Personalized Pricing and Competition

The paper examines the welfare impact of personalized pricing enabled by advances in data and AI. Policymakers worry such pricing extracts surplus from consumers. The authors analyze the limit case of perfect (first-degree) discrimination in a general oligopoly framework to reconcile opposing benchmark results: under monopoly, perfect discrimination benefits the firm and harms consumers; under Hotelling duopoly with full coverage, it lowers prices paid by all consumers, harming firms but benefiting consumers. The study asks how market characteristics—costs, number of firms (competition), market coverage, endogenous entry, and asymmetric access to consumer data—shape the welfare effects of personalized pricing. It previews that short-run impacts hinge on coverage, while in the long run, personalized pricing induces socially optimal entry and benefits consumers. It also highlights asymmetric-information environments where only some firms can personalize, which can be particularly detrimental to consumers.

The work builds on classic price discrimination and spatial pricing literatures. Thisse and Vives (1988) show in a Hotelling duopoly with full market coverage that discriminatory pricing is dominant and reduces all consumers’ prices (a Prisoner’s dilemma for firms). Subsequent papers use this benchmark to study branding advantages, advertising, data intermediaries, and consumer identity management. The authors show this pro-consumer result need not hold once partial market coverage is allowed. They relate closely to Anderson, Baik, and Larson (2021), who also use a discrete-choice framework but assume full coverage and costly targeting (yielding mixed strategies and potential misallocation). The paper also discusses empirical evidence of personalized pricing and algorithmic differentiation, and connects to competitive third-degree discrimination and auction theory strands for partial information cases.

The authors develop a general discrete-choice oligopoly model with n single-product firms, constant marginal cost c, and a unit mass of consumers who buy at most one product or take an outside option (normalized to zero). Consumers’ product valuation vector v = (v1,...,vn) follows an exchangeable joint distribution, allowing arbitrary dependence (with IID as a special case). Two pricing regimes are analyzed: (1) uniform pricing (same price to all consumers), and (2) personalized pricing with full information (firms observe each consumer’s entire valuation vector and set individualized prices). Key objects include order statistics of valuations and the distribution of the margin between a consumer’s top valuation and the best alternative, used to derive equilibrium prices and profits. Existence and uniqueness of uniform-price equilibria rely on log-concavity and related regularity (Assumption 1). The short-run compares welfare across regimes with a fixed number of firms, distinguishing full vs partial market coverage. The long-run introduces a free-entry game with fixed entry costs and Assumption 2 (entry does not change valuations for existing products), enabling a comparison between private entry incentives and social surplus increments. Additional analyses cover: (i) asymmetric information where k firms can personalize (using a two-stage timing: uniform-pricing firms set prices first, then data-rich firms set personalized prices); (ii) partial discrimination where each firm observes only its own valuation (mapped to a first-price auction analogue); and (iii) constrained personalized pricing via list prices and capped personalized discounts ∆, bridging uniform (∆=0) and fully flexible personalized pricing.

- Short-run, full coverage: Under log-concavity (Assumption 1), personalized pricing reduces industry profit and increases aggregate consumer surplus for any n ≥ 2 (generalizing Thisse and Vives, 1988). Although some personalized prices can exceed the uniform price (for strong-preference consumers), on average consumers gain and firms lose (Proposition 1). - Short-run, partial coverage: Personalized pricing can increase industry profit and reduce consumer surplus, reversing the full-coverage result (Proposition 2). Intuition: personalized pricing brings in low-valuation consumers (small surplus gains) while extracting more from infra-marginal consumers who value a specific product highly; with sufficiently high marginal costs, firms face local monopoly segments and extract more surplus. In the IID exponential example, whenever uniform pricing does not fully cover the market, personalized pricing raises profit and reduces consumer surplus. Numerical results for Extreme value (logit), Normal (probit), and Uniform distributions show cutoff patterns in c: low c (high coverage) reproduces Thisse-Vives-type outcomes (firms worse, consumers better); high c (low coverage) yields firm gains and consumer losses; intermediate c can raise both profit and consumer surplus (expanding the market). - Effect of the number of firms: With many firms (IID, tail index conditions), personalized pricing again harms firms and benefits consumers (Proposition 3). With few firms, effects resemble monopoly; with many, they resemble the full-coverage competitive case. - Long-run with free entry: Under Assumption 2, personalized pricing aligns private entry incentives with social surplus improvements; the free-entry equilibrium is unique and socially optimal (Lemma 3). Consequently, relative to uniform pricing, personalized pricing benefits consumers in the long run (Proposition 4), as firms break even after entry costs while total surplus is maximized. - Asymmetric access to data (mixed regime): When some firms personalize and others set uniform prices, consumer surplus can be lower than in either all-uniform or all-personalized regimes, especially when coverage is high. Data-rich firms can poach via targeted discounts, creating match inefficiency and potentially lower total welfare; when costs are high (local monopolies), the fully discriminatory regime is worst for consumers (Section 5). - Correlation in valuations: Higher positive correlation diminishes differentiation and competition; as correlation increases, the profit difference between regimes shrinks, and in the limit of perfect correlation both regimes converge to marginal-cost pricing (Section 6.1). - Partial discrimination (own-valuation only): With IID valuations, partial and full discrimination yield the same total welfare, profit, and consumer surplus (revenue equivalence via auction analogy). With positive affiliation, firms earn more (consumers less) under partial discrimination; with negative affiliation, the opposite (Proposition 5). - Constrained personalization (capped discounts ∆): Results hinge on coverage. In covered markets, increasing ∆ lowers profit and raises consumer surplus; in uncovered markets, allowing small ∆ increases profit and can reduce consumer surplus (Proposition 6). Overall, coverage and competition intensity determine whether personalized pricing is pro- or anti-competitive, and in the long run it improves consumer welfare by inducing efficient entry.

The findings reconcile opposing benchmark results by identifying market coverage and competition intensity as the key mediators of personalized pricing’s welfare effects. In highly competitive or low-cost environments (high coverage), personalized pricing intensifies price competition across consumers, lowering average payments and benefiting consumers at firms’ expense. In less competitive or high-cost environments (low coverage), personalized pricing amplifies market power over local monopoly segments, raising prices for infra-marginal consumers and reducing consumer surplus while boosting profit. Endogenizing market structure reveals that personalized pricing aligns private entry incentives with social welfare, so consumers gain in the long run even if short-run effects may be adverse. In mixed-information markets, targeted poaching by data-rich firms can reduce match efficiency and harm consumers relative to symmetric regimes, highlighting policy relevance for data-sharing or restrictions on personalization. Extensions to correlated valuations, partial information, and capped discounts show the robustness of the coverage-based logic while indicating when information structure or constraints modulate outcomes.

The paper shows: (i) with full coverage, competitive personalized pricing is pro-consumer and anti-profit under broad conditions; (ii) without full coverage, effects can reverse—personalization may increase profit and reduce consumer surplus, with cutoff patterns in costs and number of firms; and (iii) with endogenous entry, personalized pricing induces socially optimal market structure and benefits consumers in the long run. Asymmetric access to data can be particularly harmful to consumers when coverage is high. The results underscore that policy toward personalized pricing should be context-dependent: in competitive, high-coverage markets, bans may reduce consumer surplus, whereas in concentrated, low-coverage markets, limits on personalization or mandated data sharing may improve outcomes. Future research directions noted by the authors include modeling consumers’ privacy choices and data-sharing incentives, exploring richer information structures and design, and analyzing settings where entry repositions incumbent products (violating Assumption 2).

- The uniform-price equilibrium and several results rely on log-concavity and related regularity (Assumptions 1 and 4) and on exchangeability/symmetry; some conclusions may not hold with non-log-concave densities or strong asymmetries. - The long-run optimal entry result (Lemma 3) requires Assumption 2 (entry does not alter valuations over existing products). It fails in models with endogenous repositioning (e.g., Salop circle), where entry can be excessive under perfect discrimination. - Personalized pricing assumes complete information about each consumer’s valuation vector; real-world data are noisy and constrained, though the paper studies partial information and constrained discounts as robustness checks. - The mixed regime uses a specific timing to ensure equilibrium existence (uniform pricers move first); simultaneous-move equilibria can be mixed and complex. - Some results depend on IID assumptions (e.g., revenue equivalence under partial discrimination), and comparative statics with correlation use specific examples. - Several insights (e.g., coverage cutoffs) are supported by numerical simulations rather than general proofs. - The analysis abstracts from dynamic learning, fairness/regulatory constraints, behavioral biases, and potential consumer backlash beyond the simple discount-cap extension.