Friendship markets

We consider a situation in which the members of a group have preferences for the intensity of contact with other members of that group. A situation is considered stable if there are no two players who would both like to have a more intense relationship with one another, and there is no individual player who would prefer to have a less intense relationship with somebody else. An interesting feature of this model is that it is based on ordinal preferences defined on the set of players, but it predicts how intense the relationships between players will be (where intensity is scaled cardinally). We show that an equilibrium generally exists and prove equilibrium properties which can be tested in empirical networks. We also discuss various applications of this model