Group learning versus local learning: Which is prefer for public cooperation?

We study the evolution of cooperation in public goods games on various graphs, focusing on the effects that are brought by different kinds of strategy donors. This highlights a basic feature of a public good game, for which there exists a remarkable difference between the interactive players and the players who are imitated. A player can learn from all the groups where the player is a member or from the typically local nearest neighbors, and the results show that the group learning rules have better performance in promoting cooperation on many networks than the local learning rules. The heterogeneity of networks' degree may be an effective mechanism for harvesting the cooperation expectation in many cases, however, we find that heterogeneity does not definitely mean the high frequency of cooperators in a population under group learning rules. It was shown that cooperators always hardly evolve whenever the interaction and the replacement do not coincide for evolutionary pairwise dilemmas on graphs, while for PG games we find that breaking the symmetry is conducive to the survival of cooperators.