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Sprint projectOct 25, 2026India

Auditing Belief-Correction Prompts for LLM Pricing Agents with a Ground-Truth Rival

Sachin Ruhil · Team X

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

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Report: Auditing Belief-Correction Prompts for LLM Pricing Agents with a Ground-Truth Rival

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We audit belief-correction prompts for an LLM pricing agent against a ground-truth scripted rival in a Calvano duopoly. The LLM reports a retaliation forecast each round; we compare control, placebo, and corrected (true rival policy) over 21 episodes (7×3×120 rounds). Supra-Nash pricing is rare but real and one-sided (rival stays near Nash): clear high-price runs in 2/7 control and 2/7 corrected, 0/7 placebo. Mean late-window elevation: control +0.44, placebo +0.02, corrected +0.78. Belief correction did not reliably reduce supra-Nash pricing; outcomes are path-dependent. Cut-round Brier stayed poor (corrected 0.42 vs control 0.43, both worse than a 50% forecast), so the main finding is that this correction prompt barely changed beliefs, not that correct beliefs fail to lower prices.

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  1. I like the core idea. A placebo arm of matched length, plus retaliation forecasts scored against a rival whose policy you actually know, is a cleaner way to test “just tell the model the truth” than most prompt studies. You’re also honest about the weak spots, which I appreciate. I’d just bring that honesty up into the title and abstract, because right now the headline claims more than the results support.

    My main concern is the outcome itself. Firm B always posts Nash and never follows a price up, so Firm A’s best move is simply Nash. Pricing at 7–7.7, above the monopoly price, isn’t collusion; it’s Firm A leaving money on the table. I’d drop the “COLLUSION” labels and report Firm A’s profit against its Nash profit instead.

    I also think the corrected prompt may be working against you. Telling the agent “cuts get punished” is exactly the kind of message that props prices up. A correction meant to lower prices should also say the rival will never match a price increase.

    On the Brier scores: retaliation always follows a cut, so on cut rounds the outcome is always 1. A score near 0.42 means the model forecast roughly 0.35 for something the corrected arm was told is certain. Please show mean forecasts by arm and Brier on non-cut rounds too.

    Figure 3 suggests the “path dependence” may just be the first move. Episodes open around 12–14 and either crash to Nash or get stuck near 7–8. Please report round-1 prices by arm, and any parse failures.

    With n=7, a 2/7 vs 0/7 vs 2/7 split is noise, so I wouldn’t highlight “never under placebo.” A positive control (a rival that matches high prices) is the right next step, as you say. Small thing: there’s a stray “Shorter” in Methods, and the repo README still describes the Romero/Sauer thesis.

    Read full reviewShow less

Cite this project

@misc{ruhil2026auditing,
  title = {{Auditing Belief-Correction Prompts for LLM Pricing Agents with a Ground-Truth Rival}},
  author = {Sachin Ruhil},
  year = {2026},
  month = oct,
  note = {Submitted to AI Collusion Research Sprint, an Apart Research Sprint},
  howpublished = {\url{https://apartresearch.com/sprints/projects/auditing-beliefcorrection-prompts-for-llm-pricing-agents-with-a-groundtruth-rival-zs5g}},
  url = {https://apartresearch.com/sprints/projects/auditing-beliefcorrection-prompts-for-llm-pricing-agents-with-a-groundtruth-rival-zs5g}
}

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