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Sprint projectOct 26, 2026

Which Single Restriction Removes the Most Collusion at the Least Cost?

Zhi Yilang · Team ZhiYiLab

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

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Six pricing agents set prices for sixty rounds under a common demand shock. We measure which single restriction removes collusion at the least cost, with cost defined on markets that contain no cartel. Removing the carrier is free and removes 0.633 of the collusion index, but only against the carrier it matches — removing the shared channel removes exactly 0.000 from a cartel that signals through an inert listing field. The only restriction that works without knowing the carrier is a price ceiling: 0.560 removed on both, at a cost of 0.590 of innocent producer surplus. Separately, we show that price parallelism is worthless as evidence (it is 1.000 on a purely competitive market) and that a detector built on channel fit achieves a 0.000 false positive rate and 1.000 detection on both carriers over 8 seeds. We also report two traps: the cheapest-per-unit restriction is cheap because it is ineffective — it delays the cartel 9x without stopping it — and consumer surplus is a degenerate cost metric in this demand system, so cost has to be measured on the producer side.

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  1. Great work! I ran the offline checks and all 214 passed. Swapping text for metadata makes the channel issue very clear. Please fix the monitor-alarm mismatch, 0.076 in code versus 0.099 in the PDF. Then let one seller adapt its signaling channel and see if the restriction still works.

Cite this project

@misc{yilang2026which,
  title = {{Which Single Restriction Removes the Most Collusion at the Least Cost?}},
  author = {Zhi Yilang},
  year = {2026},
  month = oct,
  note = {Submitted to AI Collusion Research Sprint, an Apart Research Sprint},
  howpublished = {\url{https://apartresearch.com/sprints/projects/which-single-restriction-removes-the-most-collusion-at-the-least-cost-omfd}},
  url = {https://apartresearch.com/sprints/projects/which-single-restriction-removes-the-most-collusion-at-the-least-cost-omfd}
}

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