This paper explores the stability and efficiency of social and economic networks when individuals have the discretion to form or sever links. The authors study two stylized models and a general model to characterize the sets of stable and efficient networks. They find that these sets do not always intersect, and that this tension is not unique to the models. To ensure at least one efficient network is stable, resources must be allocated to nodes that are not responsible for production. The paper characterizes two allocation rules: the equal split rule and a rule based on equal bargaining power. The equal split rule ensures stability of efficient networks, while the equal bargaining power rule arises naturally from bargaining outcomes. The paper also discusses the implications of these findings for the organization of firms and the structure of airline routes.This paper explores the stability and efficiency of social and economic networks when individuals have the discretion to form or sever links. The authors study two stylized models and a general model to characterize the sets of stable and efficient networks. They find that these sets do not always intersect, and that this tension is not unique to the models. To ensure at least one efficient network is stable, resources must be allocated to nodes that are not responsible for production. The paper characterizes two allocation rules: the equal split rule and a rule based on equal bargaining power. The equal split rule ensures stability of efficient networks, while the equal bargaining power rule arises naturally from bargaining outcomes. The paper also discusses the implications of these findings for the organization of firms and the structure of airline routes.