Can Mean Field Game Equilibria Amongst Exchangeable Agents Survive Under Partial Observability of Their Competitors' States?
Bibliographic record
Abstract
Classical mean field games (MFG) have been concerned with large games amongst symmetrically influential agents with asymptotically negligible weight. In the absence of a common driving noise, propagation of chaos occurs. The analysis assumes that the initial agent's state probability distribution is known, making its future deterministic and computable via a fixed-point calculation under a limiting equilibrium policy, if it exists. However, oftentimes, despite equal mutual influence, a given agent can only observe a limited number of neighboring agents due to the agent observability structure characterized by an information access graph. This graph may have a low degree even with a large number of agents. The main question addressed is whether an MFG equilibrium can still potentially emerge asymptotically over time. The answer is affirmative, contingent on specific conditions that rely on the stability properties of agents' dynamics and the relative speed of communication to reactions, as derived in this study. The focus is on independent linear scalar agents correlated through a quadratic cost related to the mean state of the agents, which remains unobservable. To tackle convergence to a mean field equilibrium, the proposed model involves a fast communication time scale using a consensus algorithm, alongside a slower agent dynamic time scale. The research explores agents' ability to accurately estimate the system mean as both time and agent numbers increase.
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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 | 0.022 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 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".