  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 such distributional knowledge, 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 makes the design problem fairly intricate.
Nonetheless, we develop an efficiently computable solution whose corresponding
equilibrium achieves at least 1/4 of the optimal social welfare. Our directed
search design is simple and easy-to-implement, as its corresponding bipartite
graph consists of disjoint stars. Furthermore, our solution implies that the
platform can substantially limit choice and yet induce an equilibrium with an
approximately optimal welfare. Finally, we show that approximation is the
likely best we can hope by establishing that the problem of designing optimal
directed search is NP-hard to approximate beyond a certain constant factor.
