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Sprint projectOct 25, 2026

When Does Net Influence Catch Colluders? Replication and Stress Tests of an Information-Theoretic Collusion Detector

WANG QINYI · Team 11111111

Submitted to AI Collusion Research Sprint. Sprint projects are early-stage work by participants, not Apart Research publications.

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Report: When Does Net Influence Catch Colluders? Replication and Stress Tests of an Information-Theoretic Collusion Detector

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Bonjour, Aggarwal and Bhargava (UAI 2022) proposed pairwise net influence, a conditional-mutual-information statistic that flags two agents as colluding when each influences the other more than any third agent does. The method is a candidate black-box auditor for multi-agent systems, but no public implementation exists and it has not been stress-tested. We re-implement it from the paper’s equations and reproduce its iterated Rock–Paper–Scissors results: with logs in bits and the previous round’s joint action as the state, our detection accuracy matches the paper’s Table 2 within a few percentage points. We then probe three failure modes in simulation. (1) The fixed threshold α = 0.05 fixes a minimum detectable collusion strength (collusion probability ≈ 0.195, derived analytically); weaker collusion is never flagged, even after 10,000 rounds, while it also produces up to 41% false positives on short logs. A G-test with Bonferroni correction keeps false positives near 5% at every sample size and detects collusion probability 0.1 in 96–97% of runs at 3,000–10,000 rounds. (2) Two agents with no agreement that follow a shared public signal are flagged by both detectors (95–100% at signal-following probability 0.5) unless the signal is included in the conditioning state. (3) A three-agent coalition defeats the net- influence rule (≤ 38.5% detection), because subtracting the strongest other influence cancels coalition members against each other; a dependency graph of significant pairs recovers the coalition in 95.5–100% of runs. All experiments are CPU-only simulations with hand-coded agents; we did not test LLM agents.

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  1. This is a strong submission, and the part I liked most is how carefully the replication was done. The author re-implements Bonjour et al. and pins down two things the original paper leaves unclear, the state definition and the log base, which is real detective work and not just a re-run. The analytic result is the highlight for me. Showing that the fixed threshold of 0.05 sets a hard floor at collusion probability around 0.195, below which nothing gets flagged no matter how much data you collect, turns a puzzling pattern into something you can actually explain. Then the three stress tests all land on problems a real auditor would run into: false positives on short logs, innocent agents flagged because they follow the same public signal, and a three-agent coalition slipping past the pairwise rule. Each one comes with a fix that works, which makes the paper useful rather than just critical.

    Two things would make it stronger. First, the calibrated G-test still needs the permutation null implemented, because right now it breaks in the 27-state replication setting, where the chi-squared approximation gives 73% false positives. That is the one gap between the fix the paper recommends and the setting the replication lives in. Second, the obvious next step is the one the author already sketches: run the same detectors on LLM agents in the double-auction harness, using same-model pairs as a common-cause control. That is where this work has to go to matter for AI agents rather than toy ones. One smaller thing: with 100 to 300 simulations per cell, the reported percentages carry real Monte Carlo error, so confidence intervals would help the reader judge how much weight to put on the finer comparisons.

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Cite this project

@misc{qinyi2026net,
  title = {{When Does Net Influence Catch Colluders? Replication and Stress Tests of an Information-Theoretic Collusion Detector}},
  author = {WANG QINYI},
  year = {2026},
  month = oct,
  note = {Submitted to AI Collusion Research Sprint, an Apart Research Sprint},
  howpublished = {\url{https://apartresearch.com/sprints/projects/when-does-net-influence-catch-colluders-replication-and-stress-tests-of-an-informationtheoretic-collusion-detector-b3r6}},
  url = {https://apartresearch.com/sprints/projects/when-does-net-influence-catch-colluders-replication-and-stress-tests-of-an-informationtheoretic-collusion-detector-b3r6}
}

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