Mean Field (NCE) stochastic control: Populations of major and egoist-altruist agents
Bibliographic record
Abstract
For noncooperative games the Nash Certainty Equivalence (NCE), or Mean Field (MF) methodology [1], [2] provides decentralized strategies which asymptotically yield Nash equilibria. An extension of this theory to populations of altruistic agents (defined with so-called social cost functions) and to mixed populations was carried out in [3], and a theory treating populations of egoistic agents and one or more so-called major agents was developed in [4]. In this paper we study the equilibria and the overall stability of dynamic LQG games, where (i) there is a single major agent and a large population of mixed minor agents, and (ii) the cost for each minor agent is a convex combination of its own cost and the social cost of the minor agents. We analyse the resulting equilibria, provide experimental results, and present a mean field stochastic control algorithm, which when applied by all agents in the system, gives rise to system behaviour where (i) all agents systems are L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> stable, (ii) the set of controls yields an ε-Nash equilibrium for all ε, and (iii) if each minor agent in the system only considers the social cost, then the difference between (i) the cost observed by each minor agent and (ii) the social cost that would be observed if a centralized controller minimizes the social cost tends to zero as the population size grows to infinity.
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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 | 0.000 | 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) | 0.002 | 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 teacher head, 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".