Can a seller infer what a buyer really wants to pay?

A controlled experiment in which a language-model buyer agent shops for wireless headphones on behalf of a described consumer finds that a seller-side inference agent reading only the dialogue transcript recovers the consumer's target willingness to pay (WTP) nearly one-for-one. Across six WTP levels ($50 to $500, N = 60 trials per cell), the OLS slope of inferred WTP on target WTP is 1.00 (bootstrap 95% CI [0.96, 1.05]) with Spearman rank correlation 1.00, when the buyer agent is given only a verbal consumer profile ("I'm a graduate student... and I'd rather not spend too much") with no dollar figure anywhere in the prompt. A contrasting numeric condition, where the agent instead receives a literal budget figure under an explicit instruction to keep it confidential, produces a slope of only 0.21 (CI [0.17, 0.26]) — the two intervals do not overlap.

The paper names this mechanism role coherence: when a model is asked to inhabit a consumer character grounded in occupation, life stage, and stated preferences, it generates questions, feature priorities, and price reactions that are coherent with that character — "asking about audiophile features is appropriate for the audiophile profile and inappropriate for the graduate-student profile" — not because of an external reward signal but because the agent is producing behavior consistent with the persona it was given. The authors show this signal is behavioral rather than a demographic-labeling artifact: stripping all financial vocabulary from the profile only drops the slope to 0.85, and stripping all identity cues from the transcript while preserving the shopping behavior itself leaves the slope at 0.93. A factorial replication across profile variants and prompt scaffolds returns a design-aware bootstrap CI of [0.93, 1.09] around the same slope of 1.00. The paper's framing is explicit that this is not an instruction-following failure or a guardrail bypass: "there is no number the consumer asked the agent to conceal... the information that reaches the seller is the information the consumer asked the agent to express."

This gives a concrete, measured mechanism for the privacy leg of the dynamic described in Does chatbot personalization build trust or expose privacy risks?: that note frames rising privacy concern as a byproduct of how much a model comes to know about a user, while this experiment shows the exposure can run the other direction too — the model's expression of what it already knows, filtered through its own role-consistent behavior, is itself legible to a third party (the seller) who was never granted access to the user's profile. It also sits alongside Does personalization make large language models worse at their jobs? as a second cost of giving a model rich personal context: that note documents degraded response quality from personalization, and this paper documents an economic cost — the same persona that lets an agent shop well is the substrate a counterparty can price against.

The experiment is a simulated two-agent dialogue over wireless headphones with six discrete WTP levels described in the excerpt; it does not establish how the slope would look with different product categories, real human sellers, longer negotiations, or production shopping agents operating under platform-level constraints. The excerpt also does not specify which model(s) played buyer and seller, limiting any claim about whether role coherence is a general LLM property or particular to the models tested. Within that scope, the finding supports a narrower but still consequential claim: for AI-mediated shopping as currently architected, giving an agent enough context to personalize is close to sufficient for a seller-side agent to re-derive the number the consumer never stated.