Subsidizing Sequential Search

We study markets where firms compete for consumer attention by subsidizing costly product inspection. These subsidies do not change product quality, but they alter the order in which consumers search by lowering inspection costs. We establish a subsidy-sorting principle: in any equilibrium, higher-quality firms provide weakly larger subsidies, leading consumers to search in descending subsidy order. A unique equilibrium survives forward-induction reasoning in the spirit of the Intuitive Criterion: low-quality firms are never inspected, intermediate-quality firms separate with strictly increasing subsidies, and high-quality firms pool at the full subsidy. This equilibrium maximizes information revelation among all possible outcomes and ensures efficient inspection. We then extend the analysis to AI-mediated platforms that can create and price inspection tokens. The platform's optimal linear pricing leads to excessive inspection relative to the social optimum. While this distortion does not reduce consumer welfare, it reallocates surplus from sellers to the platform and consumers.