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In this paper, the interactions between a large informed trader (IT, for
short) and a high-frequency trader (HFT, for short) who can anticipate the
former's incoming order are studied in an extended Kyle's (1985) model.
Equilibria under various specific situations are discussed. Relying on the
speed advantage, HFT always trades in the same direction as the large order in
advance. However, whether or not she provides liquidity depends on her
inventory aversion, the prediction accuracy, and the market activeness. She may
supply liquidity back (act as a front-runner) or continue to take it away (in
this case we call her a small IT). Small IT always harms the large trader while
front-runner may benefit her. Besides, we find surprisingly that (1) increasing
the noise in HFT's signal may in fact decrease IT's profit; (2) although
providing liquidity, a front-runner may harm IT more than a small IT.
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