  We study the design of a decentralized two-sided matching market in which
agents' search is guided by the platform. There are finitely many agent types,
each with (potentially random) preferences drawn from known type-specific
distributions. Equipped with knowledge of these distributions, the platform
guides the search process by determining the meeting rate between each pair of
types from the two sides. Focusing on symmetric pairwise preferences in a
continuum model, we first characterize the unique stationary equilibrium that
arises given a feasible set of meeting rates. We then introduce the platform's
optimal directed search problem, which involves optimizing meeting rates to
maximize equilibrium social welfare. We first show that incentive issues
arising from congestion and cannibalization make the design problem fairly
intricate. Nonetheless, we develop an efficiently computable search design
whose corresponding equilibrium achieves at least 1/4 the social welfare of the
optimal design. In fact, our construction always recovers at least 1/4 the
first-best social welfare, where agents' incentives are disregarded. Our
directed search design is simple and easy-to-implement, as its corresponding
bipartite graph consists of disjoint stars. Furthermore, our design implies the
platform can substantially limit choice and yet induce an equilibrium with an
approximately optimal welfare. Finally, we show that approximation is likely
the best we can hope for by establishing that the problem of designing optimal
directed search is NP-hard to even approximate beyond a certain constant
factor.
