From Acquaintances to Friends: Homophily and Learning in Networks

TL;DR

This paper models how agents' learning and homophily influence the evolution of social networks, revealing complex effects on network density, clustering, and differences between complete and incomplete information scenarios.

Contribution

It introduces a stochastic model of network evolution driven by learning and homophily, highlighting their impact on network structure and the differences between complete and incomplete information.

Findings

Higher homophily reduces the number of links formed.

Incomplete information leads to sparser networks and less clustering.

Differences between complete and incomplete networks are most pronounced at intermediate homophily levels.

Abstract

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 from these interactions. Agents have homophilous preferences and limited capacity, so they maintain links with others who are learned to be similar to themselves and cut links to others who are learned to be dissimilar to themselves. Thus learning influences the evolution of the network, but learning is imperfect so the evolution is stochastic. Homophily matters. 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. There may be big differences between the networks that emerge under complete and incomplete information. Homophily matters here as well: 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 the most when the degree of homophily is intermediate. With multiple stages of life, the effects of incomplete information are large initially but fade somewhat over time.