  We analyze novel portfolio liquidation games with self-exciting order flow.
Both the N-player game and the mean-field game are considered. We assume that
players' trading activities have an impact on the dynamics of future market
order arrivals thereby generating an additional transient price impact. Given
the strategies of her competitors each player solves a mean-field control
problem. We characterize open-loop Nash equilibria in both games in terms of a
novel mean-field FBSDE system with unknown terminal condition. Under a weak
interaction condition we prove that the FBSDE systems have unique solutions.
Using a novel sufficient maximum principle that does not require convexity of
the cost function we finally prove that the solution of the FBSDE systems do
indeed provide existence and uniqueness of open-loop Nash equilibria.

Optimization and Control;Mathematical Finance