This paper considers the formation of risk-sharing networks. Following empirical findings, we build a model where risk-sharing takes place between pairs of individuals. We ask what structures emerge when pairs can agree to form links, but people cannot coordinate links across a population. We consider a benchmark model where identical individuals commit to share their monetary holdings equally with linked partners. We compare efficient networks to equilibrium networks. Efficient networks can (indirectly) connect all individuals and involve full insurance. However, equilibrium networks connect fewer individuals. There is an externality: when breaking a link individuals do not take into account the negative effect on others distant in the network. The network formation process can lead identical individuals to be in different positions and thus have different risk-sharing outcomes. These results may help explain empirical findings that risk-sharing is often not symmetric or complete.