Infinite Horizon Dynamic Games with Coupled State Constraints
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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.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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 it