们考虑具有三类主体的 PGG，即合作者、叛逃者和有条件的合作者。应用进化博弈方法研究有条件的合作者如何影响不同类型激励的有效性。全面的，有条件的合作者不能在标准 PGG 或有机构奖励的 PGG 中带来更高的贡献水平。但是，它们可以提高制度惩罚的有效性，即使是轻微的惩罚也可以保持较高的贡献水平。因此，在具有条件合作者的 PGG 中，惩罚总是导致比奖励更高的贡献率。数值分析表明，该结果对决策错误具有鲁棒性。