Designing Approximately Optimal Search on Matching Platforms

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.