Second-order freeriding on antisocial punishment restores the effectiveness of prosocial punishment

TL;DR

This study explores how second-order freeriding on antisocial punishment can unexpectedly support the effectiveness of prosocial punishment in public goods games, especially under certain conditions of synergy and cost-to-fine ratios.

Contribution

It extends the spatial public goods game theory by including four strategies and reveals how second-order freeriding can stabilize cooperation against antisocial punishment.

Findings

Antisocial punishment does not hinder cooperation when synergy is high.

High cost-to-fine ratios enable cooperation to dominate despite antisocial punishment.

Second-order freeriding forms a protective layer around punishing cooperators.

Abstract

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.