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

Abstract

We consider a multiperiod 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 that differs significantly i.e., is misspecified relative to the underlying demand curve? We measure performance by analyzing the price trajectory induced by this misspecified model and quantifying the magnitude of revenue losses as a function of the time horizon relative to an oracle that knows the true underlying demand curve. The "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 need not be the case. This paper was accepted by Gerard Cachon, stochastic models and simulation.