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Sprint projectOct 26, 2026Hong Kong

When Subsidies Backfire: The Budget–Audit Frontier for Collusion-Resistant Procurement

Xianrun Chen, Ziqi Zhao · Team G2

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

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Report: When Subsidies Backfire: The Budget–Audit Frontier for Collusion-Resistant Procurement

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Loser subsidies can discourage an agent from capturing a task, yet reward a coalition for manipulating the winning bid. We derive the exact tradeoff between payment budgets and worst-case auditing in procurement with a fixed winner award and trusted cost verification. Balancing capture and subsidy amplification yields an optimal capped-linear subsidy and a budget threshold beyond which further spending cannot reduce auditing. In 54 prescribed-witness games, model agents attain every exact finite-action payoff maximum, with larger budgets reducing capture gains and increasing amplification gains under reduced auditing. A separate repeated-game dataset shows that negative aggregate gains can conceal profitable pair-level deviations. The mechanism result and the payoff diagnostic connect two tasks in evaluating collusion: preventing joint deviations and measuring their consequences for coalition members, the sponsor, and execution cost.

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  1. This project studies collusion in a procurement setting where agents can form coalitions and the losers get subsidies to disincentivize coalition-forming. The project considers a theoretical model to solve for the optimal subsidy. It further conducts experiments with LLM agents to support the findings. However, the theoretical framework is not clearly stated. Some essential formal definitions are missing: For example, what are "these requirements" in Proposition 1? What are the incentive constraints formally?

  2. The paper tackles an interesting problem and does a good job of showing how subsidies intended to discourage collusion can actually create new incentives for it. The theoretical analysis is particularly interesting, as it provides an exact characterization of the tradeoff between subsidies and auditing, while the experiments offer a clear illustration of the underlying mechanisms. I also liked the observation that aggregate payoffs can hide profitable deviations by smaller coalitions. My main concern is that the theoretical guarantees rely on fairly strong assumptions, especially perfect cost verification and enforceable payments, which limit their applicability to realistic procurement settings. There is also a bit of a disconnect between the theoretical results and the experiments, since the latter mainly illustrate the predicted incentives rather than testing how robust the proposed mechanism is. A useful direction for future work would be to investigate whether similar guarantees can hold under weaker verification assumptions, or whether the mechanism can be adapted to settings where auditing is imperfect or costly.

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1 judge declined to score this project.

Cite this project

@misc{chen2026subsidies,
  title = {{When Subsidies Backfire: The Budget–Audit Frontier for Collusion-Resistant Procurement}},
  author = {Xianrun Chen and Ziqi Zhao},
  year = {2026},
  month = oct,
  note = {Submitted to AI Collusion Research Sprint, an Apart Research Sprint},
  howpublished = {\url{https://apartresearch.com/sprints/projects/when-subsidies-backfire-the-budgetaudit-frontier-for-collusionresistant-procurement-1l3s}},
  url = {https://apartresearch.com/sprints/projects/when-subsidies-backfire-the-budgetaudit-frontier-for-collusionresistant-procurement-1l3s}
}

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