ε-Nash equilibria for a partially observed mean field game with major player
Bibliographic record
Abstract
Consider a dynamic game with a population of N minor agents, where N is very large, and a major agent where the agents are coupled in their nonlinear dynamics and cost functions such that even asymptotically as the population size goes to infinity the major agent has a non-vanishing effect on the minor agents. Such games are referred to as mean field games with major-minor agents (MM-MFG) and for MM-MFG, it has been demonstrated the mean field term is stochastic and the best response control actions of the minor agents depend on the state of the major agent as well as this stochastic mean field. In practical applications one is led to consider the situation where the minor agents partially observe (PO) the state of the major agent. In this work, we consider a restricted case of this scenario and demonstrate that in the case the minor agents are coupled to the major agent only through their cost functions, one can obtain the ε-Nash equilibrium property for the PO-MM-MFG best response control actions as the population size N goes to infinity.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".