Computational Analysis of Perfect-Information Position Auctions
Bibliographic record
Abstract
After experimentation with other designs, the major search engines converged on the weighted, generalized second-price auction (wGSP) for selling keyword advertisements. Notably, this convergence occurred before position auctions were well understood (or, indeed, widely studied) theoretically. While much progress has been made since, theoretical analysis is still not able to settle the question of why search engines found wGSP preferable to other position auctions. We approach this question in a new way, adopting a new analytical paradigm we dub "computational mechanism analysis." By sampling position auction games from a given distribution, encoding them in a computationally efficient representation language, computing their Nash equilibria, and then calculating economic quantities of interest, we can quantitatively answer questions that theoretical methods have not. We considered seven widely studied valuation models from the literature and three position auction variants (generalized first price, unweighted generalized second price, and wGSP). We found that wGSP consistently showed the best ads of any position auction, measured both by social welfare and by relevance (expected number of clicks). Even in models where wGSP was already known to have bad worse-case efficiency, we found that it almost always performed well on average. In contrast, we found that revenue was extremely variable across auction mechanisms, and was highly sensitive to equilibrium selection, the preference model, and the valuation distribution.
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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 | 0.006 | 0.033 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 0.000 |
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".