Group formation in the spatial public goods game with continuous strategies

We study group formation in the spatial public goods game with continuous strategies. An active group will become inactive with high (low) probability if the collective contribution is below (above) a threshold value. Meanwhile, an inactive group recovers to be active with some probability. We have found that the cooperation level and the average payoff of players are maximized at moderate values of the threshold and the recovery rate. Spatial distributions of strategies and active groups are plotted to understand the evolution of cooperation.