Optimal Solutions to Infinite-Player Stochastic Teams and Mean-Field\n Teams
Bibliographic record
Abstract
We study stochastic static teams with countably infinite number of decision\nmakers, with the goal of obtaining (globally) optimal policies under a\ndecentralized information structure. We present sufficient conditions to\nconnect the concepts of team optimality and person by person optimality for\nstatic teams with countably infinite number of decision makers. We show that\nunder uniform integrability and uniform convergence conditions, an optimal\npolicy for static teams with countably infinite number of decision makers can\nbe established as the limit of sequences of optimal policies for static teams\nwith $N$ decision makers as $N \\to \\infty$. Under the presence of a symmetry\ncondition, we relax the conditions and this leads to optimality results for a\nlarge class of mean-field optimal team problems where the existing results have\nbeen limited to person-by-person-optimality and not global optimality (under\nstrict decentralization). In particular, we establish the optimality of\nsymmetric (i.e., identical) policies for such problems. As a further condition,\nthis optimality result leads to an existence result for mean-field teams. We\nconsider a number of illustrative examples where the theory is applied to\nsetups with either infinitely many decision makers or an infinite-horizon\nstochastic control problem reduced to a static team.\n
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".