Dynamic Online Pricing with Incomplete Information

Consider the pricing decision for a manager at large online retailer, such as Amazon.com, that sells millions of products. The pricing manager must decide on real-time prices for each of these product. Due to the large number of products, the manager must set retail prices without complete demand information. A manager can run price experiments to learn about demand and maximize long run profits. There are two aspects that make the online retail pricing different from traditional brick and mortar settings. First, due to the number of products the manager must be able to automate pricing. Second, an online retailer can make frequent price changes. Pricing differs from other areas of online marketing where experimentation is common, such as online advertising or website design, as firms do not randomize prices to different customers at the same time. In this paper we propose a dynamic price experimentation policy where the firm has incomplete demand information. For this general setting, we derive a pricing algorithm that balances earning profit immediately and learning for future profits. The proposed approach marries statistical machine learning and economic theory. In particular we combine multi-armed bandit (MAB) algorithms with partial identification of consumer demand into a unique pricing policy. Our automated policy solves this problem using a scalable distribution-free algorithm. We show that our method converges to the optimal price faster than standard machine learning MAB solutions to the problem. In a series of Monte Carlo simulations, we show that the proposed approach perform favorably compared to methods in computer science and revenue management. ∗Ross School of Business, University of Michigan. Contact: [email protected] †Rady School of Management, University of California, San Diego. Contact: [email protected] ‡Department of Electrical Engineering and Computer Science, University of Michigan. Contact: [email protected]