Belief Estimation by Agents in Major Minor LQG Mean Field Games
Bibliographic record
Abstract
Obtaining equilibria for stochastic games where agents have independent partial (noisy) observations on the system's state, and each other's control actions, is an open area for general classes of games. This is mainly because agents' strategies may depend on mutual beliefs (estimates) of the beliefs of other agents, which may subsequently lead to an infinite regress where each agent must generate an infinite sequence of mutual beliefs. Consequently finding classes of games which have partial observations and which permit tractable solutions is of significance. In this paper, a result (CDC 2015-2016) for LQG mean field game systems consisting of one major agent and a large number of minor agents where all agents have (private) partial observations is reviewed. It is one of the rare examples of a partially observed game which has a terminating (second order) belief of belief recursion. This is followed by a Nash equilibrium result for LQG mean field game systems consisting of two major agents and a large number of minor agents, where all agents have complete observations. The nature, limitations and possible extensions of this result with partial observations for all the agents are discussed.
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How this classification was reachedexpand
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) | 0.008 | 0.006 |
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; both teacher heads agree on what is shown here.
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".