Comparison of Information Structures for Zero-Sum Games and a Partial\n Converse to Blackwell Ordering in Standard Borel Spaces
Bibliographic record
Abstract
In statistical decision theory involving a single decision-maker, an\ninformation structure is said to be better than another one if for any cost\nfunction involving a hidden state variable and an action variable which is\nrestricted to be conditionally independent from the state given some\nmeasurement, the solution value under the former is not worse than that under\nthe latter. For finite spaces, a theorem due to Blackwell leads to a complete\ncharacterization on when one information structure is better than another. For\nstochastic games, in general, such an ordering is not possible since additional\ninformation can lead to equilibria perturbations with positive or negative\nvalues to a player. However, for zero-sum games in a finite probability space,\nP\\k{e}ski introduced a complete characterization of ordering of information\nstructures. In this paper, we obtain an infinite dimensional (standard Borel)\ngeneralization of P\\k{e}ski's result. A corollary is that more information\ncannot hurt a decision maker taking part in a zero-sum game. We establish two\nsupporting results which are essential and explicit though modest improvements\non prior literature: (i) a partial converse to Blackwell's ordering in the\nstandard Borel setup and (ii) an existence result for equilibria in zero-sum\ngames with incomplete information.\n
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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 | 0.005 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.005 | 0.008 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".