We propose a dynamic model of the limit order book to derive conditions to test if a trading algorithm will learn to manipulate the order book. Our results show that as a market maker becomes more tolerant to bearing inventory risk, the learning algorithm will find optimal strategies that manipulate the book more frequently. Manipulation occurs to induce mean reversion in inventory to an optimal level and to execute round-trip trades with limit orders at a higher probability than was otherwise likely to occur; spoofing is a special case when the market maker prefers that manipulative limit orders are not filled. The conditions are tested with order book data from Nasdaq and we show that market conditions are conducive for an algorithm to learn to manipulate the order book. Finally, when two market makers use learning algorithms to trade, their algorithms can learn to coordinate their manipulation.  (This is joint work with Patrick Chang and Gabriel Garcia-Arenas).