A Stackelberg order execution game

Order execution is an important operational level of activity encountered in portfolio investment and risk management. We study a sequential Stackelberg order execution game which arises naturally from the practice of algorithm trading in financial markets. The game consists of two risk-neutral traders, one leader and one follower, who compete to maximize their expected payoffs respectively by trading a single risky asset whose price dynamics follows a linear-price market impact model over a finite horizon. This new Stackelberg game departs from the Nash games which have been the main focus in the algorithm trading literature. We derive a closed-form solution for the unique open-loop Stackelberg equilibrium by exploiting the special structures of the model. This analytic solution enables us to develop new and complementary managerial insights by looking at both players’ equilibrium behavior in terms of trading speeds and positions, expected price dynamics, price of anarchy, first mover’s advantage, and trading horizon effect.