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Sprint projectOct 25, 2026

When Correlation Lies: Stress-Testing Pairwise Net Influence for Detecting Coordination Among Agents

Durgesh Unde · Team XYVERION

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

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Report: When Correlation Lies: Stress-Testing Pairwise Net Influence for Detecting Coordination Among Agents

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I investigated whether information-theoretic detectors can distinguish dependence caused by shared public context from deliberately coordinated behavior among agents. I implemented and evaluated a four-agent iterated Rock–Paper–Scissors benchmark, comparing marginal mutual information (MI), conditional mutual information (CMI), and pairwise net influence (PNI).

The scripted study contains 260 trajectories and 54,000 rounds spanning independent behavior, shared-context confounding, a private-signal coordination positive control, and a coordination-strength sweep. Under the shared-context condition, marginal MI averaged 0.958 bits and flagged 120/120 non-target pairs at the evaluated threshold; CMI flagged 0/120, while PNI flagged 12/120. In the positive control, PNI ranked the designated coordinating pair first in all 20 trajectories, but flagged 20/100 non-target pairs, compared with 2/100 for CMI. These results demonstrate that pair ranking and threshold-based classification are distinct tasks.

I also evaluated Qwen2.5-1.5B-Instruct on Modal CPU across 630 trajectories and 68,400 agent decisions at horizons of 5, 20, and 50 rounds. CMI and PNI achieved 70% Top-1 ranking accuracy at five rounds and 100% at horizons of 20 rounds or more. The coordinating LLM agents were explicitly instructed to follow a shared private signal; these results demonstrate prompted compliance, not spontaneous cartel formation. The findings highlight the importance of state conditioning and adequate observation length in this controlled setting.

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  1. Your three-way comparison of marginal MI, conditional MI and PNI is the right way to separate what conditioning buys from what rival subtraction buys. The held-out calibration and exact counts also make your tables easy to trust. The main issue is that the current conditions confirm the detector's design rather than stress it. The shared context is fully observed and discrete, and the coordinating pair coordinates every round, so the outcomes are close to guaranteed.

    I would prioritize three things. First, report the coordination-strength sweep (Condition D) you describe, and add a weakly coordinating pair hidden among agents that react to shared context, ideally with part of that context unobserved. Second, fix calibration. Conditional MI flags 11% of pairs on the held-out independent baseline, PNI flags 10 to 20% in Conditions B and C, and the identical 20% rate in every Condition C seed suggests a systematic false positive worth diagnosing. Within-state permutation nulls computed per game would adapt to each agent's predictability. With 369 smoothing pseudo-counts against 200 rounds, a lighter or bias-corrected estimator would also help. Third, report marginal MI for the LLM shared-context condition so readers can see the confound appear and then disappear. Finally, state how directed PNI scores are combined into a pair score.

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Cite this project

@misc{unde2026correlation,
  title = {{When Correlation Lies: Stress-Testing Pairwise Net Influence for Detecting Coordination Among Agents}},
  author = {Durgesh Unde},
  year = {2026},
  month = oct,
  note = {Submitted to AI Collusion Research Sprint, an Apart Research Sprint},
  howpublished = {\url{https://apartresearch.com/sprints/projects/when-correlation-lies-stresstesting-pairwise-net-influence-for-detecting-coordination-among-agents-qgwc}},
  url = {https://apartresearch.com/sprints/projects/when-correlation-lies-stresstesting-pairwise-net-influence-for-detecting-coordination-among-agents-qgwc}
}

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