From Discrete to Continuous Binary Best-Response Dynamics: Discrete Fluctuations Almost Surely Vanish With Population Size
Bibliographic record
Abstract
In binary decision-making, individuals often go for a common or a rare action. In the framework of evolutionary game theory, the best-response update rule can be used to model this dichotomy. Those who prefer the common action are called coordinators or conformists, and those who prefer the rare one are called anticoordinators or nonconformists. A finite mixed population of the two types may undergo perpetual fluctuations, the characterization of which appears to be challenging. It is particularly unknown whether the fluctuations persist as the population size grows. To fill this gap, we approximate the discrete population dynamics of coordinators and anticoordinators with the associated mean dynamics in the form of differential inclusions. We show that the family of state sequences of the discrete dynamics with increasing population sizes forms a generalized stochastic approximation process for the differential inclusion. On the other hand, we show that the differential inclusion always converges to anequilibrium. This implies that the reported perpetual fluctuations in the discrete dynamics of coordinators and anticoordinators almost surely vanish with population size. The results motivate analyzing the often simpler mean dynamics, which partly reveal the asymptotic behavior of the discrete dynamics.
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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 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".