Guilty by Resemblance

AI agents that share an underlying model make similar choices without ever communicating. We ask whether collusion detectors can tell that apart from real coordination. We construct two populations: one holding a secretly coordinating pair, one where the agents merely share a model. We solve for the parameter that makes any pair in the second population identical in distribution to the colluding pair, so no detector can separate them from that pair alone. A shared model lifts the dependence of every pair at once, and an agreement lifts one. Detectors scoring the single most suspicious pair therefore read how similar it is and not how unusual it is: they invert, ranking honest groups above real cartels at AUROC 0.20 in all 26 configurations tested. Detectors comparing pairs with one another recover completely. Six instruction-tuned models from six companies show this is not hypothetical. Gemma-3-1B and Phi-4-mini agreed on 98.8% of rounds with no link between them, more than six copies of any single model we tried, so requiring different vendors does not buy what it appears to. Matching a planted cartel to that pair took coordination on 73% to 99% of rounds, after which a correlation screen named it by coin flip, while adding price level restored attribution to 100%. On 240 MMLU questions, the coin flip repeats, and the outcome repair survives with its margin cut from ninety-nine points to fourteen, because innocent models share wrong answers.