Download this Paper Open PDF in Browser

On the Minimax Complexity of Pricing in a Changing Environment

Operations Research, Vol. 59, No. 1, pp. 66-79, 2011

Columbia Business School Research Paper No. 12-6

14 Pages Posted: 12 Jan 2012  

Omar Besbes

Columbia Business School - Decision Risk and Operations

Assaf Zeevi

Columbia Business School - Decision Risk and Operations

Date Written: February 8, 2011

Abstract

We consider a pricing problem in an environment where the customers’ willingness-to-pay (WtP) distribution may change at some point over the selling horizon. Customers arrive sequentially and make purchase decisions based on a quoted price and their private reservation price. The seller knows the WtP distribution pre- and post-change but does not know the time at which this change occurs. The performance of a pricing policy is measured in terms of regret: the loss in revenues relative to an oracle that knows the time of change prior to the start of the selling season. We derive lower bounds on the worst-case regret and develop pricing strategies that achieve the order of these bounds, thus establishing the complexity of the pricing problem. Our results shed light on the role of price experimentation and its necessity for optimal detection of changes in market response/WtP. Our formulation allows for essentially arbitrary consumer WtP distributions and purchase request patterns.

Keywords: pricing, nonstationary demand, estimation, detection, change-point, price experimentation

Suggested Citation

Besbes, Omar and Zeevi, Assaf, On the Minimax Complexity of Pricing in a Changing Environment (February 8, 2011). Operations Research, Vol. 59, No. 1, pp. 66-79, 2011; Columbia Business School Research Paper No. 12-6. Available at SSRN: https://ssrn.com/abstract=1983282

Omar Besbes (Contact Author)

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

Assaf Zeevi

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States
212-854-9678 (Phone)
212-316-9180 (Fax)

HOME PAGE: http://www.gsb.columbia.edu/faculty/azeevi/

Paper statistics

Downloads
155
Rank
160,269
Abstract Views
894