On a best response problem arising in mean field stochastic growth games with common noise
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Bibliographic record
Abstract
Abstract This paper analyzes the best response control problem arising in mean field stochastic growth. We consider mean field games in the setting of stochastic growth where each player's capital stock is described by Cobb–Douglas production dynamics subject to stochastic depreciation and common noise. Each individual's utility functional consists of one's own utility and relative utility. Due to random mean field dynamics, the analysis of the best response relies on a stochastic Hamilton–Jacobi–Bellman (SHJB) equation, which in turn derives a special nonlinear backward stochastic differential equation (BSDE). We analyze the BSDE and use it to determine the solution equation system of the mean field game. Further, we extend the analysis to an AK model for the growth dynamics.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 it