  The interactions between a large population of high-frequency traders (HFTs)
and a large trader (LT) who executes a certain amount of assets at discrete
time points are studied. HFTs are faster in the sense that they trade
continuously and predict the transactions of LT. A jump process is applied to
model the transition of HFTs' attitudes towards inventories and the equilibrium
is solved through the mean field game approach. When the crowd of HFTs is
averse to running (ending) inventories, they first take then supply liquidity
at each transaction of LT (throughout the whole execution period).
Inventory-averse HFTs lower LT's costs if the market temporary impact is
relatively large to the permanent one. What's more, the repeated liquidity
consuming-supplying behavior of HFTs makes LT's optimal strategy close to
uniform trading.
