Robust Dynamic Pricing with Strategic Customers

Abstract

We consider the canonical revenue management (RM) problem 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 times of purchases. The private valuations of these customers decay over time and the customers incur monitoring costs; both the rates of decay and these monitoring costs are private information. This setting has resisted the design of optimal dynamic mechanisms heretofore. Optimal pricing schemes—an almost necessary mechanism format for practical RM considerations—have been similarly elusive. The present paper proposes a mechanism we dub robust pricing. Robust pricing is guaranteed to achieve expected revenues that are at least within 29% of those under an optimal (not necessarily posted price) dynamic mechanism. We thus provide the first approximation algorithm for this problem. The robust pricing mechanism is practical, since it is an anonymous posted price mechanism and since the seller can compute the robust pricing policy for a problem without any knowledge of the distribution of customer discount factors and monitoring costs. The robust pricing mechanism also enjoys the simple interpretation of solving a dynamic pricing problem for myopic customers with the additional requirement of a novel “restricted sub-martingale constraint” on prices that discourages rapid discounting. We believe this interpretation is attractive to practitioners. Finally, numerical experiments suggest that the robust pricing mechanism is, for all intents, near optimal.