Adjustment of link weights based on tolerance promotes cooperation in spatial prisoner's dilemma game

Understanding and explaining cooperative behavior in human society has become an open question. In this paper, we propose a dynamic adjustment of pair relationships in a spatial prisoner's dilemma game. Unlike previous studies that individuals dynamically adjust the intensity of interaction with their opponents at each step, this work consider tolerance, in which the intensity of interaction is adjusted when the time of successive defections by an individual exceeds a tolerance threshold T. We find that although the proposed mechanism can significantly improve cooperation compared to traditional versions, a higher tolerance for continuous defection behavior is not conducive to the evolution of cooperation. Furthermore, an environmental adaptor that dynamically adjusts the paired relationship with the opponent at all times is beneficial for the evolution of cooperation. And the higher the degree of adjustment in the paired relationship, the lower the probability of continuous exploitation by defector. We hope that our work can provide some insights into explaining the existence and maintenance of cooperation.