Degree mixing in multilayer networks impedes the evolution of cooperation

TL;DR

This study investigates how degree mixing in multilayer networks affects the evolution of cooperation, revealing that certain mixing patterns hinder cooperative behavior due to the roles of hubs and symmetry.

Contribution

It introduces an analysis of degree mixing effects in multilayer scale-free networks on cooperation, highlighting the impact of symmetry and hub roles in social dilemma resolution.

Findings

Assortative mixing in one layer and disassortative in the other impedes cooperation.

Symmetric assortative mixing in both layers also hinders cooperation.

Degree-dependent strategies and cluster analysis explain the influence of hubs and symmetry.

Abstract

Traditionally, the evolution of cooperation has been studied on single, isolated networks. Yet a player, especially in human societies, will typically be a member of many different networks, and those networks will play a different role in the evolutionary process. Multilayer networks are therefore rapidly gaining on popularity as the more apt description of a networked society. With this motivation, we here consider 2-layer scale-free networks with all possible combinations of degree mixing, wherein one network layer is used for the accumulation of payoffs and the other is used for strategy updating. We find that breaking the symmetry through assortative mixing in one layer and/or disassortative mixing in the other layer, as well as preserving the symmetry by means of assortative mixing in both layers, impedes the evolution of cooperation. We use degree-dependent distributions of strategies and cluster-size analysis to explain these results, which highlight the importance of hubs and the preservation of symmetry between multilayer networks for the successful resolution of social dilemmas.