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

TL;DR

This paper investigates how scale-free network structures influence metastability and fixation times in evolutionary game dynamics, revealing anomalous behaviors and stretched exponential fixation probabilities.

Contribution

It introduces an effective diffusion approach to analyze metastability and fixation in evolutionary games on scale-free networks, highlighting the impact of network topology.

Findings

Fixation probability exhibits stretched exponential behavior.

Mean fixation time depends on the degree distribution.

Scale-free structure induces anomalous fixation dynamics.

Abstract

We study the influence of complex 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 on the network's degree distribution.