On the (Surprising) Sufficiency of Linear Models for Dynamic Pricing with Demand Learning

We consider a multi-period single product pricing problem with an unknown demand curve. The seller’s objective is to adjust prices in each period so as to maximize cumulative expected revenues over a given finite time horizon; in doing so, the seller needs to resolve the tension between learning the unknown demand curve and maximizing earned revenues. The main question that we investigate is the following: how large of a revenue loss is incurred if the seller uses a simple parametric model which differs significantly (i.e., is misspecified) relative to the underlying demand curve. This “price of misspecification” is expected to be significant if the parametric model is overly restrictive. Somewhat surprisingly, we show (under reasonably general conditions) that this may not be the case.