Group penalty on the evolution of cooperation in spatial public goods games

We study the evolution of cooperation in spatial public goods games, whereby a coevolutionary rule is introduced that aims to integrate group penalty into the framework of evolutionary games. Existing groups are deleted whenever the collective gains of the focal individuals are less than a deletion threshold value. Meanwhile, newcomers are added after each game iteration to maintain the fixed population size. The networking effect is also studied via four representative interaction networks which are associated with the population structure. We conclude that the cooperation level has a strong dependence on the deletion threshold, and the suitable value range of the deletion threshold which is associated with the maximal cooperation frequency has been found. Simulation results also show that optimum values of the deletion threshold can still warrant the most potent promotion of cooperation, irrespective of which of the four topologies is applied.