Writing study: Revenue Guarantees of No-Swap-Regret Dynamics in First Price Auctions
← ICML 2026 oral writing corpus
Anders Bo Ipsen, Stratis Skoulakis · Official ICML 2026 oral record
Figure, table and section ledger
Editorial contribution type: Theory & formal analysis (primary).
Layout extraction, not a required paper template. Counts are distinct caption labels; a multi-panel figure counts once. Section spans are estimated from heading positions, including floats and whitespace. Method and limitations.
- Canonical PDF
- 22 physical pages
- Before references / appendix
- ≈ 7.92 page-equivalents
- Main figures / tables
- 3 / 0
- Attached appendix figures / tables
- 1 / 0
- Attached appendix span
- ≈ 10.91 page-equivalents
Section-by-section lengths and source pages
The title/abstract/front matter precede the first numbered heading. A span ends at the next detected top-level heading, not at the last sentence; end-page whitespace is included. References and statements are listed separately. These are not measurements of text-only or artwork area.
| Top-level heading | Starts on PDF page | Estimated span | Share of entire PDF |
|---|---|---|---|
| 1. Introduction | 1 | ≈ 2.41 pp. | 10.95% |
| 2. Preliminaries and Notation | 3 | ≈ 1.56 pp. | 7.09% |
| 3. Proof of Theorem 2.6 | 5 | ≈ 2.35 pp. | 10.68% |
| 4. Experimental Evaluations | 7 | ≈ 1.06 pp. | 4.82% |
| 5. Conclusion and Future Directions | 8 | ≈ 0.25 pp. | 1.14% |
| Impact Statement | 8 | ≈ 0.05 pp. | 0.23% |
| References | 8 | ≈ 3.17 pp. | 14.41% |
| A. Revisiting the argument in (Feldman et al., 2016) | 12 | ≈ 3.35 pp. | 15.23% |
| B. Proof of Theorem 2.8 | 15 | ≈ 0.65 pp. | 2.95% |
| C. Proof of Theorem 2.3 | 16 | ≈ 0.6 pp. | 2.73% |
| D. Omitted Proofs of Section 3.1 | 16 | ≈ 3.84 pp. | 17.45% |
| E. Experimental Evaluations in the Bayesian Setting | 20 | ≈ 2.47 pp. | 11.23% |
All detected figure and table locations
Attached appendix
Argument and organization
- Problem and contribution
Separates knowing the limiting revenue from knowing how many rounds suffice, then turns the missing polynomial dependence into an explicit question.
- Argument sequence
Informal claims are followed by formal definitions and bounds; the main proof restates its target before constructing a primal relaxation and feasible dual assignment.
- Evidence and verification
The conclusion retains the gap between epsilon-dependent upper/lower bounds and labels the sharper rate conjectural; Bayesian behavior is empirical, with proof extension left open.
Problem, claim and contribution
Separates knowing the limiting revenue from knowing how many rounds suffice, then turns the missing polynomial dependence into an explicit question.
Questions 1.5 and Theorem 1.6, p. 2 · Main paper
Argument and section order
Informal claims are followed by formal definitions and bounds; the main proof restates its target before constructing a primal relaxation and feasible dual assignment.
Sections 1.2-3.1, pp. 2-5 · Main paper
Figures, captions and visual explanation
The proof page visually separates definitions, lemmas and a notation warning. Revenue curves use time-average revenue on the vertical axis and distinguish discretization from bidder-count sweeps.
Section 3, p. 5; Figures 2-3, p. 8; both PNGs inspected · Main paper
Tables, comparisons and evidence
The conclusion retains the gap between epsilon-dependent upper/lower bounds and labels the sharper rate conjectural; Bayesian behavior is empirical, with proof extension left open.
Conclusion and future directions, p. 8 · Main paper
Appendix and reproducibility
A constructive distribution supports the upper bound, while extended Bayesian figures report conditional bidding CDFs as well as revenue.
Appendix B, p. 15; E, pp. 20-22 · Main paper
Clarity and writing conventions
Numbered questions and theorem-to-claim translations make the theoretical relevance legible; a remark explicitly disambiguates the scalar dual variable from the probability measure.
Introduction, p. 2; Remark 3.4, p. 5 · Main paper
What to reuse—and what not to infer
Transferable lesson: Translate an equilibrium statement into a finite-time operational quantity, and use empirical results to motivate—not silently establish—the next theorem.
Boundary: The results concern time-averaged revenue under the specified discrete-auction/no-swap-regret setting, not arbitrary auction markets or per-round revenue.
Apply this lesson using the argument and evidence worksheet.
Inspection record and sources
- Checked
- 2026-10-07
- Reading status
- Writing-focused manuscript scan + selected visuals inspected
- Main text
- Writing-focused distributed manuscript scan, not exhaustive technical/proof validation. Sections 1-5, pp. 1-8: asymptotic-to-finite-round gap, auction/regret definitions, revenue bounds, dual fitting and empirical extensions.
- Appendix / supplement
- Writing-focused appendix scan; code, data and external assets not executed. Appendices A-E, pp. 12-22: extensions of earlier arguments, upper-bound construction, omitted proofs and Bayesian revenue/bidding-distribution experiments.
- Visually inspected PDF pages
- 5, 8
This is a writing-focused scan of the manuscript and the stated supplementary scope: framing, organization, visual explanation, evidence presentation and wording. It is not a line-by-line proof audit, reproduction of results or exhaustive scientific review.