Conditional independence of agent values given query information

Investigate whether most dependence among bidder values in agentic markets can be eliminated by conditioning on observable query metadata, so that the values become approximately independent given the query information.

Background

The paper’s near-independence welfare guarantee applies when bidder values are close to conditionally independent after observing public query information such as the prompt text, topic, or difficulty. The authors hypothesize that shared task characteristics explain much of the correlation among model values.

Experiments using EmbedLLM suggest that the prompt explains most of the predictive information otherwise contained in a rival model’s value, but the authors explicitly note that these results do not establish small total-variation distance from conditional independence. Thus, whether the conjectured structural condition holds generally in agentic markets remains unresolved.

References

In practice, bidder values are rarely strictly independent---yet they may be nearly independent. In agentic markets, values co-vary across queries due to shared task difficulty and similar model costs, but we conjecture that much of this common variation can be explained by observable query metadata.

— Price of Anarchy of First-Price Auctions in Agentic Markets  (2610.20587 - Trivedi et al., 14 Oct 2026) in Section 3, “First-price auctions with near-independent values”; Appendix, Section “Near-independence given the prompt”