Comparison of Information Structures for Zero-Sum Games in Standard Borel Spaces
Bibliographic record
Abstract
In statistical decision theory involving a single decision-maker, one says that an information structure is better than another one if for any cost function involving a hidden state variable and an action variable which is restricted to be only a function of some measurement, the solution value under the former is not worse than the value under the latter. For finite probability spaces, Blackwell's celebrated theorem on comparison of information structures leads to a complete characterization on when one information structure is better than another. For stochastic games with incomplete information, due to the presence of competition among decision makers, in general such an ordering is not possible since additional information can lead to equilibria perturbations with positive or negative values to a player. However, for zero-sum games in a finite probability space, Peski introduced a complete characterization of ordering of information structures. In this paper, we obtain an infinite dimensional (standard Borel) generalization of Peski's result. A corollary of our analysis is that more information cannot hurt a decision maker taking part in a zero-sum game in standard Borel spaces. During our analysis, we establish two novel supporting results: (i) a refined existence result for equilibria in zero-sum games with incomplete information when compared with the prior literature and ii) a partial converse to Blackwell's ordering of information structures in the standard Borel space setup.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.009 | 0.029 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.005 | 0.009 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| 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".