Optimal interdependence between networks for the evolution of cooperation

TL;DR

This paper investigates how the level of interdependence between networks affects the evolution of cooperation, revealing that an intermediate density of strong inter-network links optimizes social dilemma resolution.

Contribution

It demonstrates that only a moderate level of interdependence between networks promotes cooperation, challenging the assumption that more interdependence is always better.

Findings

Intermediate interdependence maximizes cooperation

Results are robust across different network topologies

Optimal interdependence depends on heterogeneity and strategy flow

Abstract

Recent research has identified interactions between networks as crucial for the outcome of evolutionary games taking place on them. While the consensus is that interdependence does promote cooperation by means of organizational complexity and enhanced reciprocity that is out of reach on isolated networks, we here address the question just how much interdependence there should be. Intuitively, one might assume the more the better. However, we show that in fact only an intermediate density of sufficiently strong interactions between networks warrants an optimal resolution of social dilemmas. This is due to an intricate interplay between the heterogeneity that causes an asymmetric strategy flow because of the additional links between the networks, and the independent formation of cooperative patterns on each individual network. Presented results are robust to variations of the strategy updating rule, the topology of interdependent networks, and the governing social dilemma, thus suggesting a high degree of universality.