Robust Dynamic Pricing With Strategic Customers

We consider the canonical problem of revenue management (RM) wherein a seller must sell an inventory of some product over a finite horizon via an anonymous, posted price mechanism. Unlike typical models in RM, we assume that customers are forward looking. In particular, customers arrive randomly over time, and strategize about their time of purchase. The private valuations of these customers decay over time and the customers incur monitoring costs; both the rate of decay and these monitoring costs are private information. Moreover, customer valuations and monitoring costs are potentially correlated. This setting has proven to be a difficult one for the design of optimal dynamic mechanisms heretofore. Optimal pricing schemes -- an almost necessary mechanism format for practical RM considerations -- have been similarly elusive. We propose a class of pricing policies, and a simple to compute policy within this class, that is guaranteed to achieve expected revenues that are at least within 29% of those under an optimal (not necessarily posted price) dynamic mechanism. Moreover, the seller can compute this pricing policy without any knowledge of the distribution of customer discount factors and monitoring costs. Our scheme can be interpreted as solving a dynamic pricing problem for myopic customers with the additional requirement of a novel --restricted submartingale constraint on prices. Numerical experiments suggest that the policy is, for all intents, near optimal.