Speaker
Michael Harrison
Adams Distinguished Professor of Management
Stanford University

Abstract
Motivated by applications in financial services, we consider the following customized pricing problem. A seller of some good or service (like auto loans or small business loans) confronts a sequence of potential customers numbered 1, 2, … , T. These customers are drawn at random from a population characterized by a price-response function ρ(p). That is, if the seller offers price p, then the probability of a successful sale is ρ(p). The profit realized from a successful sale is Ï€(p) = p − c, where c > 0 is known.

If the price-response function ρ(-) were also known, then the problem of finding a price p* to maximize ρ(p)π(p) would be simple, and the seller would offer price p* to each of the T customers. We consider the more complicated case where ρ(-) is fixed but initially unknown: roughly speaking, the seller wants to choose prices sequentially so as to maximize the total profit earned from the T potential customers; each successive choice involves a trade-off between refined estimation of the unknown price-response function (learning) and immediate profit (earning).

* Joint work with Bora Keskin and Assaf Zeevi