  What networks can form and persist when agents are self-interested? Can such
networks be efficient? A substantial theoretical literature predicts that the
only networks that can form and persist must have very special shapes and that
such networks cannot be efficient, but these predictions are in stark contrast
to empirical findings. In this paper, we present a new model of network
formation. In contrast to the existing literature, our model is dynamic (rather
than static), we model agents as foresighted (rather than myopic) and we allow
for the possibility that agents are heterogeneous (rather than homogeneous). We
show that a very wide variety of networks can form and persist; in particular,
efficient networks can form and persist if they provide every agent a strictly
positive payoff. For the widely-studied connections model, we provide a full
characterization of the set of efficient networks that can form and persist.
Our predictions are consistent with empirical findings.
