Play profiles: The effect of infinite-length games on evolution in the iterated Prisoner's Dilemma
Bibliographic record
Abstract
It is well-known that the correct strategy in iterated Prisoner's Dilemma with a finite known number of rounds is to always defect. Evolution of Prisoner's Dilemma playing agents mirrors this: the more rounds the agents play against each other per encounter, the more likely the population will evolve to a cooperative state. Prior work has demonstrated that the result of evolution changes dramatically from very short games up to about 60-85 rounds, which yields substantially similar populations as those using 150 rounds. We extend this study using more powerful statistical tests and mathematical tools, including fingerprinting and play profiles, to consider the problem in the opposite direction: as the correct strategy in infinitely iterated Prisoner's Dilemma is to always cooperate, how many rounds are needed until evolution reflects this empirically? Within a very large plateau, from around 150 to a million rounds, evolution does not significantly change its behaviour. Surprisingly, behaviour does change again from millions to billions of rounds, but not further from billions to infinite-round games. This suggests that evolution operates on nontrivial categories of cooperativity depending on the number of rounds and the details of the representation.
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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 | 0.027 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".