From Acquaintances to Friends: Homophily and Learning in Networks

This paper considers the evolution of a network in a discrete time, stochastic setting in which agents learn about each other through repeated interactions and maintain/break links on the basis of what they learn. Agents exhibit homophily, the preference to link with others who are similar to themselves, and they have a limited capacity for links. They thus maintain links with others learned to be similar to themselves and cut links to those learned to be dissimilar to themselves. We introduce a new equilibrium concept we term “matching pairwise stable equilibrium”, and we prove that such equilibrium is unique in our model. We show that higher levels of homophily decrease the (average) number of links that agents form. However, the effect of homophily is anomalous: mutually beneficial links may be dropped before learning is completed, thereby resulting in sparser networks and less clustering than under complete information. Homophily also exhibits an interesting interaction with the presence of incomplete information: initially, greater levels of homophily increase the difference between the complete and incomplete information networks, but sufficiently high levels of homophily eventually decrease the difference. Complete and incomplete information networks differ most when the degree of homophily is intermediate.