Collusion with Competitive Marginals: Price-Level Audits Are Blind by Construction

Abstract:Empirical work on algorithmic collusion asks one question of the data: are prices supracompetitive? We show this can be answered "no" by a conspiracy that is nonetheless profitable. Consider bidding agents that couple only through the joint distribution of their unexplained bid components, leaving every agent's own bid law exactly at the competitive law. Any test whose input is a single agent's price or bid history then has power exactly equal to its false-positive rate, for every coupling strength up to comonotonicity. The published detection methodology is therefore blind to this conduct by construction rather than underpowered, and no sample size repairs it. Three empirical results follow. First, the mechanism appears in real language-model agents: twenty models from nineteen independent developers, three deployment prompts each, show residual correlation of $+0.053$ between two deployments of one model against $+0.0001$ across models, with a 95% interval clustered by developer of $[0.030, 0.078]$, under an auditor that sees every order feature and is fitted out of sample. Second, the coupling falls monotonically as sampling temperature rises ($p=0.002$), turning a deployment parameter into a candidate mitigation. Third, on 24 days of Ethereum block-building auction data covering 77,684 bids from 39 bidders, the honest population of bidder pairs is itself so dependent that a screen held at a 5% false-positive rate must sit above a floor of $+0.50$ to $+0.81$, which is 20 to 32 times the family-wise sampling threshold and does not fall as the audit window grows. Since lawful multi-identity operation and conspiracy are behaviourally indistinguishable here, the tractable regulatory target is not detection but counting: resolving 40 bidding identities into 23 operators raises the Herfindahl index by 247.5%, and adding behavioural clusters from public bid streams reaches 324.5%.

Computer Science and Game Theory (cs.GT); Artificial Intelligence (cs.AI); Cryptography and Security (cs.CR)

arXiv:2607.26385 [cs.GT]

(or arXiv:2607.26385v1 [cs.GT] for this version)

https://doi.org/10.48550/arXiv.2607.26385 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.