Michael Assaf, Mauro Mobilia
We study the influence of complex spatial structure on the metastability and
fixation properties of a set of evolutionary processes characterized by
frequency-dependent selection. In the framework of evolutionary game theory, we
analyze the dynamics of snowdrift games (characterized by a metastable
coexistence state) on scale-free networks. Using an effective diffusion theory
we demonstrate how the complex structure of the network 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, characterized
by the absence of metastability prior to fixation.
View original:
http://arxiv.org/abs/1202.3231
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