Evolutionary Dynamics of Cooperation in the Public Goods Game with Individual Disguise and Peer Punishment

The phenomenon of individual disguise is ubiquitous in the real world. Recent evidences show that peer punishment is successful to stabilize cooperation among selfish individuals. However, it is unclear whether peer punishment is still able to stabilize cooperation when individual disguise for escaping being punished is considered. In this paper, we thus introduce individual disguise of defectors into the public goods game with peer punishment and aim to explore how peer punishment influences the evolutionary dynamics of cooperation, defection, and punishment in this scenario. We consider both cases of infinite and finite populations. In infinite populations, by using replicator equations, we find that although low disguise cost can hinder public cooperation, peer punishment still plays a positive role in promoting the evolution of cooperation, no matter whether second-order punishment is considered or not. We further demonstrate that the larger fine on defectors or the smaller the cost of punishment, the easier to establish a state of full punishment. In addition, in finite populations we reveal that the population spends most of the time in the region of defection for low disguise cost, and the population spends most of the time in the region of cooperation for high disguise. When second-order punishment is not considered, the punishment strategy does not have evolutionary advantage, whereas when second-order punishment is considered, the population can evolve toward regime of punishment and spends most of the time in the monomorphic states with widespread punishment or cooperation.