Price Discrimination and Inventory Allocation in Bertrand Competition

90 Pages Posted: 20 Jan 2021 Last revised: 24 Jul 2021

See all articles by Maxime C. Cohen

Maxime C. Cohen

Desautels Faculty of Management, McGill University

Alex Jacquillat

Massachusetts Institute of Technology (MIT)

Haotian Song

New York University (NYU) - Department of Information, Operations, and Management Sciences

Date Written: November 17, 2020

Abstract

This paper compares uniform vs. discriminative pricing strategies in a competitive setting featuring capacity restrictions, quality differentiation, and customer heterogeneity. It tackles this overarching question through operational lenses, by studying the joint impact of price discrimination and the allocation of limited inventory across customer segments. Thanks to advances in information technology, firms have developed new capabilities in terms of customer segmentation (by clustering customers into different segments) and price discrimination (by offering different prices to different customer segments). Price discrimination, although seemingly beneficial, can hurt firms in competitive environments. It is thus critical for firms to understand when to engage in price discrimination, and how to support discriminative pricing practices with appropriate inventory management strategies. We develop a Bertrand competition game featuring capacity restrictions, quality differentiation, and customer heterogeneity. We characterize (pure- or mixed-strategy) Nash equilibria for a single-stage game reflecting uniform pricing and for a two-stage inventory-price game reflecting discriminative pricing. We identify three sources of market friction in price competition, enabling firms to earn higher profits: capacity limitations, quality differentiation, and customer heterogeneity. Price discrimination eliminates the market frictions from customer heterogeneity, but strategic inventory allocation restores (or strengthens) the market frictions from capacity limitations. Ultimately, price discrimination is only beneficial when combined with optimal inventory allocation, thus underscoring the critical role of inventory allocation in the design of competitive pricing strategies.

Keywords: Bertrand competition, customer heterogeneity, price discrimination, inventory allocation

Suggested Citation

Cohen, Maxime C. and Jacquillat, Alexandre and Song, Haotian, Price Discrimination and Inventory Allocation in Bertrand Competition (November 17, 2020). Available at SSRN: https://ssrn.com/abstract=3732463 or http://dx.doi.org/10.2139/ssrn.3732463

Maxime C. Cohen (Contact Author)

Desautels Faculty of Management, McGill University ( email )

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

Alexandre Jacquillat

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Haotian Song

New York University (NYU) - Department of Information, Operations, and Management Sciences ( email )

44 West Fourth Street
New York, NY 10012
United States

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