Joint welfare guarantee from competitive floors and near-independence

Derive a welfare bound for first-price auctions that simultaneously exploits competitive-floor conditions and near-independence of bidder values, and determine whether the combined guarantee is strictly stronger than the separate guarantees.

Background

The paper establishes two separate sources of improved welfare guarantees: competitive floors, in which several bidders frequently have values close to the best bidder’s value, and near-independence, in which values are approximately independent after conditioning on public query information.

Although taking the larger of the two existing guarantees is immediate, the authors state that a bound exploiting both properties jointly could be stronger and leave its derivation unresolved.

References

Third, we analyze competitive floors and near-independence separately, and in experiments we only compute the competitive-floor bound. Real markets like EmbedLLM appear to have both properties (\Cref{sec:experiments} and \Cref{sec:approx_condt_indep}). Taking the larger of the two guarantees is immediate, but a bound that uses both properties together could be stronger, but is non-trivial. We leave this to future work.

— Price of Anarchy of First-Price Auctions in Agentic Markets  (2610.20587 - Trivedi et al., 14 Oct 2026) in Appendix, Section 1, “Limitations and future work”

Note, however, that a similar straightforward connection cannot be made to \Cref{thm:multi_floor}! In fact, the bound in \Cref{thm:multi_floor} can get worse, since positive dependence can make bidders fall below the floor on the same queries, which raises $\epsilon$ relative to independent values with the same marginals. We leave a closer study of how dependence between values affects competitive floors to future work.

— Price of Anarchy of First-Price Auctions in Agentic Markets  (2610.20587 - Trivedi et al., 14 Oct 2026) in Appendix, Section 2.2, “Positively dependent values”