Leaving the loners alone: evolution of cooperation in the presence of antisocial punishment.

The idea that voluntary participation may promote the evolution of cooperation and punishment in public good games has been recently called into question based on the study of the complete strategy set in which anyone can punish anyone else. If punishment actions are detached from contribution and participation in the game, the combination of punishment and voluntary participation no longer leads to high levels of cooperation. We show that this result crucially depends on specific details of the role of those who abstain from the collective endeavour, and only holds for a small subset of assumptions. If these loners are truly alone, cooperators who punish only defectors prevail, even when antisocial punishment is available.