Promoting collective cooperation through temporal interactions.

Collective cooperation maintains the function of many natural and social systems, making understanding the evolution of cooperation a central question of modern science. Although human interactions involve complex contact networks, current explorations are limited to static networks, where social ties are permanent and do not change over time. In reality, human activities often involve temporal interactions, where links are impermanent, and understanding the evolution of cooperation on such temporal networks is an open problem. Here, we systematically analyze how cooperation spreads on arbitrary temporal networks, and we distill our results down to a concise condition, which integrates evolutionary game dynamics with both static and temporal interactions. We find that the emergence of cooperation is facilitated by a simple rule of thumb: Hubs (individuals with many social ties) should be temporally deprioritized in interactions. For empirical applications, we further provide a quantitative metric capturing the priority of hubs, which is validated on empirical datasets based on its effectiveness in orchestrating the ordering of interactions to best promote cooperation. Our findings unveil the fundamental advantages conferred by temporal interactions for promoting collective cooperation, transcending the specific insights gleaned from studying static networks.