Significance Understanding the patterns and processes of human cooperation is of central scientific importance. Networks can promote cooperation when their existing or emergent topology allows conditional cooperators in the network to isolate themselves from exploitation by noncooperators. We do not know from prior work whether the emergent structures that promote cooperation are driven by reputation or can emerge purely via dynamics, i.e., the severing of ties to noncooperators and the formation of new ties irrespective of reputational information. Here we demonstrate, experimentally, that dynamic networks yield very high rates of cooperation even without reputational knowledge. Further, we identify realistic conditions under which static networks (where ties cannot be altered) yield cooperation rates as high as those in dynamic networks.