We consider optimal pricing by a profit-maximizing platform running a dynamic search and matching market. Buyers and sellers enter in cohorts over time, meet and bargain under private information. The optimal centralized mechanism, which involves posting a bid-ask spread, can be decentralized through participation fees charged by the intermediary to both sides. The sum of buyers' and sellers' fees equals the sum of inverse hazard rates of the marginal types and their ratio equals the ratio of buyers' and sellers' bargaining weights. We also show that a monopolistic intermediary in a search market may be welfare enhancing.
Dynamic random matching two-sided private information intermediaries