Comparative Statics and Welfare in Heterogeneous All-Pay Auctions: Bribes, Caps, and Performance Thresholds
Bibliographic record
Abstract
Comparative statics for all-pay auctions with two heterogeneous and privately informed bidders are analyzed. General results are provided for when one bidder becomes stochastically weaker. The comparative statics are fully characterized for truncations. Moreover, we show that expected revenue may increase when one bidder weakens. In the second part of the paper we consider a dynamic contest in which beliefs change endogenously: the first bidder may preempt the auction by paying a bribe. An all-pay auction is held if the bribe is not paid, in which case the second bidder revises his beliefs. With the option to bribe, expected payoff decreases for a set of types of at least one bidder, possibly the bidder ostensibly advantaged by the preemption option. However, the expected revenue and the ex ante payoff of both bidders may improve.
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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 | 0.010 | 0.033 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.009 | 0.011 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.004 | 0.003 |
| Insufficient payload (model declined to judge) | 0.012 | 0.001 |
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".