Perfect Strategies for Non-Local Games
Bibliographic record
Abstract
We unify and consolidate various results about non-signalling games, a subclass of non-local two-player one-round games, by introducing and studying several new families of games and establishing general theorems about them, which extend a number of known facts in a variety of special cases.Among these families are reflexive games, which are characterised as the hardest non-signalling games that can be won using a given set of strategies.We introduce imitation games, in which the players display linked behaviour, and which contains as subclasses the classes of variable assignment games, binary constraint system games, synchronous games, many games based on graphs, and unique games.We associate a C*-algebra C * (G) to any imitation game G, and show that the existence of perfect quantum commuting (resp.quantum, local) strategies of G can be characterised in terms of properties of this C*-algebra, extending known results about synchronous games.We single out a subclass of imitation games, which we call mirror games, and provide a characterisation of their quantum commuting strategies that has an algebraic flavour, showing in addition that their approximately quantum perfect strategies arise from amenable traces on the encoding C*-algebra.We describe the main classes of non-signalling correlations in terms of states on operator system tensor products.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".