  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.
