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Sprint projectOct 26, 2026Chicago

Beyond Pairs: Detecting Colluding Groups of Agents from Their Moves

Tarun Trivedi, Eashan Gandotra · Team Deep Dish Learning

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

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We asked whether an auditor who sees only agents' moves can tell which agents are colluding in a multi-agent game. The existing pairwise detector misses colluding groups of three or more. We introduce GroupScan, an algorithm that scans every group of players for coordinated moves and calibrates against shuffled copies of the game to account for honest, correlated actions. We first validate it in multi-player Rock Paper Scissors, where it recovers hidden groups that pairwise methods miss with low false positive rates. We then extend it to LLM agents: in a double auction, it identifies a cartel of five LLM sellers that the pairwise method fails to detect.

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  1. This is a strong extension of the pairwise approach. I particularly like the experiments showing why honest agents reacting to the same history can look like colluders, and the comparisons identifying when simpler methods outperform GroupScan. These help establish where testing groups adds value.

    I am less convinced by the practical recipe in the discussion. As written, it seems to assess economic outcomes only after a group is flagged. Given your finding that coordination through public moves can escape detection, this could exclude economically important cases before their outcomes are examined. I would report the dependence evidence and the economic effects alongside each other, and explain what each contributes to the overall assessment.

    The “honest baseline” also needs a more precise interpretation. Higher profits can reflect better information or more effective trading, so a profit gain does not by itself establish harmful collusion. What alternative explanation should this comparison rule out, and how would the auditor construct the baseline? Answering this would strengthen the connection between the statistical contribution and the proposed use in market oversight.

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  2. The group scan and the within-state null are both worth keeping. Your own 2-seller pilot shows the real hole: coordination routed through the public state is invisible, and that is the easy cartel to build. Add the comms-only condition and a second seller model.

  3. This project determines whether collusion detectors can find a colluding group as well as a colluding pair. Current methods only test two agents at a time which can miss a larger group. The authors propose GroupScan, which scores every subset of agents, calibrates the scores against shuffled games, removes the flagged group and repeats. This method finds the exact group in about half of games in rock paper scissors, which standard detectors almost never do. In a market with five LLM sellers, GroupScan flagged this in most batches as well. This is a genuine gap in the literature, and the methodology is extremely thorough. What I am concerned about is that this method cannot tell a shared signal apart from collusion, and it should probably test a scenario such as having two or three of the five sellers share a private channel to test whether GroupScan can actually find that subgroup.

Cite this project

@misc{trivedi2026beyond,
  title = {{Beyond Pairs: Detecting Colluding Groups of Agents from Their Moves}},
  author = {Tarun Trivedi and Eashan Gandotra},
  year = {2026},
  month = oct,
  note = {Submitted to AI Collusion Research Sprint, an Apart Research Sprint},
  howpublished = {\url{https://apartresearch.com/sprints/projects/beyond-pairs-detecting-colluding-groups-of-agents-from-their-moves-4zhs}},
  url = {https://apartresearch.com/sprints/projects/beyond-pairs-detecting-colluding-groups-of-agents-from-their-moves-4zhs}
}

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