Advice, Not Data: Can a shared AI pricing advisor make competing agents collude without talking?

When competing AI agents share one advisor, its memory can carry one client's plans to the other. We test this hub-and-spoke route, the shape alleged against the rent-pricing software RealPage, with language-model agents: two LLM sellers in a logit duopoly never talk but take advice from one shared LLM pricing advisor, and seven pre-registered conditions vary only what the advisor sees and remembers (12 runs each on Qwen2.5-72B, Llama-3.1-70B and gpt-oss-120b). With one notebook shared across clients, Qwen's advice to a competitor revealed or relied on a price plan the other client had given in confidence in 18 of 24 trials, against 0 of 24 with private notebooks; a confidentiality rule or owner tags left 16 and 15 of 24. The leak was weak on Llama and not detectable on gpt-oss-120b. A planted random code never leaked on any model, so the usual canary test would have passed this advisor. Giving the advisor the rival's confidential data did not raise prices on any model, and replays show the Qwen advisor did not use it. Advice itself did: on Qwen and Llama, an advisor that kept each client's data apart raised prices above sellers without one (price index +0.29 and +0.44; exact p = 0.002 and 0.009); on gpt-oss-120b nothing did. We release an audit procedure and a tool that plant price plans instead.