The link weight adjustment considering historical strategy promotes the cooperation in the spatial prisoner’s dilemma game

Abstract

Nothing remains the same in social networks, especially the closeness of relationships between selfish individuals. With the passage of time, this relationship may change dynamically and have an important impact on cooperation. In this paper, we propose a new evolutionary game model to investigate the evolution of cooperation, in which the link weight is adaptively adjusted by comparing the individual payoff with her/his surrounding environment, and the learning ability of individual is affected by his historical strategies at the same time. To be specific, if the focal individual’s payoff is greater than the average one of his nearest neighbors, the link weight between the focal individual and nearest neighbors will be increased by one unit; however, if the focal individual’s payoff is smaller than the average one of his nearest neighbors, the link weight between them will be reduced by one unit; otherwise, the link weight between them will be unchanged. In addition, we use a specific parameter ε to determine the link weight adjustment range. Meanwhile, the focal individual will decide how to learn from her/his neighbor’s strategy according to his strategy of the last M game rounds when she/he updates the current strategy. Through extensive Monte Carlo simulations, we find that dynamic adjustment of link weights can significantly promote the evolution of cooperation. Particularly, the parameter δ determining the intensity of weight adjustment has an optimal value regarding the level of cooperation, and then the cooperation has significantly been improved with the growth of ε. Also, there is an optimal memory length M as far as the emergence and persistence of cooperation is concerned. The current results are extremely conducive to understanding how selfish individuals in social dilemma dynamically adjust their relationships to promote the collective cooperation.