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 free-riding and antisocial punishment. The latter implies that noncooperators 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 is viable, 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 free-riding 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 free-riding is not always an impediment to the evolutionary stability of punishment.
1 More- Received 21 May 2017
DOI:https://doi.org/10.1103/PhysRevX.7.041027
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Humans frequently make personal sacrifices for the common good. We are generally willing to incur costs to not only help others but also punish those that do not cooperate. One of the biggest long-term impediments to stable cooperation and punishment are people known as second-order free riders, individuals that abstain from punishing those who free ride on the contributions of others. This balance is also threatened by antisocial punishment, where individuals who do not cooperate punish those who do. We use methods from statistical physics to show that these two problems can cancel each other out and thus restore the effectiveness of prosocial punishment to promote cooperation.
We develop Monte Carlo simulations to play out a modified version of a public goods game, where goods are divided equally among players who decide to cooperate or defect. Our version introduces two more strategies: Cooperators can punish defectors (prosocial punishment), and defectors can punish cooperators (antisocial punishment). We find that antisocial punishment does not deter public cooperation if the synergistic effects are high enough to sustain cooperation based on reciprocity alone. Conversely, if punishment is needed to sustain cooperation, antisocial punishment is detrimental, but only if the cost-to-fine ratio is low. If the costs are relatively high, cooperation dominates. Counterintuitively, defectors who do not punish cooperators, and are thus second-order free riding on antisocial punishment, form a protective layer around punishing cooperators.
Our results reveal an unlikely escape from adverse effects of antisocial punishment and provide a rationale for why second-order free riding is not always an impediment to the stability of punishment.