Bibliographic record
Abstract
We study the problem of cost minimization in competitive resource allocation problems, motivated by our previous work on power minimization in MIMO interference systems. Our setup leads to a general cost minimization game in which each player wishes to minimize the cost of its resource consumption while achieving a target utility level. In general, the player strategies are coupled through both their cost functions and their utility functions. Equilibrium exists only for a certain set of target utility levels which in general is a proper set of all achievable utility levels. To characterize the set of equilibrium utility levels, we introduce the dual of a cost minimization game called a utility maximization game in which each player wishes to maximize its utility while keeping the cost of its resource consumption below a cost threshold. We associate the set of equilibrium utility levels with the set of equilibrium of the dual game corresponding to all cost thresholds, and show that the dual game always possesses an equilibrium. We also obtain an inner estimate of the set of equilibrium utility levels in the case of decoupled cost functions by a minimax approach. We then relax the hard constraint on achieving a target utility level, and introduce a weighted cost minimization game which always possesses an equilibrium. We recover the original equilibria through the equilibria of the weighted cost minimization game as the penalty on not achieving the target utility levels increases.
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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 | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 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".