Power of Dynamic Pricing in Revenue Management with Strategic (Forward-looking) Customers

Abstract

The present paper considers a canonical revenue management problem wherein a monopolist seller seeks to maximize revenue from selling a fixed inventory of a product to customers who arrive over time. We assume that customers are forward-looking and rationally strategize the timing of their purchases, an empirically confirmed aspect of modern customer behavior. We consider a broad class of customer utility models that allow customer disutility from waiting to be heterogeneous and correlated with product valuations. Chen et al. [1] show that the so-called fixed price policy is asymptotically optimal in the high-volume regime where both the seller's initial inventory and the length of the selling horizon are proportionally scaled. Specifically, the revenue loss of the fixed price policy is O( k1/2), where k is the system's scaling parameter. In the present paper, we present a novel real-time pricing policy. This policy repeatedly updates the fixed price policy in Chen et al. [1] by taking into account the volatility of the historic sales. We force the price process under this policy to be non-decreasing over time. Therefore, our policy incentivizes strategic customers to behave myopically. We show that if the seller updates the price for only a single time, then the revenue loss of our policy can be arbitrarily close to O(k1/3 ln k). If the seller updates the prices with a frequency O(lnk/ln ln k), then the revenue loss of our policy can be arbitrarily close to O((ln k)3). These results are novel and show the power of dynamic pricing in the presence of forward-looking customers, at least for the problem setting considered in this paper.