The Friendship Game

Abstract: We consider a situation where the members of a group have preferences for spending time with other members of that group. By spending time with someone else, a player can “swap” their time for the other player’s time. A situation is considered stable if it is individually rational and there are no two players who would both like to spend more time with one another than they actually do. We show that an equilibrium generally exists and prove some properties which can be tested in empirical friendship networks. We also discuss other possible applications of this model.