The Effectiveness of Single Price Change in Learning and Earning via Sequential Estimation

We study a revenue maximization problem in a congestible system with unknown demand parameters. We show that a single price change during the learning phase is sufficient to obtain a revenue regret that is on the same scale with the optimal regret achievable when demand parameters are known up front. The sufficiency of single price change in learning is due to the implementation of sequential maximum likelihood estimation (SMLE). Without knowledge of demand parameters, an initial price is randomly chosen. With a typical MLE under which a sample siae for learning is pre-fixed, the quality of estimation with the randomly chosen price is not controllable, making the choice of the second price as equally uninformative as for the first price. On the other hand, SMLE makes learning with the first price informative as it can control the estimation quality.