We study the optimal design of the rules of trade in a two-period market given that agents arrive at different times and may only trade with agents present contemporaneously. First period agents face a fixed cot of trading across periods, and their decisions of whether or not to trade in the second period result in externalities relative to the agents arriving in the second period. Given the non-convexities associated with the fixed cost, competitve trading rules can result in inefficienceis in such a market and, in fact, anonymity must be sacrificed to achieve efficiency. Efficient trading rules have a market maker (i.e., an agent who is given some market power and the right to trade across periods) who faces some competition within period trading, but not across periods. The efficient choice of who should be market maker can be made by auctionaing rights to this position. If there is uncertainty across periods, then efficient mechanisms may involve multiple market makers, and the optimal number of market makers depends on the cost of trading, level of risk aversion, and presence of scymmetric information.