Metastability and anomalous fixation in evolutionary games on scale-free networks

Details Metastability and anomalous fixation in evolutionary games on scale-free networks Metastability and anomalous fixation in evolutionary games on scale-free networks

2012-02-15

arxiv.org/abs/1202.3231v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 4 figures

Scientific paper

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.

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