The Effect of Inequity Aversion Driven Punishment on Cooperation

Unlike in the traditional punishment mechanism, punishers driven by inequity aversion punish individuals who have a higher payoff, rather than those who adopt a certain strategy, and the intensity of punishment varies with payoff difference. This paper studies the impact of this special punishment on cooperation. We obtain phase diagrams by studying the stationary state of the three-strategy system with cooperators, inequity-averse individuals and defectors under different parameters in a structured population. In addition, we observe spatial dynamics to explore the underlying mechanisms of some phases and phase transitions. The results indicate that inequity aversion driven punishment can promote cooperation due to a high-intensity punishment and network reciprocity. However, the unnecessary loss caused by the punishment on cooperators or even other inequity-averse punishers can reduce the efficiency in promoting cooperation. Although cooperators are sometimes punished, as second-order free-riders, they still have an adverse impact on the propagation of cooperation, by inhibiting the expansion of inequity-averse individuals in the interface separating three strategies for a high punishment cost coefficient, and indirectly compete for territory with inequity-averse individuals for a high synergy factor.