On the (Surprising) Sufficiency of Linear Models for Dynamic Pricing with Demand Learning
研究在未知需求曲线下，使用简单线性模型进行动态定价时，因模型误设导致的收益损失有多大。结果表明，在一般条件下，损失可能并不显著。
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 Gérard Cachon, stochastic models and simulation.