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 minimum-cost solution for a set of players. Our first reduction shows that any truthful, α-approximation mechanism for the socialcost minimization (SCM) problem satisfying a technical no-bossiness condition can be morphed into a truthful mechanism that achieves an O(α log n)-approximation where the prices recover the cost incurred. Thus, we decouple the task of truthfully computing an outcome with near-optimal social cost from the cost-sharing problem. This is fruitful since truthful mechanism-design, especially for single-dimensional problems, is a relatively well-understood and manageable task. Our second reduction nicely complements the first one by showing that any LP-based 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) log n-approximation cost-sharing mechanism). These reductions find a slew of applications, yielding, as corollaries, the first or improved polytime costsharing mechanisms for a variety of problems. For example, our first reduction coupled with the celebrated VCG mechanism shows that for any costsharing problem (with a monotone cost function) one can obtain a truthful mechanism that achieves an O(log n)-approximation where the prices recover the cost incurred. Other applications include O(log n)approximation mechanisms for: survivable network design problems, facility location (FL) problems including capacitated and connected FL problems, and minimummakespan scheduling on unrelated machines. Our results demonstrate that in contrast with our current understanding of group-strategyproof and acyclic mechanisms, strategyproofness allows for ample flexibility in cost-sharing mechanism design enabling one to effectively leverage various algorithmic results.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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; both teacher heads agree on what is shown here.
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".