Recorded punishment promotes cooperation in spatial prisoner's dilemma game

Abstract: Previous studies suggest that punishment is a useful way to promote cooperation in the well-mixed public goods game, whereas it still lacks specific evidence that punishment maintains cooperation in spatial prisoner's dilemma game as well. To address this issue, we introduce a mechanism of recorded punishment, involved with memory and punishment, into spatial prisoner's dilemma game. We find that increasing punishment rate or memory length promotes the evolution of cooperation monotonously. Interestingly, compared with traditional version, recorded punishment will facilitate cooperation better through a recovery effect. Moreover, through examining the process of evolution, we provide an interpretation to this promotion phenomenon, namely, the recovery effect can be warranted by an evolution resonance of standard deviation of fitness coefficient. Finally, we confirm our results by studying the impact of uncertainty within strategy adoptions. We hope that our work may sharpen the understanding of the cooperative behavior in the society.