  Economic experiments have shown that punishment can increase public goods
game contributions over time. However, the effectiveness of punishment is
challenged by second-order freeriding and antisocial punishment. The latter
implies that non-cooperators punish cooperators, while the former implies
unwillingness to shoulder the cost of punishment. Here we extend the theory of
cooperation in the spatial public goods game by considering four competing
strategies, which are traditional cooperators and defectors, as well as
cooperators who punish defectors and defectors who punish cooperators. We show
that if the synergistic effects are high enough to sustain cooperation based on
network reciprocity alone, antisocial punishment does not deter public
cooperation. Conversely, if synergistic effects are low and punishment is
actively needed to sustain cooperation, antisocial punishment does act
detrimental, but only if the cost-to-fine ratio is low. If the costs are
relatively high, cooperation again dominates as a result of spatial pattern
formation. Counterintuitively, defectors who do not punish cooperators, and are
thus effectively second-order freeriding on antisocial punishment, form an
active layer around punishing cooperators, which protects them against
defectors that punish cooperators. A stable three-strategy phase that is
sustained by the spontaneous emergence of cyclic dominance is also possible via
the same route. The microscopic mechanism behind the reported evolutionary
outcomes can be explained by the comparison of invasion rates that determine
the stability of subsystem solutions. Our results reveal an unlikely
evolutionary escape from adverse effects of antisocial punishment, and they
provide a rationale for why second-order freeriding is not always an impediment
to the evolutionary stability of punishment.
