Multidimensional Budget-Feasible Mechanism Design
Bibliographic record
Abstract
In budget-feasible mechanism design, a buyer wishes to procure a set of items of maximum value from self-interested players. We have a valuation function $v:2^U \to \mathbb{R}_+$, where $U$ is the set of all items, where $v(S)$ specifies the value obtained from set $S$ of items. The entirety of current work on budget-feasible mechanisms has focused on the single-dimensional setting, wherein each player holds a single item $e$ and incurs a private cost $c_e$ for supplying item $e$. We introduce multidimensional budget feasible mechanism design: the universe $U$ is now partitioned into item-sets $\{G_i\}$ held by the different players, and each player $i$ incurs a private cost $c_i(S_i)$ for supplying the set $S_i\subseteq G_i$ of items. A budget-feasible mechanism is a mechanism that is truthful, and where the total payment made to the players is at most some given budget $B$. The goal is to devise a budget-feasible mechanism that procures a set of items of large value. We obtain the first approximation guarantees for multidimensional budget feasible mechanism design. Our contributions are threefold. First, we prove an impossibility result showing that the standard benchmark used in single-dimensional budget-feasible mechanism design, namely the algorithmic optimum is inadequate in that no budget-feasible mechanism can achieve good approximation relative to this. We identify that the chief underlying issue here is that there could be a monopolist which prevents a budget-feasible mechanism from obtaining good guarantees. Second, we devise an alternate benchmark, $OPT_{Bench}$, that allows for meaningful approximation guarantees, thereby yielding a metric for comparing mechanisms. Third, we devise budget-feasible mechanisms that achieve constant-factor approximation guarantees with respect to this benchmark for XOS valuations.
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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 | 0.009 | 0.020 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.005 | 0.009 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 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".