  Liquidation is the process of selling a large number of shares of one stock
sequentially within a given time frame, taking into consideration the costs
arising from market impact and a trader's risk aversion. The main challenge in
optimizing liquidation is to find an appropriate modeling system that can
incorporate the complexities of the stock market and generate practical trading
strategies. In this paper, we propose to use multi-agent deep reinforcement
learning model, which better captures high-level complexities comparing to
various machine learning methods, such that agents can learn how to make the
best selling decisions. First, we theoretically analyze the Almgren and Chriss
model and extend its fundamental mechanism so it can be used as the multi-agent
trading environment. Our work builds the foundation for future multi-agent
environment trading analysis. Secondly, we analyze the cooperative and
competitive behaviours between agents by adjusting the reward functions for
each agent, which overcomes the limitation of single-agent reinforcement
learning algorithms. Finally, we simulate trading and develop an optimal
trading strategy with practical constraints by using a reinforcement learning
method, which shows the capabilities of reinforcement learning methods in
solving realistic liquidation problems.
