  We study the influence of the complex topology of scale-free graphs on the
dynamics of anti-coordination games (e.g. snowdrift games). These reference
models are characterized by the coexistence (evolutionary stable mixed
strategy) of two competing species, say "cooperators" and "defectors", and, in
finite systems, by metastability and large-fluctuation-driven fixation. In this
work, we use extensive computer simulations and an effective diffusion
approximation (in the weak selection limit) to determine under which
circumstances, depending on the individual-based update rules, the topology
drastically affects the long-time behavior of anti-coordination games. In
particular, we compute the variance of the number of cooperators in the
metastable state and the mean fixation time when the dynamics is implemented
according to the voter model (death-first/birth-second process) and the link
dynamics (birth/death or death/birth at random). For the voter update rule, we
show that the scale-free topology effectively renormalizes the population size
and as a result the statistics of observables depend on the network's degree
distribution. In contrast, such a renormalization does not occur with the link
dynamics update rule and we recover the same behavior as on complete graphs.
