Impact of critical mass on the evolution of cooperation in spatial public goods games

We study the evolution of cooperation under the assumption that the collective benefits of group membership can only be harvested if the fraction of cooperators within the group, i.e., their critical mass, exceeds a threshold value. Considering structured populations, we show that a moderate fraction of cooperators can prevail even at very low multiplication factors if the critical mass is minimal. For larger multiplication factors, however, the level of cooperation is highest at an intermediate value of the critical mass. The latter is robust to variations of the group size and the interaction network topology. Applying the optimal critical mass threshold, we show that the fraction of cooperators in public goods games is significantly larger than in the traditional linear model, where the produced public good is proportional to the fraction of cooperators within the group.