Stability of time-dependent elastic Nash equilibrium in oligopolistic markets under perturbation
Bibliographic record
Abstract
In this paper, we consider time-dependent elastic Nash equilibria in oligopolistic markets.Our analysis underlines the perturbation phenomena that should be taken into account in the study of such equilibrium problems.Precisely, there are both internal and external sources generating variations at any time of the commodity shipment between the supply market and the demand market.This also affects, in principle, commodity outputs as well as the commodity at demand markets.Accordingly, the three costs of production, the storage and the transportation, respectively, involved in a such model are perturbed by the same and/or another perturbation.Then, in this work, we first fix the parametric market equilibrium model for our problem, which we characterize by a time-dependent quasi-variational inequality problem what enables us to state and prove our main result on the stability of the parametric equilibrium commodity shipment in question.Our key tools make recourse to recent developments of quasi-equilibrium problems as well as the qualitative stability of fixed points of set-valued maps.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".