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We study liquidity supply in fragmented markets. Market makers intermediate heterogeneous order flows, trading off spread revenue against inventory costs. Applying our model to payment for order flow (PFOF), we demonstrate that portfolio-based considerations of inventory management incentivize market makers to segment retail orders by siphoning them off-exchange. Banning order flow segmentation reduces total welfare, can make trading more costly for all investors, and can resolve a prisoner's dilemma among market makers. These results differentiate our inventory-based model from the existing information-based theories of PFOF.
Baldauf et al. (Wed,) studied this question.
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