  Previous studies have shown that the topological properties of a complex
network, such as heterogeneity and average degree, affect the evolutionary game
dynamics on it. However, traditional numerical simulations are usually
time-consuming and demand a lot of computational resources. In this paper, we
propose the method of dynamical approximate master equations (DAMEs) to
accurately approximate the evolutionary outcomes on complex networks. We
demonstrate that the accuracy of DAMEs supersedes previous standard pairwise
approximation methods, and DAMEs require far fewer computational resources than
traditional numerical simulations. We use prisoner's dilemma and snowdrift game
on regular and scale-free networks to demonstrate the applicability of DAMEs.
Overall, our method facilitates the investigation of evolutionary dynamics on a
broad range of complex networks, and provides new insights into the puzzle of
cooperation.
