Dynamic Pricing with Online Learning and Strategic Consumers: An Application of the Aggregating Algorithm

We study the problem faced by a monopolistic company that is dynamically pricing a perishable product or service and simultaneously learning the demand characteristics of its customers. In the learning procedure, the company observes the sales history over consecutive planning horizons and predicts consumer demand by applying an aggregating algorithm (AA) to a pool of online stochastic predictors. Numerical implementation uses finite-sample distribution approximations which are periodically updated using the most recent sales data and subsequently diversified with a random Markov step characterizing the stochastic predictors. The company’s pricing policy is optimized by a simulation-based procedure integrated with AA. The methodology of this paper is general and independent of specific distributional assumptions. We illustrate this procedure on a demand model for a market where customers are aware that pricing is dynamic, may time their purchases strategically, and compete for a limited product supply. We derive the form of this demand model using a game-theoretic consumer choice model and study its structural properties. Numerical experiments demonstrate that the learning procedure is robust to deviations of the actual market response to price from the model used in learning.