Adaptive interaction driven by the learning effect in the spatial prisoner's dilemma

We propose a computing model in which individuals can automatically adjust their interaction intensity with their mentor according to the learning effect. This model is designed to investigate the cooperative dynamics of the spatial prisoner's dilemma. More specifically, when the cumulative payoff of a learner is more than his reference earning, he will strengthen his interaction with his mentor; otherwise, he will reduce it. The experimental results indicate that this mechanism can improve the emergence of cooperation in a networked population and that the driving coefficient of interaction intensity plays an important role in promoting cooperation. Interestingly, under a certain social dilemma condition, there exists a minimal driving coefficient that leads to optimal cooperation. This occurs due to a positive feedback effect between the individual's satisfaction frequency and the number of effective neighbors. Moreover, we find that the experimental results are in accord with theoretical predictions obtained from an extension of the classical pair-approximation method. Our conclusions obtained by considering relationships with mentors can provide a new perspective for future investigations into the dynamics of evolutionary games within structured populations.