Promoting cooperation by punishing minority.

A new mechanism of punishment is proposed in the spatial public goods game.Individuals with the majority strategy will punish those with the minority strategy.The results show that cooperation is greatly enhanced by punishing minority.Both of the first and the second phase transitions are found in our model. Punishment is an effective way to sustain cooperation among selfish individuals. In most of previous studies, objects of punishment are set to be defectors. In this paper, we propose a mechanism of punishment, in which individuals with the majority strategy will punish those with the minority strategy in a public goods game group. Both theoretical analysis and simulation show that the cooperation level can be greatly enhanced by punishing minority. For no punishment or small values of punishment fine, the fraction of cooperators continuously increases with the multiplication factor. However, for large values of punishment fine, there exists a critical value of multiplication factor, at which the fraction of cooperators suddenly jumps from 0 to 1. The density of different types of groups is also studied.