Doubly heterogeneous networks facilitate the emergence of collective cooperation

TL;DR

This paper demonstrates that allowing individuals in networks to update strategies at personalized rates reveals conditions under which heterogeneous networks promote cooperation, challenging previous assumptions that heterogeneity hinders cooperation.

Contribution

It introduces a new paradigm with personalized update rates, showing that certain heterogeneity patterns can enhance cooperation in complex networks.

Findings

Heterogeneous networks outperform homogeneous ones when update rates inversely relate to node degree.

A condition is derived for when collective cooperation is favored in doubly heterogeneous networks.

An efficient protocol for optimizing cooperation by tuning update rates is developed.

Abstract

There is growing recognition that the network structures arising from interactions between different entities in physical, social and biological systems fundamentally alter the evolutionary outcomes. Previous paradigm exploring evolutionary game dynamics has assumed that individuals update their strategies at an identical rate, reporting that structurally heterogeneous networks -- despite their ubiquity in real systems -- generally hinder the emergence of collective cooperation compared to their homogeneous counterparts. Here we solve this paradox by creating a new paradigm where individuals on arbitrary networks are allowed to update strategies at arbitrary, personalized rates, and provide the precise condition under which universal collective cooperation is favored. We find that when individuals' update rates vary inversely with their number of connections, heterogeneous networks actually outperform homogeneous ones in promoting cooperation. This surprising property of such "doubly heterogeneous" networks cautions against the conventional wisdom that heterogeneous networks are antagonistic to cooperation. We further develop an efficient protocol for optimizing the promotion of cooperation by tuning individuals' update rates in any structure. Our findings highlight that personalized interaction dynamics, beyond structure, in complex networks are fundamental to understanding and promoting collective cooperation.