Dynamic instability of cooperation due to diverse activity patterns in evolutionary social dilemmas

TL;DR

This paper investigates how diverse activity patterns, especially inactivity, impact the evolution of cooperation in social dilemmas, revealing that inactivity can cause cascading failures but may also temporarily boost cooperation under certain conditions.

Contribution

It introduces a probabilistic participation model in evolutionary games, highlighting the effects of inactivity on cooperation dynamics and network heterogeneity.

Findings

Inactivity causes cascading failures of cooperation, especially on scale-free networks.

Proportional activity to degree mitigates negative effects of inactivity.

Inactivity can temporarily increase cooperation levels by impairing defectors.

Abstract

Individuals might abstain from participating in an instance of an evolutionary game for various reasons, ranging from lack of interest to risk aversion. In order to understand the consequences of such diverse activity patterns on the evolution of cooperation, we study a weak prisoner's dilemma where each player's participation is probabilistic rather than certain. Players that do not participate get a null payoff and are unable to replicate. We show that inactivity introduces cascading failures of cooperation, which are particularly severe on scale-free networks with frequently inactive hubs. The drops in the fraction of cooperators are sudden, while the spatiotemporal reorganization of compact cooperative clusters, and thus the recovery, takes time. Nevertheless, if the activity of players is directly proportional to their degree, or if the interaction network is not strongly heterogeneous, the overall evolution of cooperation is not impaired. This is because inactivity negatively affects the potency of low-degree defectors, who are hence unable to utilize on their inherent evolutionary advantage. Between cascading failures, the fraction of cooperators is therefore higher than usual, which lastly balances out the asymmetric dynamic instabilities that emerge due to intermittent blackouts of cooperative hubs.