Black-Box Reductions for Cost-Sharing Mechanism Design
Bibliographic record
Abstract
We consider the design of strategyproof cost-sharing mechanisms. We give two simple, but extremely versatile, black-box reductions, that in combination reduce the cost-sharing mechanism-design problem to the algorithmic problem of finding a min-cost solution for a set of players. Our first reduction shows that any truthful, α-approximation mechanism for the social-cost minimization (SCM) problem satisfying a technical no-bossiness condition can be morphed into a truthful mechanism that achieves an O(αlogn)-approximation where the prices recover the cost incurred. Thus, we decouple the approximation and cost-recovery objectives. Our second reduction nicely complements the first one by showing that any LP-relative ρ-approximation for the problem of finding a min-cost solution for a set of players yields a truthful, no-bossy, (ρ+1)-approximation for the SCM problem (and hence, a truthful (ρ+1)logn-approximation cost-sharing mechanism). These reductions yield the first, or improved, polytime cost-sharing mechanisms for a variety of problems.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.016 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.010 | 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".