Temporality modulates the effect of network heterogeneity on cooperation fixation.

Abstract

Understanding the evolution of cooperation in structured populations remains a central challenge in multidisciplinary areas. Although previous findings suggest that structural heterogeneity in static networks hinders cooperation, real-world interactions in most natural and social systems are dynamic and best represented as temporal networks. Here, we challenge this conventional wisdom and, by developing a systematic mathematical framework, we report that structural heterogeneity in temporal networks can instead promote collective cooperation. Importantly, we reveal that such advantages depend on an often-overlooked metric-fixation time-quantifying the time required for a single cooperator to drive the entire population to cooperation. Highly heterogeneous networks accelerate this process within each subnetwork, resulting in a quantitative enhancement of cooperation in temporal networks compared to their homogeneous counterparts. By validating our results on empirical datasets through theoretical analyses and simulations, we provide a consistent framework for analysing cooperative dynamics across static and temporal networked systems.