Chasing Demand: Learning and Earning in a Changing Environment

We consider a dynamic pricing problem in which a seller faces an unknown demand model that can change over time. The amount of change over a time horizon of T periods is measured using a variation metric that allows for a broad spectrum of temporal behavior. Given a finite variation budget, we first derive a lower bound on the expected performance gap between any pricing policy and a clairvoyant who knows a priori the temporal evolution of the underlying demand model, and then we design families of near-optimal pricing policies, the revenue performance of which asymptotically matches said lower bound. We also show that the seller can achieve a substantially better revenue performance in demand environments that change in bursts than in demand environments that change smoothly, among other things quantifying the net effect of the volatility in the demand environment on the seller's revenue performance.