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.
Highlights
Cooperation is widespread in human societies [1,2,3,4,5,6,7]
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
As the value of γ increases, so does the w3 invasion rate, as shown in Fig. 8, which illustrates directly that second-order free-riding on antisocial punishment is responsible for the evolutionary success of prosocial punishment, for the survival or even for the complete dominance of the punish defectors (PC) strategy
Summary
Cooperation is widespread in human societies [1,2,3,4,5,6,7]. Like no other species, we champion personal sacrifice for the common good [8,9]. Many evolutionary models confirm the effectiveness of positive incentives for the promotion of cooperation [44,45,46,47,48,49,50,51,52], in this case too the challenges associated with second-order free-riding and antisocial rewarding persist [53,54]. As we show in detail, spatial pattern formation leads to unconditional defectors forming an active layer around punishing cooperators, which protects them against defectors that punish cooperators This is a new evolutionary escape from adverse effects of antisocial punishment, which in turn reveals unexpected benefits stemming from second-order free-riding. We first present the spatial public goods game with prosocial and antisocial punishment, and proceed with the results and a discussions of their implications for the successful coevolution of cooperation and punishment
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