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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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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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