Price Discrimination and Inventory Allocation in Bertrand Competition

Abstract

It is common practice for firms to deploy strategies based on 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 discriminatory pricing practices with appropriate inventory management strategies. This paper tackles this overarching question through operational lenses, by studying the joint impact of price discrimination and the allocation of limited inventory across customer segments. 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 discriminatory pricing along with endogenous inventory allocation. 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. As such, price discrimination is only beneficial when combined with optimal inventory allocation across segments. We discuss relevant real-world examples featuring regional price discrimination along with strategic inventory allocation, including fast fashion and vaccines. Otherwise, uniform pricing may outperform discriminatory pricing. Our results thus underscore the critical role of inventory allocation in the design of competitive pricing strategies.

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