Homophily and influence

We study how learning and influence co-evolve in a social network by extending the classical model of DeGroot (1974) in two fundamental ways:
(a) opinions are multidimensional and the learning time-span is arbitrary;
(b) the effective social network is endogenously shaped by opinion-based homophily.
Our analysis starts by establishing the existence of an equilibrium where, following (a)-(b), the learning outcome and the social network are jointly determined. This is followed by its characterization in some simple contexts. Next, we show that, at equilibrium, the strength of the link between any two agents is always given by its “support” – roughly, the amount of third-party (indirect) influence impinging on both agents. This result leads to the key insight that distinct groups may fail to integrate if their (possibly many) cross-group links lack sufficient support. Building on this, we identify sets of conditions for which social fragmentation is robust (i.e. dynamically stable) or even the unique equilibrium.