The role of punishment in the spatial public goods game

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.