Dynamic Pricing with an Unknown Demand Model: Asymptotically Optimal Semi-Myopic Policies

Abstract

We consider a monopolist who sells a set of products over a time horizon of T periods. The seller initially does not know the parameters of the products’ linear demand curve, but can estimate them based on demand observations. We first assume that the seller knows nothing about the parameters of the demand curve, and then consider the case where the seller knows the expected demand under an incumbent price. It is shown that the smallest achievable revenue loss in T periods, relative to a clairvoyant who knows the underlying demand model, is of order √T in the former case and of order logT in the latter case. To derive pricing policies that are practically implementable, we take as our point of departure the widely used policy called greedy iterated least squares (ILS), which combines sequential estimation and myopic price optimization. It is known that the greedy ILS policy itself suffers from incomplete learning, but we show that certain variants of greedy ILS achieve the minimum asymptotic loss rate. To highlight the essential features of well-performing pricing policies, we derive sufficient conditions for asymptotic optimality.

Keywords: Revenue management, pricing, sequential estimation, exploration-exploitation