We consider a market with dynamic random matching and bargaining with two-sided private information `a la Satterthwaite and Shneyerov (2007). Traders know their valuation for the good before entering the market and steady state distributions in the market are endogenously determined in equilibrium. The market is organized by a profit maximizing broker. We compare the case where the broker can only charge participation fees to buyers and sellers and can influence neither the matching technology nor the bargaining protocol with two other cases. In the first alternative case, the broker can choose the bargaining protocol, but not the matching. In the second case, he can choose both (fully centralized mechanism). We find that the broker gets the same level of profits in optimum in all three cases. Further, the broker makes sure that the same mass of buyers and sellers enters the market in each period and that buyers and sellers trade immediately after entering. We further find that the ratio of (participation) fees in the fully decentralized setup is equal to the ratio of bargaining weights of the buyer and seller and independent of the elasticities of demand. Further, the price structure (i.e. ratio of fees) matters even if bargaining (or price setting) between buyers and sellers is not restricted by the broker.
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