A 2-stage strategy updating rule promotes cooperation in the prisoner's dilemma game

In this study,we propose a spatial prisoner’s dilemma game model with a 2-stage strategy updating rule,and focus on the cooperation behavior of the system.In the first stage,i.e.,the pre-learning stage,a focal player decides whether to update his strategy according to the pre-learning factor β and the payoff difference between himself and the average of his neighbors.If the player makes up his mind to update,he enters into the second stage,i.e.,the learning stage,and adopts a strategy of a randomly selected neighbor according to the standard Fermi updating rule.The simulation results show that the cooperation level has a non-trivial dependence on the pre-learning factor.Generally,the cooperation frequency decreases as the pre-learning factor increases;but a high cooperation level can be obtained in the intermediate region of 3 < β < 1.We then give some explanations via studying the co-action of pre-learning and learning.Our results may sharpen the understanding of the influence of the strategy updating rule on evolutionary games.