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 alpha, where a positive alpha enables popular individuals to receive relatively higher fitness and a negative alpha enables popular individuals to receive relatively lower fitness. When alpha 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 alpha supports the evolution of cooperation and can even yield the full cooperation phase. In contrast, a negative alpha 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. (C) 2020 Elsevier Ltd. All rights reserved.