Promote or hinder? The role of punishment in the emergence of cooperation

- Evolution of cooperation is not always hindered by anti-social punishment.
- Whether and how punishment promotes cooperation depend on the pattern of punishment.
- Costly centralized punishment is much better in facilitating cooperation.
- Cooperation fails if pro- and anti-social punishments are in the same pattern.
- Cooperation evolves in the case of pool pro-social and peer anti-social punishments.

Investigation of anti-social punishment has shaken the positive role of punishment in the evolution of cooperation. However, punishment is ubiquitous in nature, and the centralized, apposed to decentralized, punishment is more favored by certain modern societies in particular. To explore the underlying principle of such phenomenon, we study the evolution of cooperation in the context of pro- and anti-social punishments subject to two distinct patterns: costly centralized and decentralized punishments. The results suggest that the pattern of punishment has a great effect on the role of punishment in the evolution of cooperation. In the absence of anti-social punishment, the costly centralized punishment is more effective in promoting the emergence of cooperation. Anti-social punishment can subvert the positive role of punishment when anti- and pro-social punishments are in the same pattern. However, driven by centralized pro-social punishment, cooperation can be more advantageous than defection even in the presence of decentralized anti-social punishment.