Mixed Market Structure and R &D: A Differential Game Approach
Bibliographic record
Abstract
Abstract We consider a dynamic model of an industry consisting of a few large firms, which can manipulate the market outcome, and a mass of small enterprises, each of which has a negligible impact on the market. The production costs of the respective firms depend on the stock of knowledge capital, which accumulates over time through research and development (R &D) investment made by large firms. The model is a variant of the differential game of voluntary provision of public goods, but in contrast to previous studies, we focus on the interaction between market competition and dynamic game outcomes. We derive both open-loop and Markov-perfect Nash equilibria. There exists a unique open-loop Nash equilibrium. By contrast, depending on the parameters of the model, there can be two linear Markov-perfect Nash equilibria. We also examine the short- and long-run effects of a change in the number of large firms. An increase in the number of large firms unambiguously harms both types of firms in the short run but may benefit them in the long run. In the open-loop Nash equilibrium, the relationship between the number of large firms and the steady-state stock of knowledge capital is inverted-U shaped. Concerning the Markov-perfect Nash equilibria, the effect of increased competition from large firms depends on the specific feedback strategy chosen in equilibrium.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 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".