Anomalous metastability and fixation properties of evolutionary games on scale-free graphs

Michael Assaf*, Mauro Mobilia

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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.

Original languageAmerican English
Title of host publicationSpringer Proceedings in Complexity
Number of pages9
StatePublished - 2013

Publication series

NameSpringer Proceedings in Complexity
ISSN (Print)2213-8684
ISSN (Electronic)2213-8692

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2013.


  • Complex networks
  • Diffusion theory
  • Evolutionary games
  • Fixation
  • Metastability


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