Effectiveness of conditional punishment for the evolution of public cooperation

TL;DR

This study investigates how conditional punishment influences the evolution of cooperation in spatial public goods games, revealing that it can be more effective than unconditional punishment under realistic costs.

Contribution

It introduces the concept of indirect territorial competition driven by pattern formation, highlighting the complex dynamics of conditional punishment in promoting cooperation.

Findings

Conditional punishers outperform unconditional punishers when sanctioning costs are high.

The coexistence of punishers and defectors depends on phase transitions and critical points.

Spatial structure and pattern formation are key to the success of subordinate strategies.

Abstract

Collective actions, from city marathons to labor strikes, are often mass-driven and subject to the snowball effect. Motivated by this, we study evolutionary advantages of conditional punishment in the spatial public goods game. Unlike unconditional punishers who always impose the same fines on defectors, conditional punishers do so proportionally with the number of other punishers in the group. Phase diagrams in dependence on the punishment fine and cost reveal that the two types of punishers cannot coexist. Spontaneous coarsening of the two strategies leads to an indirect territorial competition with the defectors, which is won by unconditional punishers only if the sanctioning is inexpensive. Otherwise conditional punishers are the victors of the indirect competition, indicating that under more realistic conditions they are indeed the more effective strategy. Both continuous and discontinuous phase transitions as well as tricritical points characterize the complex evolutionary dynamics, which is due to multipoint interactions that are introduced by conditional punishment. We propose indirect territorial competition as a generally applicable mechanism relying on pattern formation, by means of which spatial structure can be utilized by seemingly subordinate strategies to avoid evolutionary extinction.