Comparing the structure of probabilistic 4- and 8-state finite transducer representations for Prisoner's Dilemma
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Bibliographic record
Abstract
The fingerprint is a mathematical tool that turns a game-playing strategy into a representation-independent functional summary of its behaviour; several studies have used this to enable massive computational analyses of entire spaces of strategies. This study extends further by directly comparing two large (on the order of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">96</sup> ) state spaces, grids over the probabilistic 4- and 8-state finite transducers, as representations for playing iterated Prisoner's Dilemma. We take uniformly random samples of size 65,536 from each, fingerprint each strategy in both samples, and compute all pairwise distances within each sample. Hierarchical clustering reduces each distance matrix to size 16,384 for embedding into Euclidean space with multidimensional scaling. Results indicate that several important dimensions are strongly preserved between the representations, and we can quantify them. We additionally find an important theoretical construct, two strategies that are not identical in behaviour, but with the same fingerprint: Random and periodic (CDDC).
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it