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

School of Business, Queen's University, Kingston, Ontario, Canada K7L 3N6
School of Business, Queen's University, Kingston, Ontario, Canada K7L 3N6
School of Business, Queen's University, Kingston, Ontario, Canada K7L 3N6
School of Business, Queen's University, Kingston, Ontario, Canada K7L 3N6
tlevin{at}business.queensu.ca
ylevin{at}business.queensu.ca
jmcgill{at}business.queensu.ca
mnediak{at}business.queensu.ca

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 learning stages and predicts consumer demand by applying an aggregating algorithm (AA) to a pool of online stochastic predictors. Numerical implementation uses finite-sample distribution approximations that are periodically updated using the most recent sales data. These are subsequently altered with a random step characterizing the stochastic predictors. The company's pricing policy is optimized with a simulation-based procedure integrated with AA. The methodology of the paper is general and independent of specific distributional assumptions. We illustrate this procedure on a demand model for a market in which 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 from the model of the market used in learning.

Subject classifications: marketing; pricing; games; stochastic; artificial intelligence; online learning.
History: Received March 2006; revision received December 2007; accepted January 2008.