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Sprint projectOct 26, 2026Hong Kong

Algorithmic Diversity Can Fail: A Tolerant Q–LLM Collusion Counterexample

Arad Maleki, Mohammadpayam Taebi · Team Boozines

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

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Report: Algorithmic Diversity Can Fail: A Tolerant Q–LLM Collusion Counterexample

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Algorithmic diversity has been proposed as a safeguard against AI price collusion. We report a counterexample using tolerant Q-learning, which downweights negative value-prediction errors and makes disappointing outcomes less influential during learning. We compare it with ordinary Q-learning, which weights positive and negative errors equally. Both optimize only their own monetary profit. Each learner faces three LLM rivals in a four-seller market without direct communication. We observe that ordinary Q improves profit without sustained collusion. Tolerant Q sustains cooperative pricing and develops a small late-game profit advantage over its LLM partners. The result challenges treating architectural diversity as sufficient protection against collusion. A reinforcement learner can learn to benefit from a cooperative LLM market, making adaptation and the distribution of gains essential targets for safety audits. This shifts the focus from architecture labels to the behavior learned through repeated interaction.

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  1. This is a thoughtful and focused investigation of whether algorithmic diversity can prevent collusion after agents adapt. The comparison between ordinary and tolerant Q-learning is particularly useful, highlighting how learning dynamics may matter alongside architectural differences. The report explains the approach clearly, includes relevant controls, and acknowledges important limitations.

    The team has developed a promising experimental foundation. A useful next step would be to replace the schematic figures with measured results and report outcomes across seeds, including the size of the late-game profit advantage. These additions would make the findings easier to assess and strengthen the case for further investigation. Overall, this is a worthwhile exploratory contribution to understanding collusion risks in mixed-agent systems.

Cite this project

@misc{maleki2026algorithmic,
  title = {{Algorithmic Diversity Can Fail: A Tolerant Q–LLM Collusion Counterexample}},
  author = {Arad Maleki and Mohammadpayam Taebi},
  year = {2026},
  month = oct,
  note = {Submitted to AI Collusion Research Sprint, an Apart Research Sprint},
  howpublished = {\url{https://apartresearch.com/sprints/projects/algorithmic-diversity-can-fail-a-tolerant-qllm-collusion-counterexample-z8d5}},
  url = {https://apartresearch.com/sprints/projects/algorithmic-diversity-can-fail-a-tolerant-qllm-collusion-counterexample-z8d5}
}

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