Topological conditions of scale-free networks for cooperation to evolve

TL;DR

This paper investigates how specific topological features of scale-free networks, especially Apollonian Networks, facilitate the widespread evolution of cooperation through evolutionary game theory analysis.

Contribution

It introduces the concept of a degree-skeleton in Apollonian Networks and demonstrates its role in promoting cooperation, providing new insights into network organization and cooperation dynamics.

Findings

Apollonian Networks enable cooperation to spread from few cooperative hubs.

Constructing degree-skeletons in random networks enhances cooperation levels.

Degree-skeletons in ANs and BA networks promote cooperation similarly.

Abstract

Evolutionary game theory is employed to study topological conditions of scale-free networks for the evolution of cooperation. We show that Apollonian Networks (ANs) are perfect scale-free networks, on which cooperation can spread to all individuals, even though there are initially only 3 or 4 hubs occupied by cooperators and all the others by defectors. Local topological features such as degree, clustering coefficient, gradient as well as topology potential are adopted to analyze the advantages of ANs in cooperation enhancement. Furthermore, a degree-skeleton underlying ANs is uncovered for understanding the cooperation diffusion. Constructing this kind degree-skeleton for random scale-free networks promotes cooperation level close to that of Barab\'asi-Albert networks, which gives deeper insights into the origin of the latter on organization and further promotion of cooperation.