We develop a dynamic model of an order-driven market populated by discretionary liquidity traders. These traders must trade, yet can choose the type of order and are fully strategic in their decision. Traders differ by their impatience: less patient traders demand liquidity, more patient traders...

In this paper, the authors develop a dynamic model of trading with two specialized sides: traders posting quotes (“market makers”) and traders hitting quotes (“market takers”). Traders monitor the market to seize profit opportunities, generating high frequency make/take liquidity cycles....