Strategy changing penalty promotes cooperation in spatial prisoner's dilemma game

Many classical studies suggest that punishment is a useful way to promote cooperation in the well-mixed public goods game, whereas relative evidence in the research of spatial prisoner's dilemma game is absent. To address this issue, we introduce a mechanism of strategy changing penalty, combining memory and penalty during the update process, into spatial prisoner's dilemma game. We find that increasing penalty rate or memory length is able to promote the evolution of cooperation monotonously. Compared with traditional version, recorded penalty could facilitate cooperation better. Moreover, through examining the process of evolution, we provide an interpretation for this promotion phenomenon, namely, the effect of promotion can be warranted by an evolution resonance of standard deviation of fitness coefficient. Finally, we validate our results by studying the impact of uncertainty within strategy adoptions on the evolution of cooperation. We hope that our work may shed light on the understanding of the cooperative behavior in the society.