Popularity-driven fitness calculation promotes cooperation in spatial prisoner’s dilemma game

It has been shown that an individual’s popularity is a crucial factor that favors cooperation. However, it is not yet well understood how an individual’s popularity affects the evolution of cooperation. In this paper, we propose a simple model to explore this important and interesting issue in spatial prisoner’s dilemma game. Our proposed model integrates an individual’s popularity into the calculation of an individual’s fitness via a single parameter α, where a positive α enables popular individuals to receive relatively higher fitness and a negative α enables popular individuals to receive relatively lower fitness. When α equals to zero, our model leaves the popularity out and degenerates into the traditional version, in which cooperation goes extinct rapidly. Extensive numerical simulations show that a positive α supports the evolution of cooperation and can even yield the full cooperation phase. In contrast, a negative α can still facilitate cooperation but hardly dominate in the population. We study its potential mechanism from the viewpoint of evolutionary snapshots. Besides, we further use the mean-field theory to analyze the proposed model, and the theoretical results are consistent with those from simulations. Therefore, our findings provide a deeper understanding of the role of popularity in the evolution of cooperation.