Infinite Horizon Dynamic Games with Coupled State Constraints
Bibliographic record
Abstract
In this paper we investigate the existence of equilibrium solutions to a class of infinite-horizon differential games with a coupled state constraint. These differential games typically represent dynamic oligopoly models where each firm controls its own dynamics (decoupled controls). In the absence of a coupled state constraint, the interactions among players take place essentially in the objective function. The introduction of a coupled state constraint in such models can be motivated, for example, by the consideration of a global environmental constraint imposed on competing firms. Our approach for the characterization of asymptotic equilibria under such a constraint is an adaptation of Rosen’s normalized equilibrium concept [10] to this infinite-horizon dynamic game framework. We utilize the Turnpike property and the notion of an attracting normalized steady-state equilibrium for the definition of a time invariant multiplier to provide conditions for the existence of dynamic equilibria. We consider discounted and undiscounted dynamic game models in our investigation. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".