Anomalous Metastability and Fixation Properties of Evolutionary Games on Scale-Free Graphs

This contribution concerns the influence of scale-free graphs on the metastability and fixation properties of a set of evolutionary processes. In the framework of evolutionary game theory, where the fitness and selection are frequency-dependent and vary with the population composition, we analyze the dynamics of snowdrift games (characterized by a metastable coexistence state) on scale-free networks. Using an effective diffusion theory in the weak selection limit, we demonstrate how the scale-free structure affects the system’s metastable state and leads to anomalous fixation. In particular, we analytically and numerically show that the probability and mean time of fixation are characterized by stretched exponential behaviors with exponents depending nontrivially on the network’s degree distribution. Our approach is also shown to be applicable to models, like coordination games, not exhibiting metastability prior to fixation.