Evolutionary dynamics of cooperation in [formula omitted]-person snowdrift games with peer punishment and individual disguise

Abstract

We introduce individual disguise of non-cooperators into N-person snowdrift games with peer punishment in a well-mixed population to explore the effects of individual disguise and peer punishment on the cooperation in such games. Firstly, we formulate the reasonable payoffs corresponding to cooperation, non-cooperation and punishment strategy, followed by the establishment of the resulting replicator dynamics to investigate the evolution of the frequencies of the three strategies. Secondly, from a macroscopic perspective, this work provides two-dimensional evolutionary state figures on full cooperation. Moreover, this paper studies the sensitivities of the two-dimensional evolutionary state figures to the third parameter. Specifically, high disguise cost, low cost-to-benefit ratio, severe punishment and large competing size tend to curb non-cooperators and guide the cooperation between cooperators and punishers, which is frozen as non-cooperators vanish. Conversely, low disguise cost, high cost-to-benefit ratio, light punishment and small competing size are disadvantageous to punishers and lead to a continual dynamic with cooperators and non-cooperators, which is a dynamical phase once the punishers disappear. Thirdly, we propose another stochastic evolutionary dynamic for finite but large populations. The corresponding results are in precise agreement with those of the replicator dynamics.