Bibliographic record
Abstract
We discuss the problem of setting prices in an electronic market that has more than one buyer. We assume that there are self-interested sellers each selling a distinct item that has an associated cost. Each buyer has a submodular valuation for purchasing any subset of items. The goal of the sellers is to set a price for their item such that their profit from possibly selling their item to the buyers is maximized. Our most comprehensive results concern a multi copy setting where each seller has m copies of their item and there are m buyers. In this setting, we give a necessary and sufficient condition for the existence of market clearing pure Nash equilibrium. We also show that not all equilibria are market clearing even when this condition is satisfied contrary to what was shown in the case of a single buyer in [2]. Finally, we investigate the pricing problem for multiple buyers in the limited supply setting when each seller only has a single copy of their item.
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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 | 0.003 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.004 | 0.003 |
| Insufficient payload (model declined to judge) | 0.014 | 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".