Competition and cooperation among different punishing strategies in the spatial public goods game

TL;DR

This paper investigates how different punishing strategies evolve and interact in a spatial public goods game, revealing that strategy success depends on invasion speeds and that cooperation can be maximized through selection mechanisms.

Contribution

It introduces a model with multiple punishing strategies and analyzes their competition and cooperation dynamics, highlighting the role of invasion velocities in strategy success.

Findings

Highest cooperation level achieved through selection among punishing strategies

Success of punishing strategies depends on invasion velocities

Mild punishment can dominate when strict sanctions are unnecessary

Abstract

Inspired by the fact that people have diverse propensities to punish wrongdoers, we study a spatial public goods game with defectors and different types of punishing cooperators. During the game, cooperators punish defectors with class-specific probabilities and subsequently share the associated costs of sanctioning. We show that in the presence of different punishing cooperators the highest level of public cooperation is always attainable through a selection mechanism. Interestingly, the selection not necessarily favors the evolution of punishers who would be able to prevail on their own against the defectors, nor does it always hinder the evolution of punishers who would be unable to prevail on their own. Instead, the evolutionary success of punishing strategies depends sensitively on their invasion velocities, which in turn reveals fascinating examples of both competition and cooperation among them. Furthermore, we show that under favorable conditions, when punishment is not strictly necessary for the maintenance of public cooperation, the less aggressive, mild form of sanctioning is the sole victor of selection process. Our work reveals that natural strategy selection can not only promote, but sometimes also hinder competition among prosocial strategies.