Making Friends : The Role of Assortative Interests and Capacity Constraints

We study friendship networks under the assumption that agents are constrained in their efforts to build up links. Using a fairly general model, we investigate the relation between the prevailing (exogenous) assortative interests and the (endogenous) homophilic degrees of friendship patterns, and the welfare implications for such patterns. For intermediate assortative interests, extreme forms of homophilic (or heterophilic) patterns may coexist with more moderate forms. Under a very simple technology of link formation, the presence of capacity constraints leads to an interesting mechanism that makes certain amounts of heterophily (resp., homophily) necessary for extreme forms of homophilic (resp., heterophilic) patterns to be stable. Efficiency requires a form of common aggregate qualities of connections across all agents within each different population group. Under high (resp., low) assortative interests, some particular forms of only extreme homophilic (resp., heterophilic) patterns are simultaneously stable and efficient. For intermediate assortative interests, we identify a class of friendship networks that feature intermediate levels of homophily, and for which stability and efficiency are compatible