Source Entropy Is Not Collusion: Why Sequential Net-Influence Audits Accuse Honest Agents, and How to Fix Them

When AI agents collude, they may leave no readable messages, so auditors often have to judge from behaviour alone. A popular behavioural detector, pairwise net influence, flags two agents when each one's actions carry information about the other's. We show that in sequential settings, where agents act in turn and see earlier moves, this detector has a built-in blind spot. Its score is exactly the sum of two parts: how unpredictable the earlier agent is, and how much the later agent uses the earlier agent's private information. Only the second part indicates collusion. The first part rewards honest randomness, so the detector can point at innocent agents while missing real colluders. In a simple four-player game, no threshold setting can ever find the colluders. This matters most for language-model agents, whose answers are inherently random. In a sequential card game played by DeepSeek V4.1 Flash agents, the original detector accuses an innocent pair in six of seven conditions, including every condition with no collusion at all, and GLM-5.3 Flash agents behave the same way. We propose a repaired audit that removes the randomness term, calibrates against honest mistakes, and combines the evidence from both orders in which two agents can move. The repaired audit finds the colluding pair in every collusion condition, including one where the agents share information only occasionally, and in its best form never blames a bystander for someone else's collusion. In four-player Kuhn poker, with large audits, it nearly triples the detection rate of weak collusion.