Dynamic Pricing with Fairness Constraints

38 Pages Posted: 28 Sep 2021 Last revised: 3 Nov 2021

See all articles by Maxime C. Cohen

Maxime C. Cohen

Desautels Faculty of Management, McGill University

Sentao Miao

McGill University - Desautels Faculty of Management

Yining Wang

University of Florida - Warrington College of Business Administration

Date Written: September 25, 2021

Abstract

Following the increasing popularity of personalized pricing, there is a growing concern from customers and policy makers regarding fairness considerations. This paper studies the problem of dynamic pricing with unknown demand under two types of fairness constraints: price fairness and demand fairness. For price fairness, the retailer is required to (i) set similar prices for different customer groups (called group fairness) and (ii) ensure that the prices over time for each customer group are relatively stable (called time fairness). We propose an algorithm based on an infrequently-changed upper-confidence-bound (UCB) method, which is proved to yield a near-optimal regret performance. In particular, we show that imposing group fairness does not affect the demand learning problem, in contrast to imposing time fairness. On the flip side, we show that imposing time fairness does not impact the clairvoyant optimal revenue, in contrast to imposing group fairness. For demand fairness, the retailer is required to satisfy that the resulting demand from different customer groups is relatively similar (e.g., the retailer offers a lower price to students to increase their demand to a similar level as non-students). In this case, we design an algorithm adapted from a primal-dual learning framework and prove that our algorithm also achieves a near-optimal performance.

Keywords: Dynamic Pricing, Demand Learning, Fairness, Revenue Management

Suggested Citation

Cohen, Maxime C. and Miao, Sentao and Wang, Yining, Dynamic Pricing with Fairness Constraints (September 25, 2021). Available at SSRN: https://ssrn.com/abstract=3930622 or http://dx.doi.org/10.2139/ssrn.3930622

Maxime C. Cohen (Contact Author)

Desautels Faculty of Management, McGill University ( email )

1001 Sherbrooke St. W
Montreal, Quebec H3A 1G5
Canada

Sentao Miao

McGill University - Desautels Faculty of Management ( email )

1001 Sherbrooke St W
Montreal, Quebec h3A 1G5

Yining Wang

University of Florida - Warrington College of Business Administration ( email )

Gainesville, FL 32611
United States

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