Multiple‐quality Cournot oligopoly and the role of market size
Bibliographic record
Abstract
Abstract We model an oligopoly where firms are allowed to freely enter and exit the market and choose the quality level of their products by incurring different setup costs. Using this framework, we study the mix of firms in the long‐run Cournot–Nash equilibrium under different cost structures and the effects of market size on market outcomes. Specifically, we consider two alternative specifications of cost structure. In the first specification, quality upgrading requires a large increment in the setup cost or R&D investment. Under this cost structure, we show that in the Nash equilibrium, each firm specializes in a single quality level, and an increase in the market size leads to (a) an increase in the fraction of firms that specialize in the high‐quality product, (b) an increase in the market share of the high‐quality product, and (c) a reduction in firms’ markups and in markup dispersion. Under the second type of cost structure where quality upgrading only requires higher marginal cost, we find that all firms will produce both types of product, and the value share of the high‐quality product increases as the market expands, but in quantity terms, the market share of the high‐quality product does not change. Finally, we find that trade liberalization has broadly similar effects to that of a market expansion, but the supply of the high‐quality product from the smaller economy may decrease.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".