Market Segmentation through Information

This paper asks what market outcomes an information designer — modeled as an internet platform that knows consumers’ preferences — can achieve by choosing what information to disclose to competing oligopolistic firms who then make personalized price offers. The model features n firms each producing a single differentiated product at zero cost, a continuum of consumers with unit demand and multidimensional valuations (one per product), and a designer who commits to a mapping from consumer types to joint distributions over messages sent to firms before they play a simultaneous pricing game. The designer’s objective spans the full range from maximizing producer surplus to maximizing consumer surplus.

The paper establishes two main results. First, under a necessary and sufficient condition called Aggregate Incentive Compatibility (AIC), the designer can implement full surplus extraction by firms — the producer-optimal outcome — in which every consumer buys her most preferred product at a price exactly equal to her valuation for it, capturing 100% of available surplus for producers. The AIC condition requires, for each firm i and each candidate deviation price p_hat_i, that the infra-marginal losses firm i would bear on its natural customers (those in Ei who value i most) from lowering price to p_hat_i must be weakly greater than the maximum business-stealing profit available from consumers who prefer other products but have valuation for i above p_hat_i. The condition is easier to satisfy when consumer preferences are more polarized, i.e., when consumers have stronger relative preferences for their most-preferred product. When firms offer homogeneous products the condition fails everywhere and no information structure can generate any producer surplus — Bertrand competition drives all profits to zero under any signal structure.

Second, the paper characterizes the consumer-optimal information structure, which achieves the maximum possible consumer surplus across all equilibria induced by any information structure. The upper bound on consumer surplus is CS* = (total surplus) minus sum_i Pi*_i, where Pi*_i is the profit firm i can guarantee itself by ignoring the designer’s signal and setting the best uniform price assuming all rivals price at zero. This bound is tight: the designer can implement it by publicly partitioning consumers into groups by most-preferred product, inducing rival firms to price at marginal cost (zero) for consumers who prefer another firm’s product, and then applying the Bergemann-Brooks-Morris (2015) extremal segmentation within each firm’s natural customer set to preserve each firm’s guarantee profit while achieving efficiency.

The illustrative two-firm example shows the quantitative stakes concretely. With no information disclosure, firms charge 4/5 and total producer surplus is about 76% of total surplus S*, consumer surplus is just under 10% of S*, and some consumers are excluded. With full disclosure, producer surplus rises to about 81% of S* and consumer surplus to 19%. The producer-optimal information structure (Case 3) achieves 100% of S* as producer surplus by pooling consumers who prefer different products into the same message submarket, giving each firm an incentive to price for its highest-valuing customers and ignore the others. The consumer-optimal information structure (Case 4) brings producer surplus down to about 57% of S* — its guaranteed lower bound — and delivers roughly 43% of S* to consumers, an outcome unattainable by full disclosure alone.

Both producer-optimal and consumer-optimal outcomes are efficient: all consumers buy their most-preferred product in both cases. The paper further characterizes the full efficient frontier between consumer- and producer-optimal outcomes, showing that mixing the consumer-optimal and full-information structures (or consumer-optimal, full-information, and producer-optimal structures when the latter is implementable) spans every point on the frontier.

The model assumes firms will price-discriminate if they can, that the designer has full knowledge of consumer types, and that the game is played once. The core results extend to continuous type distributions as shown in Online Appendix B.2. The analysis is restricted to a monopoly platform; competition among platforms is left for future work.

Q: What is the central research question and why does the two-benchmark comparison used by antitrust authorities miss important possibilities?

A: The paper asks what market outcomes — combinations of consumer and producer surplus — an information designer (a platform) can achieve by choosing among all possible information structures, not just the two benchmarks of no-information and full-information. Antitrust analysis that compares only those two cases misses a vast middle ground: an intermediary can package information in ways that, for instance, implement perfect collusion (extracting all surplus as producer surplus) while appearing to use privacy-protective technologies, or can intensify competition well beyond the full-information benchmark to benefit consumers.

Q: What is the producer-optimal information structure and when does it exist?

A: A producer-optimal information structure is one that induces an equilibrium in which every consumer buys her most-preferred product at a price exactly equal to her valuation — full surplus extraction. It exists if and only if, for every firm i and every candidate deviation price p_hat_i, the Aggregate Incentive Compatibility (AIC) condition holds: the aggregate infra-marginal losses firm i would suffer on its natural customers Ei from lowering price to p_hat_i must be at least as large as the maximum business-stealing profit from consumers outside Ei who have valuation for i weakly above p_hat_i. This is a condition on the distribution of consumer valuations, not on the information structure per se.

Q: What is the economic mechanism behind the producer-optimal structure — how does pooling consumers implement full surplus extraction?

A: The designer assigns consumers who prefer product A to the same message submarket as consumers who prefer another product but have a lower valuation for A. Firm A is then price-recommended its highest-valuing customers’ willingness to pay. The presence of the “outside” consumers in the same message makes it unprofitable for firm A to deviate downward to capture them, because the infra-marginal loss on the natural customers exceeds the additional revenue. Simultaneously, the rival firm cannot identify and undercut for A’s natural customers because the messages do not allow it to distinguish them. The result is that each firm plays a niche strategy, setting price equal to the valuation of its highest-type natural customers and excluding the others from its offer.

Q: When does polarization of consumer preferences help achieve the producer-optimal outcome?

A: Proposition 1 states that if a producer-optimal information structure exists under distribution f, it also exists under any distribution f_tilde that is more polarized than f — where more polarized means the mass of consumers who prefer i and have valuation above any threshold for i increases, and the mass of consumers who prefer j but have valuation above that threshold for i decreases. Intuitively, polarization slackens the Firm IC constraints because it reduces the business-stealing temptation: fewer consumers with high cross-product valuations are available for firm i to capture by undercutting. Concrete continuous-distribution examples include: uniform over the unit square (producer-optimal always exists), Hotelling anti-correlated values (exists everywhere), and truncated normal with mean 1/2 — producer-optimal is feasible for all standard deviations sigma > 0.15.

Q: Why does the producer-optimal outcome fail entirely when products are homogeneous?

A: Proposition 2 states that when all consumer types have equal valuations across products (the support of f lies on the diagonal of V^n), then for any information structure and any induced equilibrium, every consumer buys at price zero and all firms earn zero profit. The logic extends the standard Bertrand undercutting argument: with homogeneous products, any positive price a firm charges is undercut by a rival who can always profitably steal demand, and this applies to any posterior distribution induced by any signal realization. Even private signals cannot prevent this outcome because no signal realization can give a firm a non-contestable position.

Q: How is the consumer-optimal information structure constructed, and what is its key economic logic?

A: Theorem 2 shows the consumer-optimal structure has three layers. First, consumers are partitioned into n groups by most-preferred product (Ei). Second, firms j not equal to i are induced — by publicly revealing which group a consumer belongs to — to set price zero for consumers outside their group, because competing for those consumers is hopeless when their preferred firm is identified. Third, within each Ei, consumers are further partitioned into submarkets using the Bergemann-Brooks-Morris (2015) extremal segmentation applied to residual valuations (theta_i minus the maximum of competing valuations), ensuring firm i earns exactly its guarantee profit Pi*_i. By holding each firm down to its guarantee profit, the residual goes to consumers, maximizing CS.

Q: What is the guarantee profit Pi*_i and how does it bound consumer surplus?

A: Pi*i is the maximum profit firm i can achieve by ignoring all designer signals and setting a single uniform price to all consumers, against the worst-case scenario in which all other firms price at zero. Formally, Pi*i = max{pi} sum{theta in Ei: theta_i - pi >= max_{j not equal i} theta_j} pi * f(theta). Since firm i can always achieve Pi*_i regardless of the information structure (by simply ignoring signals), no information structure can push firm i’s profit below Pi*_i. The sum of these guarantee profits across all firms provides a lower bound on total producer surplus — and therefore an upper bound on consumer surplus — achievable by any information structure.

Q: In the two-firm numerical example, what is the quantitative comparison across the four cases?

A: Total available surplus S* = 0.84. Under no information (Case 1): producer surplus approximately 76% of S*, consumer surplus just under 10% of S*, and consumers of types (3/5, 2/5) and (2/5, 3/5) do not trade. Under full disclosure (Case 2): producer surplus approximately 81% of S*, consumer surplus 19% of S*, efficient. Under the producer-optimal structure (Case 3): producer surplus = 100% of S* (all surplus extracted), consumer surplus = 0%, efficient. Under the consumer-optimal structure (Case 4): producer surplus approximately 57% of S*, consumer surplus approximately 43% of S*, efficient. All cases except Case 1 are efficient; the no-information case excludes some consumers from trading.

Q: Is the full-information disclosure structure consumer-optimal?

A: Not in general. Proposition 3 states that full information is consumer-optimal if and only if all consumers in Ei have identical residual valuations (theta_i minus their second-best alternative) — a condition that generically fails. When residual valuations within Ei are heterogeneous, the designer can do strictly better for consumers by applying the extremal segmentation within each Ei rather than revealing full information, which would allow firms to price-discriminate on individual residual valuations and extract more surplus.

Q: Can the designer trace out the entire efficient frontier between consumer- and producer-optimal outcomes?

A: Yes, under two conditions. First, by mixing the consumer-optimal structure (point A) with the full-information structure (point B) using fractions lambda and 1-lambda respectively, the designer can implement any point on the efficient frontier between A and B. Second, when the producer-optimal outcome (point C) is also implementable, mixing the full-information structure with the producer-optimal structure by applying them to fractions lambda and 1-lambda of the consumer population respectively spans every point between B and C. The key insight is that the AIC condition, if it holds for f, also holds for any rescaled sub-distribution of f (it is scale-invariant), so the producer-optimal sub-problem remains feasible.

Q: What are the regulatory implications of the analysis?

A: The paper identifies a fundamental tension: banning information use sacrifices efficiency (some consumers excluded, wrong products purchased), but unrestricted use permits platforms to implement perfect collusion through information design. Critically, the paper shows that privacy-enhancing technologies that pool consumers into cohorts — like Google’s Privacy Sandbox — are equally consistent with the producer-optimal (collusive) and consumer-optimal (competitive) structures; the two differ only in the principle by which consumers are grouped. The paper suggests regulators could mandate that consumers in the same cohort share the same most-preferred product and that information be disclosed symmetrically across firms — the defining features of the consumer-optimal structure. This would block the producer-optimal grouping (which mixes consumers with different most-preferred products) while preserving efficiency.

Q: How does this paper relate to and extend Bergemann, Brooks, and Morris (2015)?

A: Bergemann, Brooks, and Morris (2015) characterize achievable consumer and producer surplus outcomes when a designer discloses information to a single monopolist who can price-discriminate. The present paper extends this to oligopoly, where competition between firms creates both additional constraints (firms may undercut each other) and additional instruments (the designer can play firms against each other). The consumer-optimal construction directly applies the BBM (2015) extremal segmentation within each firm’s natural customer set Ei, but the outer layer — using public revelation of group membership to induce rival firms to price at zero — is new and arises specifically from the oligopoly setting.

Information designer: An entity (modeled as a platform) that observes the full joint distribution of consumer valuations over all products and commits, before firms price, to a mapping from consumer types to joint distributions over messages sent to competing firms; the designer can be interpreted as an internet intermediary choosing how to package and share consumer data.

Aggregate Incentive Compatibility (AIC): The necessary and sufficient condition on the distribution of consumer valuations for the existence of a producer-optimal information structure; for each firm i and each candidate deviation price p_hat_i, the aggregate infra-marginal losses firm i would incur on its natural customers by lowering price to p_hat_i must weakly exceed the maximum revenue firm i could gain by attracting consumers who prefer rival products but have valuation for i above p_hat_i.

Producer-optimal information structure: An information structure that induces an equilibrium in which every consumer buys her most-preferred product at a price exactly equal to her full valuation for it, extracting 100% of available surplus as producer surplus — the outcome equivalent to the firms’ fully collusive joint surplus maximum.

Consumer-optimal information structure: An information structure that achieves the maximum consumer surplus attainable across all equilibria induced by any information structure, holding each firm to its guarantee profit Pi*_i (the best uniform-price profit the firm can secure by ignoring all signals) and allocating all residual surplus to consumers while maintaining allocative efficiency.

Guarantee profit (Pi*i): The maximum profit firm i can secure unilaterally by ignoring the designer’s signal and setting an optimal uniform price, computed against the worst case in which all rival firms price at zero; it equals max{pi} times the sum of f(theta) over all types in Ei for which theta_i minus pi exceeds all rival valuations.

Polarization of preferences: A stochastic dominance condition under which, relative to a baseline distribution, the mass of consumers who prefer product i and have high valuations for it increases while the mass of consumers who prefer rival products but have high valuations for i decreases; higher polarization weakens the Firm IC constraints and makes the producer-optimal outcome easier to implement (Proposition 1).

Separation and Consistency: Two structural properties any producer-optimal information structure must satisfy: Separation requires that the messages firm i sends to different consumers in Ei who have distinct valuations for i are disjoint in support; Consistency requires that every message firm i can send to any consumer type is contained in the union of messages firm i sends to consumers in Ei, preventing firm i from ever inferring that a consumer prefers a rival’s product.