Friendship Selection

Abstract

We model the formation of friendships as repeated cooperation within a set of heterogeneous players. The model builds around three of the most important facts about friendship: friends help each other, there is reciprocity in the relationship and people usually have few friends. In our results we explain how similarity between people affects the friendship selection. We also characterize when the friendship network won’t depend on the random process by which people meet each other. Finally, we explore how players’ patience influences the length of their friendship relations. Our results match and explain empirical evidence reported in social studies on friendship. For instance, our model explains why troublesome subjects have few friends.