This paper considers the formation of risk-sharing networks. Following empirical findings, we build a model where pairs form links, but a population cannot coordinate links. As a benchmark, individuals commit to share monetary holdings equally with linked partners. We find efficient networks can (indirectly) connect all individuals and involve full insurance. But equilibrium networks connect fewer individuals. When breaking links, individuals do not consider negative externalities on others in the network. Thus identical individuals can end up in different positions in a network and have different outcomes. These results may help to explain empirical findings that risk-sharing is often asymmetric.