Behavior‐based price discrimination with nonuniform distribution of consumer preferences

Abstract

Firms commonly price discriminate across consumers based on purchase history, a practice known as behavior-based price discrimination (BBPD). Existing studies usually assume that consumer preferences follow uniform distribution, and find that BBPD benefits consumers at the cost of firms, prisoners' dilemma. In this paper, we consider a class of consumer preferences distribution and show that new profit and welfare results arise. In particular, when consumer preferences are sufficiently clustered at the center of the market (e.g. triangular distribution), BBPD boosts industry profits at the expense of consumers. This is opposite to the standard prisoners' dilemma results under uniform distribution. On the other hand, when consumer preferences are not clustered at the center of the market, the usual findings prevail. Our results highlight the important role of the shape of preferences and provide useful implications for relevant players including managers, regulators and consumer advocates. * We thank Ramon Casadesus-Masanell (the editor), a co-editor and two anonymous referees whose comments and suggestions helped us improve this paper significantly. We are grateful to Luis Cabral for inspiring us to model a class of non-uniform distribution, and to participants at the China Meeting of the Econometric Society (Chengdu, 2016) and the International Workshop on Innovation and Industrial Economics (Nanjing University, China, 2016) for helpful comments and suggestions. This research has been financed by Portuguese public funds through FCT (Fundação para a Ciência e a Tecnologia) within the projects PTDC/IIM-ECO/2280/2014 and PTDC/EGE-ECO/28540/2017. Any errors are our own responsibility.

Can personalized pricing be a winning strategy in oligopolistic markets with heterogeneous demand customers? Yes, it can

“…Esteves, 2009b) 3 or imperfect targetability (Chen et al, 2001). 4 In dynamic settings, pro…ts may increase with BBPD due to imperfect correlated preferences across time (Chen andPearcy, 2010, andShin andSudhir, 2010), consumers'demand heterogeneity (Shin and Sudhir, 2010), heterogeneity in price sensitivity (Colombo, 2018), nonuniform distribution of consumer preferences (Esteves et al, 2020), imperfect informed consumers (Chen and Zhang 2009, Esteves, 2009a, and Esteves and Resende, 2016.…”

How does cross‐platform externality impact pricing strategies? A two‐stage discriminatory pricing model analysis

“…However, when both manufacturers and retailers employ BBP, it results in an increase in profits for channel members and a decrease in consumer surplus. Esteves et al (2022) assessed whether price discrimination based on purchasing history benefit/harm industry profits and consumers in markets where the density of consumer preferences is nonuniform; they showed that when consumers are sufficiently massed at the center of the market, BBPD boosts industry profits at the expense of consumers. Ma et al (2023) examined information disclosure strategies and BBPD strategies within horizontal competition channels.…”

Customer‐Based Customization and Price Competition*

“…Finally, we discuss the distribution of the consumers. As in Esteves et al [2022], we assume the following non-uniform distribution, with f (x) being the density function of the cumulative distribution function F(x) over the support x ∈ [0, 1]:…”

“…As in Esteves et al . [2022], we assume the following non‐uniform distribution, with f ( x ) being the density function of the cumulative distribution function F ( x ) over the support $$$ x\in \left[0,1\right] $$$: $$$$ f(x)=\left\{\begin{array}{cc}4\beta x+\left(1-\beta \right)& if\kern0.5em x\in \left[0,1/2\right]\\ {}4\beta \left(1-x\right)+\left(1-\beta \right)& if\kern0.5em x\in \left(1/2,1\right]\end{array}\right.. $$$$ Parameter $$$ \beta \in \left[-\underset{\_}{\beta },1\right] $$$, with $$$ \underset{\_}{\beta }=\left(3-\sqrt{5}\right)/2 $$$, is half the difference between the density of the endpoints of the market and the centre, that is $$$ \beta =\frac{f\left(1/2\right)-f(0)}{2}=\frac{f\left(1/2\right)-f(1)}{2} $$$. Note that the distribution is symmetric around …”

“…𝛽 ≥ −𝛽 is needed to ensure that the second-order conditions of the problem are satisfied (seeEsteves et al [2022].11 The proof of Proposition 1 inEsteves et al [2022] can be directly applied here and later in Section IV to show that, even if the demand has a kink at h = 1/2, the first-order condition still works at the symmetric equilibrium and the second-order conditions are also satisfied (seeEsteves et al [2022], pp. 22-23).…”