Parameterizing the winner determination problem for combinatorial auctions
Bibliographic record
Abstract
Combinatorial auctions (CAs) have been studied by the multiagent systems community for some time, since these auctions are an effective mechanism for resource allocation when agents are self-interested. One challenge, however, is that the winner-determination problem (WDP) for combinatorial auctions is NP-hard in the general case. However, there are ways to leverage meaningful structure in the auction so as to achieve a polynomial-time algorithm for the WDP. In this paper, using the formal scope of parameterized complexity theory, we systematically investigate alternative parameterizations of the bids made by the agents (i.e. the input to the WDP for combinatorial auctions) and are able to determine when a parameterization reduces the complexity of the WDP (fixed-parameter tractable), and when a particular parameterization results in the WDP remaining hard (fixed-parameter intractable). Our results are relevant to auction designers since they provide information as to what types of bidding-restrictions are effective for simplifying the winner determination problem, and which would simply limit the expressiveness of the agents while not providing any additional computational gains.
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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 | 0.047 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.005 | 0.012 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.003 | 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".