Value‐based distance between information structures
Bibliographic record
Abstract
We define the distance between two information structures as the largest possible difference in value across all zero‐sum games. We provide a tractable characterization of distance and use it to discuss the relation between the value of information in games versus single‐agent problems, the value of additional information, informational substitutes, complements, or joint information. The convergence to a countable information structure under value‐based distance is equivalent to the weak convergence of belief hierarchies, implying, among other things, that for zero‐sum games, approximate knowledge is equivalent to common knowledge. At the same time, the space of information structures under the value‐based distance is large: there exists a sequence of information structures where players acquire increasingly more information, and ε > 0 such that any two elements of the sequence have distance of at least ε . This result answers by the negative the second (and last unsolved) of the three problems posed by Mertens in his paper “Repeated Games” (1986).
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 | 0.007 | 0.045 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.006 | 0.013 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".