The Effect of Structural Properties of Complex Networks on Evolutionary Game Dynamics

Network structures, which depict the intertwined interactions between individuals, affect the outcomes of evolutionary game dynamics on complex networks. In the prisoner's dilemma game, previous studies reveal that how readily cooperative strategies evolve is determined by the condition for strategy dominance. However, this condition is an implicit function of intuitive structural properties such as the average degree and clustering coefficient, preventing us from a better understanding of the relationship between network structures and the evolution of cooperation. Here, to fill this gap, we investigate the effect of five typical structural properties of networks on the condition for strategy dominance. By designing a series of controlled numerical experiments, we find that the average degree and degree variance have the largest impact on the condition for the dominance of cooperation. In contrast, the clustering coefficient, average path length, and assortativity have relatively negligible influence. Our work thus helps build more direct links between network structures and evolutionary outcomes, and highlights the decisive role that the average degree and degree variance play in shaping the evolution of cooperation.