  Humans interact and cooperate in structured societies, which are often
represented by complex networks. Previous explorations mainly focus on pairwise
and static network structures, where each link connects two nodes permanently
and never changes. However, empirical human collective interactions go beyond
static time-invariant one-to-one relationships. Recently, researchers have made
vital progress in modelling higher-order interactions using hypernetworks,
where a link may connect more than two individuals. Here, we study collective
cooperation through temporal hypernetworks, capturing the time-varying
higher-order interactions in human societies. We find that temporal
hypernetworks may promote cooperation compared with their static counterparts,
and the traditional static pairwise network may underestimate the positive
effect of local interactions on fostering cooperators. Moreover, temporal
hypernetworks with sparse components and higher-order interactions can
facilitate cooperation. Surprisingly, we report that when the scale of
interactions is of the same order as population size, moderately small
hyperlink sizes best facilitate cooperation. Our findings underscore the
significant impact of real-world temporal higher-order interactions on the
evolution of cooperation.
