Synergy punishment promotes cooperation in spatial public good game

In previous work, punishment has been proved to an effective way to promote cooperation, and punish is introduced as a strategy just like cooperate or defect. In this paper, however, we introduce a new synergy punishment mechanism into a spatial public good game which is different from the previous works, every cooperator has a probability to be a punisher, additionally if punishment is carried out by several punishers, the cost of punishment will be reduced by synergistic effect. The simulation results show that punishment can promote cooperation and the synergistic effect has an obvious influence on cooperation for a small punishment fine but has little influence for a big punishment fine.