Cheating Is Not Collusion: Says-vs-Does Monitors and a Matched Control for LLM Collusion Detection

Monitors usually see what agents say and what they do. We ask whether combining the two detects collusion better than either alone (Sprint question 2.2). Building on LLM-Trust-Breaking, we seed a secret pact between two of four agents in a Diner's Dilemma and add a matched control: two agents who receive the same cheating instruction individually, with no partner. A frozen gpt-4o-mini monitor judged 80 pre-registered games under four views. A claims-vs-actions table scored best (64% accuracy) and separated pacts from honest play (AUC 0.95), but no public view separated pacts from lone cheaters (AUC 0.41 to 0.62). This held across fresh games, prompts and monitors; only the agents' private plans carried the signal (AUC 0.86). We then gave agents an optional private chat with no collusion instruction. Across 119 gpt-5-mini chat games, the author-checked collusion count was 2 clear plus 1 borderline, while an action-based label fired in 106 of 120 games and the monitor flagged 98% of them. When collusion paid, concealed pacts rose to 4 of 30 games, and only the claims-vs-actions table caught some (42% of only 4 pact games) with few false alarms (9%). Two top-5 frontier models showed no collusion. Says-vs-does monitoring detects cheating, and collusion only when colluders lie in public; we propose the matched lone-cheater control as a minimum evidence standard.