• Open Access

Second-Order Free-Riding on Antisocial Punishment Restores the Effectiveness of Prosocial Punishment

Attila Szolnoki and Matjaž Perc
Phys. Rev. X 7, 041027 – Published 30 October 2017

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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
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)

Interdisciplinary Physics

Authors & Affiliations

Attila Szolnoki1,* and Matjaž Perc2,†

  • 1Institute of Technical Physics and Materials Science, Centre for Energy Research, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
  • 2Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia; CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia; and Complexity Science Hub, Josefstädterstraße 39, A-1080 Vienna, Austria

  • *szolnoki.attila@energia.mta.hu
  • matjaz.perc@uni-mb.si

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.

Key Image

Article Text

Click to Expand

References

Click to Expand
Issue

Vol. 7, Iss. 4 — October - December 2017

Subject Areas
Reuse & Permissions
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review X

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

×

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×