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

¹ Key Laboratory of Computer Vision and System and Tianjin Key Laboratory of Intelligence Computing and Novel Software Technology, Tianjin University of Technology - Tianjin 300191, PRC
² Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza - E-50018 Zaragoza, Spain
³ Department of Theoretical Physics, University of Zaragoza - E-50009, Zaragoza, Spain
⁴ Faculty of Natural Sciences and Mathematics, University of Maribor - Koroška cesta 160, SI-2000 Maribor, Slovenia
⁵ Department of Physics, Faculty of Science, King Abdulaziz University - Jeddah, Saudi Arabia
⁶ Complex Networks and Systems Lagrange Lab, Institute for Scientific Interchange - Turin I-10126, Italy

Received: 22 December 2014
Accepted: 20 February 2015

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.