Stable marriages and search frictions

We embed a two-sided matching market with non-transferable
utility, a marriage market, into a random search model. We study steady-state equilibria and characterize the limit of the corresponding equilibrium matchings as exogenous search frictions become small. The central question is whether the set of such limit matchings coincides with the set of stable matchings for the underlying marriage market. We show that this is the case if and only if there is a unique stable matching. Otherwise, the set of limit matchings contains the set of all stable deterministic matchings, but also contains unstable random matchings. These unstable random matchings are Pareto dominated. Thus, vanishing frictions do not guarantee the efficiency of decentralized marriage markets.