Almost-Sure Convergence of a Class of Nonautonomous Fictitious Play
Bibliographic record
Abstract
A nonautonomous version of continuous-time fictitious play is considered to achieve global asymptotic stability of a unique Nash equilibrium of a game. The proposed approach to prove global asymptotic stability consists of combining successively in time a continuous-time static fictitious play characterized by a time-varying rate of convergence with a continuous-time proportional derivative fictitious play, which has been recently proposed. Convergence to the basin of attraction of the empirical frequency of the proportional derivative fictitious play, if it exists, is obtained by means of contraction tools, reminiscent of the small-gain theorem, provided a set of inequalities involving the parameter of the continuous-time dynamics is satisfied. Furthermore, a discrete-time fictitious play is derived from its continuous-time counterpart. Convergence with probability one to the unique Nash equilibrium is shown. The approach is illustrated with a modified version of the Shapley game for which the proposed scheme is shown to be convergent to the unique equilibrium with the additional flexibility of selecting the rate of convergence
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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 | 0.004 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".