Though contradicting with natural selection, cooperative behaviors widely exist in practice and seem to be an effective measure to maintain the functioning of complex systems. As revealed by previous studies, punishment is capable of promoting cooperation and therefore various types of punishment are proposed. Previously, scholars mainly focus on investigating either peer punishment or pool punishment, whereas in social and biological systems, an individual might function as different roles when facing different players. Thus, we mainly investigate these two types of punishment together and the effects of punishment-type transfer on the evolutionary dynamics are further provided with sufficient analyses in this manuscript. Role of different type of punishment on cooperation seems to be related to the number of punishers (being denoted as T) among corresponding neighbors. Simulations are conducted in order to investigate the effect of threshold reflecting the punishment-type switching on evolutionary dynamics, while peer punishment is proved to be more effective than pool punishment in promoting cooperation. We hope our findings here can shed some lights on the investigation of punishment.

尽管与自然选择相矛盾，但是合作行为在实践中广泛存在，并且似乎是维持复杂系统功能的有效措施。正如以前的研究所揭示的那样，惩罚能够促进合作，因此提出了各种惩罚措施。以前，学者主要研究同伴惩罚或共同惩罚，而在社会和生物系统中，当面对不同的参与者时，个人可能会扮演不同的角色。因此，我们主要一起研究这两种惩罚，并在本文中提供了足够的分析，进一步探讨了惩罚型转移对进化动力学的影响。不同类型的惩罚在合作中的作用似乎与惩罚者的数量有关（表示为T）在相应的邻居之间。为了研究反映惩罚类型转换的阈值对进化动力学的影响，进行了模拟，而事实证明，同伴惩罚在促进合作方面比集合惩罚更为有效。我们希望我们在这里的发现可以对惩罚的调查有所启发。