We introduce capacity constrained competition between market-making intermediaries in a model in which agents can choose between trading with intermediaries, joining a search market or remaining inactive. Recently, market-making by a monopolistic intermediary has been analyzed by Rust and Hall (2003) and Gehrig (1993). Market-makers set publicly observable ask and bid prices. Because market-making involves price setting, without further restrictions competition between market-making intermediaries is Bertrand-like and yields the Walrasian outcome, where the ask-bid spread is zero (Rust and Hall 2003, Gehrig 1993). However, positive ask-bid spreads and competition between market-makers can be observed in reality, e.g. in banking and in retailing. Following Kreps and Scheinkman (1983) and Boccard and Wauthy (2000), we therefore introduce physical capacity constraints. This allows for a gradual transition from monopolistic to perfectly competitive intermediation as the number of intermediaries increases. In particular, we show that given Cournot capacities, intermediaries will set Cournot bid and ask prices in the subsequent subgames, so that the equilibrium of the intermediated market coincides with the Walrasian equilibrium as the number of intermediaries becomes large
