Dynamic Pricing with Model Uncertainty: Learning & Earning

This tutorial focuses on dynamic pricing under model uncertainty: a class of problems whose first instance dates back at least 40 years, is relatively simple in structure, is widely considered fundamental, and has numerous manifestations across multiple application domains and academic disciplines. While significant progress has been made throughout the last several decades, including a flurry of recent work, many variants of this problem class remain essentially unsolved. Briefly stated, the problem can be described as sequential pricing when the underlying demand model (or demand curve) is unknown and the market response to any given price is confounded by statistical noise. It will be helpful to hold in mind the following simple problem instance. The decision maker (“seller”) faces demand for a product s/he is selling. At every successive time unit the seller fixes a price for the product, subsequent to which demand is realized. The demand realizations are “noisy” observations of an ambient demand curve which is unbeknownst to the seller. The seller’s objective is to maximize expected cumulative (either discounted or not) profits over the time horizon that governs the interactions with the buyers. This situation is a quintessential example of a trade-off between exploration of the environment (to learn demand characteristics) and exploitation of that knowledge (via pricing) to maximize expected rewards.