Prisoners' dilemma in real-world acquaintance networks: Spikes and quasi-equilibria induced by the interplay between structure and dynamics

TL;DR

This paper investigates how the structure of real-world social networks influences the complex dynamics of cooperation in the Prisoner's Dilemma game, revealing spikes and quasi-stable states driven by network topology.

Contribution

It identifies key structural factors like degree distribution and connection sparsity as causes of complex cooperation dynamics and constructs model networks to replicate these behaviors.

Findings

Complex cooperation dynamics with spikes and quasi-stable states observed.

Inhomogeneous degree distribution and sparse high-degree connections are crucial.

Model networks replicate the complex time-evolution of cooperation levels.

Abstract

We study Nowak and May's spatial prisoners' dilemma game driven by mutations (random choices of suboptimal strategies) on empirical social networks. The time evolution of the cooperation level is highly complex containing spikes and steps between quasi-stable levels. A statistical characterization of the quasi-stable states and a study of the mechanisms behind the steps are given. We argue that the crucial structural ingredients causing the observed behavior is an inhomogeneous degree distribution and that the connections within vertices of highest degree are rather sparse. Based on these observations we construct model networks with a similarly complex time-evolution of the cooperation level.