Strategy imitation behavior driven influence adjustment promotes cooperation in spatial prisoner’s dilemma game

In social and biological systems, besides interaction payoffs, individual fitness which is used in strategy evolution, can also be influenced by other extrinsic factors. In this paper, individual influence is introduced into the spatial prisoner’s dilemma game, which is dependent on the adjustment sensitivity, the duration of the current strategy and strategy imitation behaviors during the game. Tuned by the individual influence, the fitness of some individuals with the same interaction payoffs may be different. The effect of individual influence on improving cooperation has been researched, and the result shows that the level of cooperation is effectively promoted when the individual influence is considered. Moreover, with the adjustment sensitivity becomes larger, a greater degree of cooperation can be warranted even the temptation to defect is relatively large. The role of individual memory length threshold has also been investigated. Interestingly, individual memory length is not the primary factor that enforces the emergence of cooperative behavior among selfish competitors, it only accelerates the velocity of population evolution. By configurational analysis, the reason for the improvement of cooperation level has been carefully explained. It occurs mainly because some cooperator clusters can resist the invasion of defectors by interacting with defectors that have lower individual influences. Finally, the robust with respect to the cooperation evolution in other network structures is further studied. We find out that scale-free and small-world networks make the system as efficient as lattice network. Our work provides a new perspective on understanding of cooperative behaviors in societies.