Contractually stable networks

We consider situations where players are part of a network and belong to coalitions in a given coalition structure. We propose the concept of contractual stability to predict the networks that are going to emerge at equilibrium when the consent of coalition partners is needed for adding or deleting links. Two different decision rules for consent are analyzed: simple majority and unanimity. We characterize the coalition structures that make the strongly efficient network contractually stable under the unanimity decision rule and the coalition structures that sustain some critical network as contractually stable under the simple majority decision rule and under any decision rule requiring the consent of any proportion of coalition partners. Requiring the consent of coalition members may help to reconcile stability and efficiency in some classical models of network formation.