Metric clusters in evolutionary games on scale-free networks

Kaj-Kolja Kleineberg

doi:10.1038/s41467-017-02078-y

Abstract

The evolution of cooperation in social dilemmas in structured populations has been studied extensively in recent years. Whereas many theoretical studies have found that a heterogeneous network of contacts favors cooperation, the impact of spatial effects in scale-free networks is still not well understood. In addition to being heterogeneous, real contact networks exhibit a high mean local clustering coefficient, which implies the existence of an underlying metric space. Here we show that evolutionary dynamics in scale-free networks self-organize into spatial patterns in the underlying metric space. The resulting metric clusters of cooperators are able to survive in social dilemmas as their spatial organization shields them from surrounding defectors, similar to spatial selection in Euclidean space. We show that under certain conditions these metric clusters are more efficient than the most connected nodes at sustaining cooperation and that heterogeneity does not always favor—but can even hinder—cooperation in social dilemmas.

Highlights

The evolution of cooperation in social dilemmas in structured populations has been studied extensively in recent years
We show that evolutionary dynamics on scale-free, highly clustered networks lead to the formation of patterns in the underlying metric space, similar to the aforementioned spatial selection in Euclidean space
The effect of scale-free topologies has attracted a lot of attention, and many theoretical studies have found that heterogeneous networks of contacts favor cooperation in social dilemmas[15,16,17,18], this behavior has not been confirmed in recent experiments with human players[22]

Summary

Introduction

The evolution of cooperation in social dilemmas in structured populations has been studied extensively in recent years. In addition to being heterogeneous, real contact networks exhibit a high mean local clustering coefficient, which implies the existence of an underlying metric space. We show that evolutionary dynamics in scale-free networks self-organize into spatial patterns in the underlying metric space. In addition to being heterogeneous, exhibit a high mean local clustering coefficient[19, 20] (this means that the network contains a high number of closed triangles) This is important because a high clustering coefficient implies the existence of an underlying metric space[21]. We show that evolutionary dynamics on scale-free, highly clustered networks lead to the formation of patterns in the underlying metric space, similar to the aforementioned spatial selection in Euclidean space. Heterogeneity does not always favor—but can even hinder—the evolution of cooperation in social dilemmas

Methods

Results

Conclusion