Bibliographic record
Abstract
Pay-as-bid (or discriminatory or multiple-price) auctions are used to sell homogenous goods such as treasury securities and commodities.We prove the uniqueness of their pure-strategy Bayesian Nash equilibrium and establish a tractable representation of equilibrium bids for symmetrically-informed bidders.Analyzing design, we show that supply transparency and full disclosure are revenue-maximizing in pay as bid, though not necessarily in uniform-price (or single-price) auctions, the main alternative auction format.Pay as bid raises weakly more revenue than uniform price and may lead to higher welfare.Our results provide an explanation for the revenue equivalence observed in empirical studies of treasury auctions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.036 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.003 | 0.005 |
| Scholarly communication | 0.010 | 0.015 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.009 | 0.007 |
| Insufficient payload (model declined to judge) | 0.019 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".