Bibliographic record
Abstract
It has been previously shown that a finite well-mixed population of individuals imitating the highest earners in a two-strategy game can undergo perpetual fluctuations. However, it remains unknown whether the fluctuations in the population proportions of the two strategies persist as population size grows. In this paper, we answer this question for an imitative population with diagonal anticoordination matrices. We show that the collection of Markov chains corresponding to the population dynamics is a family of generalized stochastic approximation process for a good upper semicontinuous differential inclusion. We additionally show that the differential inclusion always converges to an equilibrium. This convergence, based on the available results in the stochastic approximation theory, implies that the lengths of the fluctuations in the population proportions of the two strategies in a finite population of imitators with diagonal anticoordination payoff matrices vanish with probability one as population size grows. Furthermore, taking the same steps for a population of imitators with diagonal coordination payoff matrices results in a similar conclusion, which is consistent with the previously reported results for finite populations of imitators with coordination payoff matrices. The results suggest that fluctuations are more pronounced in smaller populations of imitators who follow the highest earners.
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How this classification was reachedexpand
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 | 0.001 |
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 teacher head, 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".