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.