Efficient Computation of Optimal Auctions via Reduced Forms
Bibliographic record
Abstract
We study an optimal auction problem for selecting a subset of agents to receive an item or service, whereby each agent’s service can be configured, the agent has multidimensional preferences over configurations, and there is a limit on the number of agents that can be simultaneously served. We give a polynomial time reduction from the multiagent problem to appropriately defined single-agent problems. We further generalize the setting to matroid feasibility constraints and obtain exact and approximately optimal reductions. As applications of this reduction we give polynomial time algorithms for the problem with quasi-linear preferences over configurations or with private budgets. Our approach is to characterize, and in polynomial time optimize and implement feasible interim allocation rules. With a single item, we give a new characterization showing that any mechanism has an ex post implementation as a simple token-passing process. These processes can be parameterized and optimized with a quadratic number of linear constraints. With multiple items, we generalize Border’s characterization and give algorithms for optimizing interim and implementing ex post allocation rules. These implementations have a simple form; they are randomizations over greedy mechanisms that serve types in a given order.
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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 | 0.003 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".