Making friends: the role of assortative interests and capacity constraints

We study friendship networks under the assumption that people are constrained to build the qualities of their relations. We investigate the connection between (exogenous) assor- tative interests and (endogenous) homophilic patterns, and its welfare implications. Un- der a simple link formation technology, capacity constraints bolster an interesting mech- anism that leads to asymmetric investments in the formation of links and, furthermore, makes relatively good-quality heterophilic relations necessary for extreme forms of ho- mophilic patterns to be stable. For intermediate assortative interests, extreme forms of either homophilic (or heterophilic) patterns may coexist with more moderate forms. We present empirical evidence on the identified features of stable patterns. Efficiency requires common aggregate qualities of relations across all agents within each different popula- tion group. Although efficiency of stable patterns needs not follow in general, we identify particular forms of extreme stable homophilic and heterophilic patterns that are efficient. Additionally, we identify a class of patterns that feature intermediate levels of homophily, and for which stability and efficiency are compatible. Such particular constructions provide insightful guidance on the role of population sizes to facilitate efficiency of stable patterns.