A standard presumption of market microstructure models is that competition between risk neutral market makers inevitably leads to prices schedules that leave market makers zero expected profits conditional on the order flows. This paper shows that this result does not hold when traders can split orders between market makers. When traders can split orders, market makers set less competitive price schedules that earn them strictly positive profits and hence raise trading costs. Indeed, if noise traders have completely inelastic demands (as in Kyle 1985), market makers want to set arbitrarily uncompetitive price schedules: no equilibrium exists. Our results imply that if feasible, regulation banning order splitting on an exchange is optimal. Analogous results obtain when price schedules are set by any finite number of agents who compete using limit orders. Further, since limit orders, by their very nature, are split against incoming market orders, the analysis suggests that regulated market maker competition will provide better prices.
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