Stable Hedonic Networks

We consider a model in which players can form links between themselves under mutual agreement, and the set of all pairwise agreements is called a network. We stress that we are particularly interested in the case when some players are antagonistic, i.e., that they are separately “desirable” for someone, but “undesirable” when they are together. We define a class of preferences that ensures the stability of networks, if each player is sensitive to her direct neighbors only. However, it turns out that if players are sensitive to their indirect neighbors, antagonism between player may easily prevent stable networks to exist, for a large class of preference profile.