How do seller subsidies sort quality in search markets?

A formal model of "directed search" ("Subsidizing Sequential Search," arXiv 2605.28985) studies "markets where firms compete for consumer attention by subsidizing costly product inspection." A firm can pay a consumer a subsidy toward her cost of inspecting its product; the subsidy does not change product quality but lowers her net cost of looking. The paper's central result is a "subsidy–sorting principle: in any equilibrium, higher–quality firms provide weakly larger subsidies, leading consumers to search in descending subsidy order." Applying a forward-induction refinement "in the spirit of the Intuitive Criterion," a unique equilibrium survives: "low–quality firms are never inspected, intermediate–quality firms separate with strictly increasing subsidies, and high–quality firms pool at the full subsidy." The paper states this equilibrium "maximizes information revelation among all possible outcomes and ensures efficient inspection."

Mechanically, each firm privately knows its own type — the probability its product matches the consumer's needs — and simultaneously picks a subsidy in [0, c], where c is the shared cost of inspecting a listing. A subsidy costs the firm a per-unit price and pays off only if inspection leads to a match, so, in the paper's words, "only firms confident in high match value find it worthwhile to subsidize": the subsidy is at once an instrumental discount (it lowers the consumer's net inspection cost) and a costly signal of quality. The consumer observes the full subsidy profile, updates her beliefs, and chooses an inspection order trading off lower net cost against inferred quality. The surviving equilibrium has a three-part shape — a lower cutoff below which no subsidy buys inspection, a separating middle band where the subsidy schedule strictly increases with type, and an upper pooling band where every firm above a cutoff offers the same full subsidy.

The paper frames this as reaching the efficient sorting of the sponsored-search and position-auction literature (citing Edelman et al. 2007 and Athey and Ellison 2011) "without auctions or slot constraints," calling the mechanism "simpler and more direct," though it notes subsidy caps, unlike auction bids, "create pooling at the top, generating excessive search." This sits alongside the formal agentic-commerce models in Why does manual search fail as product choices become complex? and Why do consumers delay adopting agentic search?: those models locate the binding scarcity in a consumer's effort to articulate preferences to an agent, while this one locates it in what sellers are willing to pay just to be inspected at all — a complementary account of how attention gets allocated before any ranking, human or AI, even happens. It is the direct predecessor to Does platform pricing of inspection tokens encourage excess search? (same paper), which prices this baseline mechanism through a profit-seeking platform.

The result is an equilibrium of a stylized Perfect Bayesian game — one inspection cost shared by all firms, subsidies capped at that cost, and a single consumer choosing a sequential order — not a measurement of any live marketplace; the paper's comparative statics (inspection intensity, match probability, and consumer surplus all falling as the per-unit subsidy price or inspection cost rises, and rising with the number of competing firms) are theorems about the model, not observed figures, and the paper offers no empirical test of where real subsidies — travel reimbursements, test-drive cash, promotional receptions — actually fall on the predicted schedule. The implication the model supports, at that strength, is that any mechanism, human-curated or AI-mediated, that lets sellers pay toward a buyer's cost of looking should be expected to separate sellers into roughly this three-band pattern by quality, and that capping how much a seller can subsidize will tend to bunch the best sellers together rather than let them fully distinguish themselves.