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

While the paper delivers a strong statistical fix for sequential audits by isolating secret leakage and preventing false accusations against innocent agents, it remains constrained by high sample size requirements in complex settings and unproven against adaptive adversaries.

This one stood out to me. You took a detector people actually use, showed exactly where it goes wrong, and then fixed it. That is the whole paper in one sentence, and it is a good paper.

The part I kept coming back to is Proposition 1. The net influence score splits cleanly into two pieces: how unpredictable the earlier agent is on its own, and how much the later agent actually uses the earlier agent's private information. Only the second piece is collusion. The first piece is just honest randomness, and in a sequential game it is big enough to flip the ranking entirely. Your coin game makes that concrete. The colluding pair ends up at minus 0.427 bits and the honest pair at plus 0.714, so no threshold setting can ever point at the right pair. That is not a borderline result. It is a proof that the detector fails in this setting, and it reframes what an audit should even be measuring.

I also liked how you ran the LLM experiments. Writing the validation protocol down on Oct 26, before any validation calls, and then using fresh seeds, is exactly the discipline this kind of result needs. One correction, though: that frozen protocol covered conditions C1 to C5 only. The C6/C7 dose conditions and the GLM repeat came later, Oct 28 and 29, after the freeze, so they should be labelled exploratory rather than presented as part of the frozen run. The seven conditions separate collusion from rumor exposure properly, and the intermittent case, where the secret only arrives in 30% of rounds, is the one that would have caught a weaker repair. Repeating C1 and C2 with GLM-5.3 Flash was the right call too. It rules out the easy objection that this is one model's quirk.

Three things would make the work land harder.

First, put the code and data somewhere public. The frozen protocol is one of your best selling points, but "available on request" means nobody can check it without emailing you. A repo with the prompts, seeds, and raw logs would do more for this paper than another experiment.

Second, say a bit more about where this goes next in the real world. Your two testbeds are a binary guessing game and Kuhn poker. Readers will want to know what changes with continuous actions, like posted prices, and with coalitions bigger than two. You do not need to solve those cases here. A short, honest discussion of what breaks and what carries over would help people judge where the repair applies.

Third, give auditors a way to check Fix 4 before they trust it. Reduced grouping is powerful, and pooling both move orders is what rescues intermittent collusion in C5, where the entropy-only and per-direction versions miss it. But the reduced-groups assumption can fail without any warning, and you show it failing in poker. Even a rough diagnostic, some test an auditor can run in a new setting to see whether the assumption holds, would make the method much more usable.

None of that takes away from the core result. You found a real flaw in a published detector, proved it, and built a repair that works in two very different settings. That is strong work, and I hope you keep pushing it toward deployment.