Limited punishment pool may promote cooperation in the public goods game

Abstract

Finding ways to overcome the temptation to exploit one another is still a challenge. In practice, there exists numerous examples indicating that punishment is a key mechanism to maintain cooperation. However, the executors of the punishment institution are costly and limited in reality. To reveal potential explanations here we introduce the limited punishment pool into the public goods game. It means that when the punishment pool is occupied by the pure punishers, who just contribute to the punishment pool but not to the common pool in the public goods game, the extra individuals who want to participate in punishing but miss out will passively withdraw and become exiters. The game model is verified by empirical analysis. Results demonstrate that the existence of punishment group can effectively weaken the defectors in the population. By reasonably adjusting the capacity of the punishment pool, the cooperators can prevail in the population. Surprisingly, there will be a special strategy fixation, that is, the fixation of the punishment group. Moreover, the existence of a certain limit of punishment pool capacity will promote the cooperative behavior and accelerate the disappearance of defectors.