Dynamic Pricing: A Learning Approach

Abstract

We present an optimization approach for jointly learning the demand as a function of price, and dynamically setting prices of products in order to maximize expected revenue. The models we consider do not assume that the demand as a function of price is known in advance, but rather assume parametric families of demand functions that are learned over time. In the first part of the paper, we consider the noncompetitive case and present dynamic programming algorithms of increasing computational intensity with incomplete state information for jointly estimating the demand and setting prices as time evolves. Our computational results suggest that dynamic programming based methods outperform myopic policies often significantly. In the second part of the paper, we consider a competitive oligopolistic environment. We introduce a more sophisticated model of demand learning, in which the price elasticities are slowly varying functions of time, and allows for increased flexibility in the modeling of the demand. We propose methods based on optimization for jointly estimating the Firm’s own demand, its competitors’ demands, and setting prices. In preliminary computational work, we found that optimization based pricing methods offer increased expected revenue for a firm independently of the policy the competitor firm is following.