Dynamic Pricing with Demand Learning and Reference Effects

75 Pages Posted: 29 Dec 2017 Last revised: 4 Sep 2020

See all articles by Arnoud den Boer

Arnoud den Boer

University of Amsterdam - Korteweg-de Vries Institute for Mathematics; University of Amsterdam Business School

N. Bora Keskin

Duke University - Fuqua School of Business

Date Written: August 22, 2020

Abstract

We consider a seller's dynamic pricing problem with demand learning and reference effects. We first study the case where customers are loss-averse: they have a reference price that can vary over time, and the demand reduction when the selling price exceeds the reference price dominates the demand increase when the selling price falls behind the reference price by the same amount. Thus, the expected demand as a function of price has a time-varying "kink" and is not differentiable everywhere. The seller neither knows the underlying demand function nor observes the time-varying reference prices. In this setting, we design and analyze a policy that (i) changes the selling price very slowly to control the evolution of the reference price, and (ii) gradually accumulates sales data to balance the tradeoff between learning and earning. We prove that, under a variety of reference-price updating mechanisms, our policy is asymptotically optimal; i.e., its T-period revenue loss relative to a clairvoyant who knows the demand function and the reference-price updating mechanism grows at the smallest possible rate in T. We also extend our analysis to the case of a fixed reference price, and show how reference effects increase the complexity of dynamic pricing with demand learning in this case. Moreover, we study the case where customers are gain-seeking and design asymptotically optimal policies for this case. Finally, we design and analyze an asymptotically optimal statistical test for detecting whether customers are loss-averse or gain-seeking.

Keywords: reference-price effect, dynamic pricing, sequential estimation, learning and earning

Suggested Citation

den Boer, Arnoud and Keskin, N. Bora, Dynamic Pricing with Demand Learning and Reference Effects (August 22, 2020). Available at SSRN: https://ssrn.com/abstract=3092745 or http://dx.doi.org/10.2139/ssrn.3092745

Arnoud Den Boer

University of Amsterdam - Korteweg-de Vries Institute for Mathematics ( email )

Netherlands

University of Amsterdam Business School ( email )

Roetersstraat 18
Amsterdam, 1018WB
Netherlands

N. Bora Keskin (Contact Author)

Duke University - Fuqua School of Business ( email )

100 Fuqua Drive
Durham, NC 27708-0120
United States

HOME PAGE: http://faculty.fuqua.duke.edu/~nk145/

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