Robust Incentive Stackelberg Games With a Large Population for Stochastic Mean-Field Systems
Bibliographic record
Abstract
A static output feedback (SOF) strategy for robust incentive Stackelberg games with a large population for mean-field stochastic systems is investigated. First, the saddle point equilibrium condition of external disturbance and control strategy is derived based on stochastic algebraic matrix equations (SAMEs). Then, a centralized SOF incentive Stackelberg strategy is derived through restructuring the follower’s strategies and the leader’s incentive strategy. Moreover, to avoid the high dimension of design procedure, a new designing algorithm of low-dimensional approximation SOF incentive Stackelberg strategy is proposed. It is shown that the difference in the equilibrium values between using the centralized SOF incentive Stackelberg strategy and using the low-dimensional approximation SOF incentive Stackelberg strategy is$O(\sqrt {\varepsilon })=O(1/\sqrt {N})$, where$N$denotes the population size. Finally, a numerical example with a large population size demonstrates the effectiveness of the proposed approximation SOF incentive Stackelberg strategy.
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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 | 0.003 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| 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".