Watched, Warned, or Neither: LLM Seller Agents under Oversight with a Side Channel

When LLM agents are told they are monitored, do they stop colluding, move collusion elsewhere, or stop only what the rules spell out? We extend the continuous double auction of Agrawal et al. (2025) with a second channel (order notes), varying what sellers are told about its monitoring, and an LLM overseer that gags sellers who collude in chat. Across 58 fifteen-hour markets with GPT-4.1, Claude Sonnet 5.5 and Gemini 3.1 Pro sellers, we find three behavioural profiles. Without any cue, all three models collude openly. A cue almost completely switches Claude off: it sends no messages under an oversight warning or a one-line legal reminder, and 3 messages in 3 games when told messages are merely recorded. GPT-4.1 keeps talking until punished, then obeys the gag's literal scope: if it names only chat, sellers keep writing price signals in the notes (about 78 characters versus 1.6 in chat). Gemini 3.1 Pro (preliminary, one game per condition) evades openly: told that notes are not reviewed, it runs an explicit cartel there, keeps the chat as a neutral cover and says so in its reasoning; under a 5-character gag it signals its price as a number and holds it in sync. A recording notice restrains neither GPT-4.1 nor Gemini. GPT-4.1's shift is almost invisible in its reasoning but clear when channels are compared. For oversight design: monitor every channel agents can use, phrase restrictions by effect rather than by channel, and do not tell agents which channel is unmonitored.