Generative AI is shifting digital commerce from browsing toward agentic search, in which consumers delegate product discovery to AI agents. We compare manual search, which accurately evaluates a limited product set, with agentic search, which screens a broad catalog through noisy representations of preferences and products. Preference complexity is the number of satisfaction-relevant dimensions that are difficult to articulate before search but readily evaluated upon inspection. Consumers have finite attention and choose search intensity: products inspected manually or preference-refinement depth with an agent. We obtain three findings. First, manual search collapses beyond a finite complexity threshold: inspection ceases, mismatch reaches the no-search benchmark, and platform revenue falls to zero. Agentic search avoids this collapse. Once refinement becomes worthwhile, it remains worthwhile as complexity rises; mismatch stays below the no-search benchmark and revenue remains positive, although articulation effort and mismatch may increase. Second, platforms rank the regimes by conversion revenue, whereas consumers also bear search expenditure. When manual inspection is sufficiently inexpensive, agentic search becomes revenue-superior before consumers voluntarily adopt it, creating an adoption lag in which consumers rationally continue manual search. Third, conditional on agentic participation, platforms may assign lower fidelity to consumers with larger attention budgets because they can offset noisier representations through additional refinement, yielding an inverted fidelity allocation. Agentic commerce thus shifts scarcity from product inspection to preference articulation, making consumers' willingness and ability to interact central to voluntary use and platform fidelity design.

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