Writing study: Equilibrium Pricing in Oligopolistic Data Markets
← ICML 2026 oral writing corpus
Bhaskar Ray Chaudhury, Jugal Garg, Eklavya Sharma, Jiaxin Song · 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
- 10 physical pages
- Before references / appendix
- ≈ 8.15 page-equivalents
- Main figures / tables
- 0 / 0
- Attached appendix figures / tables
- 0 / 0
- Attached appendix span
- No boundary detected; not assumed zero
Extraction notes: No attached appendix boundary detected. Zero means no recognized caption, not independently verified absence.
Source-bound correction: The physical p.8 chart has two panel labels but no numbered parent figure caption. Main text refers to Figure 1b, and the writing study records the visible chart. The caption-based figure count of zero is not evidence that the source has no visual; no missing caption label is fabricated.
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 | ≈ 2.47 pp. | 24.7% |
| 2. Preliminaries | 3 | ≈ 0.49 pp. | 4.9% |
| 3. Non-existence of (Approximate) NE | 4 | ≈ 0.92 pp. | 9.2% |
| 4. PLC Pricing and Approximate NE | 5 | ≈ 1.58 pp. | 15.8% |
| 5. Empirics | 6 | ≈ 1.42 pp. | 14.2% |
| 6. Sparsity of PLC Strategies | 8 | ≈ 0.89 pp. | 8.9% |
| Impact Statement | 9 | ≈ 0.05 pp. | 0.5% |
| References | 9 | ≈ 1.85 pp. | 18.5% |
All detected figure and table locations
Main text
No recognized caption labels.
Attached appendix
No recognized caption labels.
Argument and organization
- 1 Introduction; 2 Preliminaries; 3 Non-existence of (Approximate) NE
Derives buyer utility, specifies tie-breaking and develops an impossibility example.
- 4 PLC Pricing and Approximate NE
Changes the allowed pricing profile while restricting the comparison class of deviations.
- 5 Empirics; 6 Sparsity of PLC Strategies
Uses a simulated news marketplace to motivate a further structural sparsity question.
Problem, claim and contribution
Non-rivalry motivates asking whether data-pricing games inherit familiar equilibrium guarantees; the answer is organized around a negative result and a carefully relaxed positive result.
Introduction and contributions, pp.1-2 · Main paper
Argument and section order
The two-seller example is explained through undercutting and price-raising cases before the formal inapproximability statement.
Section 3, p.4 · Main paper
Figures, captions and visual explanation
The sparse display page separates iteration count from number of positive shards, with distinct seller ranges; neighboring text turns the observation into a formal sparsity question.
Two-panel Figure 1 and Section 6, p.8 · Main paper
Tables, comparisons and evidence
The reported incentive ratio tests deviations to linear prices, not arbitrary PLC deviations, and the news-market valuations are derived from logistic-regression error proxies.
Section 5, pp.6-7 · Main paper
Appendix and reproducibility
The paper provides proof sketches and explicit pointers to an external full version rather than a local appended proof block.
Theorem 3.2 proof sketch, p.5; Lemmas 4.2-4.3, p.6 · Main paper
Clarity and writing conventions
The theorem title repeats the restricted deviation class, but broader phrases such as exact Nash equilibrium should be read with the later linear-strategy qualification.
Theorem 4.1, p.6; empirical incentive-ratio discussion, p.7 · Main paper
What to reuse—and what not to infer
Transferable lesson: State what changes in the strategy space and what stays restricted in the deviation benchmark whenever a negative result is followed by a relaxed guarantee.
Boundary: The 2-approximate guarantee and empirical ratio concern linear deviations from PLC profiles; the simulations do not prove unrestricted PLC equilibrium or general convergence, and externally deferred proofs were not checked.
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-oriented scan of the main argument through physical p.9, with focused physical-page text inspection on 1, 2, 3, 4, 5, 6, 7, 8, 9. Framing, section progression, mechanism/proof explanation, displays, comparison conditions and conclusions were inspected. This is not exhaustive technical reading, proof verification or reproduction.
- Appendix / supplement
- The published 10-page PDF has no appendix. Several full proofs and extensions are explicitly deferred to a separately cited full version, which was not inspected in this scan.
- Visually inspected PDF pages
- 4, 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.