Repeated thinking promotes cooperation in spatial prisoner's dilemma game

Abstract

Inspired by the realistic process of taking decisions in social life, we have proposed a repeated thinking mechanism in the evolutionary spatial prisoner's dilemma game where players are denoted by the vertices and play games with their direct neighbors. Under our mechanism, a player i will randomly select a neighbor j and then deliberate for M times before strategy updating. It will remain unchanged if not all M considerations suggest it to learn the strategy of j. We mainly focus on the evolution of cooperation in the systems. Interestingly, we find that the cooperation level fC is remarkably promoted and fC has a monotonic dependence on the caution parameter M, indicating that being cautious facilitates the emergence and persistence of cooperation. We give a simple but clear explanation for this cooperation promotion via detecting the cooperator–defector transition process. Moreover, the robustness of this mechanism is also examined on different noise levels and game models.