Evaluating reinforcement learning for game theory applicationlearning to price airline seats under competition

Applied Game Theory has been criticised for not being able to model real decision making situations. A game's sensitive nature and the difficultly in determining the utility payoff functions make it hard for a decision maker to rely upon any game theoretic results. Therefore the models tend to be simple due to the complexity of solving them (i.e. finding the equilibrium).In recent years, due to the increases of computing power, different computer modelling techniques have been applied in Game Theory. A major example is Artificial Intelligence methods e.g. Genetic Algorithms, Neural Networks and Reinforcement Learning (RL). These techniques allow the modeller to incorporate Game Theory within their models (or simulation) without necessarily knowing the optimal solution. After a warm up period of repeated episodes is run, the model learns toplay the game well (though not necessarily optimally). This is a form of simulation-optimization.The objective of the research is to investigate the practical usage of RL within a simple sequential stochastic airline seat pricing game. Different forms of RL are considered and compared to the optimal policy, which is found using standard dynamic programming techniques. The airline game and RL methods displays various interesting phenomena, which are also discussed. For completeness, convergence proofs forthe RL algorithms were constructed.