When order execution meets informed trading

Various participants trade simultaneously in modern financial markets. We study the interaction between the institutional investor driven by a position target and multiple informed traders possessing long-lived information. The problem is formulated as a Stackelberg-Nash game in the linear price impact model. We solve the problem explicitly and obtain the unique equilibrium. Informed traders first engage in predatory trading and then quickly provide much liquidity to the institutional investor. The advantage in transaction costs encourages informed traders to intensify predation but fierce competition forces them to focus on liquidity provision. The institutional investor always employs a well-known U-shape trading strategy regardless of the magnitude of transaction costs and the number of informed traders, and tends to trade more uniformly with high transaction costs and more informed traders. Orders posted by the institutional investor distort the originally efficient price while informed traders trade in the opposite direction to keep the price from deviating too far from the value. We propose a conjecture that transient price impact may be caused by informed trading. An approximately exponential decay is derived with linear permanent and temporary price impacts, and the convergence speed depends on informed traders' transaction costs.