Personalized Pricing and Competition

The increasing ability of firms to utilize consumer data and AI to implement personalized pricing, offering different prices to individual consumers based on their preferences, necessitates a comprehensive welfare impact assessment. This practice, documented across various industries, raises concerns regarding the potential transfer of value from consumers to shareholders. This paper addresses these concerns through a general oligopoly model focused on the limit case of perfect price discrimination—a scenario increasingly feasible with advancements in data access and AI. The authors posit that the welfare impact of personalized pricing is contingent on several factors: market characteristics (cost conditions and competition, impacting market coverage); the endogeneity of market structure; and asymmetries in firms' data access. The paper aims to reconcile the contrasting impacts of personalized pricing observed in existing literature, notably the pro-consumer effects in duopoly settings versus the anti-consumer effects in monopoly scenarios.

The paper begins by reviewing two established benchmarks: the monopoly case, where personalized pricing allows for the complete extraction of social surplus, benefiting the firm but harming consumers; and the Hotelling duopoly, where Thisse and Vives (1988) demonstrate that personalized pricing reduces prices for all consumers due to intensified competition for customers at the edges of each firm's market. This latter model serves as a cornerstone for subsequent studies on data privacy and data brokers. The authors' first contribution is to reconcile these contrasting findings by introducing a more general discrete-choice model which includes both monopoly and Hotelling duopoly as special cases. This model, extending Perloff and Salop (1985), incorporates an arbitrary number of firms, correlated product valuations, and the possibility of partial market coverage. The paper further relates to the literature on competitive third-degree price discrimination, while noting that the existing methodologies aren't directly applicable to their analysis. A key distinction is made between the authors' model, which assumes freely offered personalized prices leading to a pure-strategy pricing equilibrium, and Anderson, Baik, and Larson (2021), where costly targeted discounts lead to a mixed-strategy equilibrium. This distinction highlights the role of fixed costs associated with data acquisition and AI development.

The authors develop a discrete-choice model with n firms, each producing a single product at constant marginal cost c. Consumers have heterogeneous valuations for the products, represented by a vector v drawn from an exchangeable joint distribution F(v). Consumers choose to buy at most one product or opt for an outside option with zero surplus. Two pricing regimes are analyzed: uniform pricing, where firms offer the same price to all consumers, and personalized pricing, where firms offer tailored prices based on individual consumer valuations. The model uses a Perloff and Salop (1985) framework but extends it by allowing for correlated valuations and partial market coverage. For uniform pricing, a symmetric pure-strategy Nash equilibrium is derived under Assumption 1 (a log-concavity condition ensuring the uniqueness of the equilibrium). The equilibrium price p is determined by the first-order condition, reflecting the trade-off between profit margin and demand sensitivity. For personalized pricing, the equilibrium involves asymmetric Bertrand competition where each firm undercuts its rivals, resulting in prices slightly above marginal cost. Industry profit and aggregate consumer surplus are calculated under both regimes, considering cases with full and partial market coverage. The analysis extends to a long-run free-entry game where firms decide whether to enter the market and then compete in prices. This extension allows for the evaluation of market structure's endogeneity under personalized and uniform pricing regimes. The authors also investigate the effects of asymmetric information structures where some firms have access to consumer data while others do not, modeling this as a two-stage game where uninformed firms price first.

The paper's key findings challenge the conventional wisdom that competitive personalized pricing always benefits consumers. Under a mild regularity condition, some personalized prices exceed the uniform price, indicating a heterogeneous impact on consumers. When the market is fully covered under uniform pricing, personalized pricing lowers industry profit and increases aggregate consumer surplus (generalizing the Thisse and Vives (1988) result). However, if the market isn't fully covered, this result can be reversed: competitive personalized pricing can increase industry profit and decrease consumer surplus, mirroring the monopoly case. The intuition lies in the interplay between market expansion and the impact on average prices paid by consumers. High marginal costs lead to low market coverage, generating a situation similar to a monopoly with distinct segments. With partial coverage, the expansion of the market through personalized pricing primarily benefits low-valuation consumers whose surplus gain is limited. Conversely, high-valuation consumers, who often have strong preferences for one product, may end up paying higher prices. The long-run analysis, incorporating free entry, demonstrates that personalized pricing always leads to the socially optimal level of firm entry under certain conditions, guaranteeing consumer benefits relative to uniform pricing. Finally, the analysis of asymmetric information reveals that the mixed case (some firms personalize, others do not) can be worse for consumers than either full personalization or uniform pricing, mainly because the discriminatory firm can poach consumers from their second choice, introducing match inefficiency.

The paper's findings directly address the concerns surrounding the welfare impact of personalized pricing. By demonstrating that the impact of personalized pricing depends critically on market coverage, it highlights the importance of considering market characteristics and competition levels in policy evaluations. The reversal of the pro-consumer effect under partial market coverage, a frequent scenario in reality, significantly alters our understanding of the competitive dynamics and welfare implications of personalized pricing. The long-run analysis, showing the socially optimal entry level under personalized pricing, provides strong support for the consumer-beneficial outcome. The results concerning asymmetric information structures offer policy insights: interventions forcing data sharing or restricting personalization might be welfare enhancing, particularly in competitive markets. The findings provide a nuanced perspective on the debate surrounding the use of consumer data, demonstrating the complex interplay between competition, information asymmetry, and welfare.

This paper makes substantial contributions to the understanding of personalized pricing. It shows the impact hinges on market coverage, challenging the common assumption that personalized pricing always benefits consumers. The long-run analysis highlights the efficiency-enhancing effect of personalized pricing due to optimal market entry. The study of asymmetric information provides valuable policy implications concerning data sharing and price discrimination restrictions. Future research could explore further the dynamics of data sharing and privacy choices, analyzing the interactions between competition, information, and consumer welfare.

The model assumes perfect price discrimination and perfect consumer information. In reality, firms may not have perfect information about consumer preferences, and consumers may not be perfectly aware of their own preferences. The model's assumption of risk neutrality could be relaxed to consider risk-averse consumers and firms. The paper focuses primarily on the aggregate consumer surplus, but future research could focus on analyzing the distributional effects of personalized pricing. The analysis assumes a sequential entry game to avoid coordination problems, and ignores integer constraints on the number of firms.