On the (Surprising) Sufficiency of Linear Models for Dynamic Pricing with Demand Learning
Coauthor(s): Omar Besbes.
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 so doing, the seller needs to resolve the tension between learning the unknown demand curve, and earning revenues by solving the dynamic optimization problem. 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, and under reasonably general conditions, it can be made to be essentially negligible, in a precise mathematical sense, if the seller uses a two parameter linear model.
Source: Working paper
Besbes, Omar, and Assaf Zeevi. "On the (Surprising) Sufficiency of Linear Models for Dynamic Pricing with Demand Learning." Working paper, Columbia University, 2012.