Price of anarchy bounds for core-selecting mechanisms
Bibliographic record
Abstract
Core-selecting auction mechanisms are auctions that select player utilities which satisfy certain stability properties. They are currently of theoretical and practical interest in mechanism design, having already been used to conduct multi-billion dollar auctions. We generalize the concept of a Core-selecting auction mechanism to a large class of complete information games and demonstrate that several well-known games can be described by these Core-selecting mechanisms. Our main result is a bound on the Price of Anarchy of Core-selecting mechanisms. Provided some simple conditions are met, there are Core-selecting mechanisms with Price of Anarchy at most 1 + 1/D^2, where D in [0,1] is a measure of the degree of submodularity of the game's social welfare function, expressed as a set function. In addition to this result, we show that there exist special Core-selecting mechanisms which have two additional properties: they are player-Pareto optimal and they provide a local, individual utility guarantee.
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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 | 0.015 | 0.069 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.005 | 0.012 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.004 | 0.008 |
| Insufficient payload (model declined to judge) | 0.011 | 0.001 |
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".