Suppose, there is a HF strategy (agent) that is based on order book microstructure, and it is able to make good executions locally. More formally, in average its execution price is better than asset price $\tau$ sec. after the execution. Suppose, we manage two such agents: one for long orders, another for short orders.
The question is how to develop a controller that synchronizes between two and manages their mutual position given position limit
N on each side, and maximal order size
I assume, this is a very broadly studied problem, especially among market makers. Can you please recommend relevant articles and ideas that provide overview of this topic and most sophisticated approaches. I'm especially interested in the very details such as: 1) Timing. is it prudent to generate random time intervals between last execution and new orders placement? 2) Pricing. How many orders can be executed on the same price? Thank you.