  Trading algorithms that execute large orders are susceptible to exploitation
by order anticipation strategies. This paper studies the influence of order
anticipation strategies in a multi-investor model of optimal execution under
transient price impact. Existence and uniqueness of a Nash equilibrium is
established under the assumption that trading incurs quadratic transaction
costs. A closed-form representation of the Nash equilibrium is derived for
exponential decay kernels. With this representation, it is shown that while
order anticipation strategies raise the execution costs of a large order
significantly, they typically do not cause price overshooting in the sense of
Brunnermeier and Pedersen.
