Learning continuous and consistent strategy promotes cooperation in prisoner’s dilemma game with mixed strategy

Research on cooperative evolution behavior based on memory mechanism has been a hot topic of many scholars in recent years. However, most previous studies have considered neighbors’ historical payoffs when individuals choose role models whom they will learn from, but paid less attention to the stability of neighbors’ strategy which indicates how frequently they change their strategies in memory length. In this paper, we study the memory length M and the strategy persistence level u of individuals and the change rate of cooperative tendency δ on the cooperative evolution under the mixed strategy of the prisoner’s dilemma. Strategy persistence level is measured by the number of times which the strategy in neighbor’s memory length is continuous and consistent with neighbor’s current strategy, and can determine the probability that the individual learns the neighbor’s strategy when updating the strategy; the change rate of cooperative tendency δ is described by the standard deviation of the normal distribution. We investigate the effects of M and δ on the evolutionary of cooperation. The results show that the persistence strategy mechanism which we proposed in the memory length can improve network reciprocity and facilitate the generation and maintenance of cooperation, the larger the memory length is, the smaller the standard deviation value is, the more conducive to cooperation.