Dynamic optimization and learning : how should a manager set prices when the demand function is unknown?

This paper considers the problem of changing prices over time to maximize expected revenues in the presence of unknown demand distribution parameters. It provides and compares several methods that use the sequence of past prices and observed demands to set price in the current period. A Taylor series expansion of the future reward function explicitly illustrates the tradeoff between short term revenue maximization and future information gain and suggests a promising pricing policy referred to as a one-step look-ahead rule. An in-depth Monte Carlo study compares several different pricing strategies and shows that the one-step look-ahead rules dominate other heuristic policies and produce good short term performance. The reasons for the observed bias of parameter estimates are also investigated.