Here we consider a matching model where agents are heterogeneous and u
tilities nontransferable. We utilize this framework to study how equil
ibrium sorting takes place in marriage markets. We impose conditions t
hat guarantee the existence of a steady state equilibrium and then cha
racterize it. Several examples are developed to illustrate the richnes
s of equilibria. The model reveals an interesting sorting externality
that can support multiple steady state equilibria, even with constant
returns to matching.