# Metric clusters in evolutionary games on scale-free networks

## TL;DR

This paper reveals that in scale-free networks, evolutionary dynamics form spatial clusters in an underlying metric space, which can promote cooperation by shielding cooperators from defectors, challenging previous assumptions about heterogeneity always favoring cooperation.

## Contribution

It demonstrates that scale-free networks exhibit metric clustering that influences cooperation, providing new insights into spatial effects in structured populations.

## Key findings

- Metric clusters of cooperators can survive by shielding from defectors.
- Heterogeneity can hinder cooperation under certain conditions.
- Spatial organization in scale-free networks influences evolutionary outcomes.

## 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. Our findings provide a new perspective to understand the emergence of cooperation in evolutionary games in realistic structured populations.