The topological issues of cooperation

TL;DR

This paper investigates how the clustering coefficient of networks influences the emergence of cooperation in spatial Prisoner Dilemma models, revealing complex dependencies and the impact of initial population composition.

Contribution

It systematically analyzes the relationship between network clustering and cooperation success across various network types and dynamics, highlighting multiple underlying mechanisms.

Findings

Cooperation success depends non-trivially on network clustering.

Initial population composition significantly affects cooperation outcomes.

Ordered and random networks exhibit different mechanisms influencing cluster expansion.

Abstract

In the last years the Prisoner Dilemma (PD) has become a paradigm for the study of the emergence of cooperation in spatially structured populations. Such structure is usually assumed to be given by a graph. In general, the success of cooperative strategies is associated with the possibility of forming globular clusters, which in turn depends on a feature of the network that is measured by its clustering coefficient. In this work we test the dependence of the success of cooperation with the clustering coefficient of the network, for several different families of networks. We have found that this dependence is far from trivial. Additionally, for both stochastic and deterministic dynamics we have also found that there is a strong dependence on the initial composition of the population. This hints at the existence of several different mechanisms that could promote or hinder cluster expansion. We have studied in detail some of these mechanisms by concentrating on completely ordered networks (large clustering coefficient) or completely random networks (vanishing clustering coefficient).