Feature-Based Dynamic Pricing

44 Pages Posted: 29 Feb 2016 Last revised: 30 May 2019

See all articles by Maxime Cohen

Maxime Cohen

Desautels Faculty of Management, McGill University

Ilan Lobel

New York University (NYU)

Renato Paes Leme

Google Inc.

Date Written: February 23, 2016

Abstract

We consider the problem faced by a firm that receives highly differentiated products in an online fashion. The firms needs to price these products to sell them to its customer base. Products are described by vectors of features and the market value of each product is linear in the values of the features. The firm does not initially know the values of the different features, but can learn the values of the features based on whether products were sold at the posted prices in the past. This model is motivated by applications such as online marketplaces, online flash sales, and loan pricing. We first consider a multi-dimensional version of binary search over polyhedral sets and show that it has a worst-case regret which is exponential in the dimension of the feature space. We then propose a modification of the prior algorithm where uncertainty sets are replaced by their Lowner-John ellipsoids. We show that this algorithm has a worst-case regret which is quadratic in the dimension of the feature space and logarithmic in the time horizon. We also show how to adapt our algorithm to the case where valuations are noisy. Finally, we present computational experiments to illustrate the performance of our algorithm.

Keywords: online learning, contextual bandits, ellipsoid method, revenue management

JEL Classification: C61, D42, D81, D83

Suggested Citation

Cohen, Maxime and Lobel, Ilan and Paes Leme, Renato, Feature-Based Dynamic Pricing (February 23, 2016). Available at SSRN: https://ssrn.com/abstract=2737045 or http://dx.doi.org/10.2139/ssrn.2737045

Maxime Cohen

Desautels Faculty of Management, McGill University ( email )

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

Ilan Lobel (Contact Author)

New York University (NYU) ( email )

Bobst Library, E-resource Acquisitions
20 Cooper Square 3rd Floor
New York, NY 10003-711
United States

Renato Paes Leme

Google Inc. ( email )

1600 Amphitheatre Parkway
Second Floor
Mountain View, CA 94043
United States

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