Fee setting intermediaries: on real estate agents, stock brokers, and auction houses

Mechanisms where intermediaries charge a commission fee and have the sellers set the price are widely used in practice e.g. by real estate agents, stock brokers, art galleries, or auction houses. We model competition between intermediaries in a dynamic random matching model, where in every period a buyer, a seller, and an intermediary are randomly matched. In any period, every intermediary has a temporary monopoly and designs an exchange mechanism that maximizes his own expected profits. Traders' valuations for the indivisible good depend on their option value of future trade. The following results obtain. First, we show that the intermediary can achieve the highest possible profit with a fee setting mechanism. Second, we characterize when these fees are linear. Third, fee setting is an equilibrium outcome in a dynamic market. Fourth, when the rematching probability ncreases or, equivalently, the period length decreases, the equilibrium fees become smaller. Our model is applicable to stock brokers and auction houses as intermediaries. It can further explain several of the stylized facts observed in real estate brokerage, such as the 6 percent fee, the relation between listing price and time on market, inefficient free entry, higher prices for houses owned by brokers, and home owners who bought during a boom asking higher prices. We also provide various extensions