We study the stability and efficiency of social and economic networks, when self-interested individuals can form or sever links. First, for two stylized models, we characterize the stable and efficient networks. There does not always exist a stable network that is efficient. Next, we show that this tension persists generally: to assure that there exists a stable network that is efficient, one is forced to allocate resources to nodes that are not responsible for any of the production. We characterize one such allocation rule: the equal split rule, and another rule that arises naturally from bargaining of the players.Journal Economic LiteratureClassification Numbers: A14, D20, J00.