Games can be easy to construct but difficult to solve due to current methods available for finding the Nash Equilibrium. This issue is one of many that face modern game theorists and those analysts that need to model situations with multiple decision-makers. This paper explores the use of reinforcement learning, a standard artificial intelligence technique, as a means to solve a simple dynamic airline pricing game. Three different reinforcement learning approaches are compared: SARSA, Q-learning and Monte Carlo Learning. The pricing game solution is surprisingly sophisticated given the game's simplicity and this sophistication is reflected in the learning results. The paper also discusses extra analytical benefit obtained from applying reinforcement learning to these types of problems.