Intermediation in a directed search model

We provide an example where establishing competitive coordination service platforms is so lucrative that they end up reducing welfare. We consider a canonical directed search model in which buyers have unit demands and sellers' capacity constraint leads to a coordination problem: in a symmetric equilibrium without intermediation some sellers receive too many and some too few buyers. We compare this equilibrium to one where sellers and buyers can choose to become intermediaries who coordinate the meetings. In this setup, roughly one-fifth of agents become intermediaries. As a result, a large part of the supply and demand in the economy vanishes. Moreover, the large amount of intermediaries actually reduces the meeting efficiency. Jointly, these effects imply that the gains from trade are lower than that in the economy without intermediation.