Monopolistic Intermediation in the Gehrig (1993) Search Model Revisited

We modify the basic Gehrig (1993) model. In this model, individual agents are either buyers or sellers. They can choose between joining the search market, joining the monopolistic intermediary or remaining inactive. In the search market, agents are randomly matched and the price at which exchange takes place is set bilaterally. If agents join the intermediary, buyers have to pay an ask price set in advance by the intermediary. Likewise, if sellers decide to deal through the intermediary, they get the bid price set by the intermediary. As Gehrig shows, this model has an equilibrium in which the search market and the market of the monopolistic intermediary are simultaneously open. The intermediary makes positive profits because he trades at a positive ask-bid spread, and the set of individual agents is tripartite: High valuation buyers and low cost sellers deal through the intermediary, buyers and sellers with average valuations and average costs are active in the search market, and low valuation buyers and high cost sellers remain inactive. We modify this basic model by imposing a sequential structure. We assume that the monopolistic intermediary first has to buy the good from sellers on the input market before he can sell it to buyers on the output market. As a consequence of the sequential structure, the subgame following capacity setting has a unique subgame perfect equilibrium with an active search market. On the equilibrium path, the equilibrium analyzed by Gehrig is replicated.