The Ebbs and Flows of the Game: Multiple Equilibria in a Sports League Model
Why this work is in the frame
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Bibliographic record
Abstract
The history of professional sports leagues is rich with examples of clubs that enjoy success on the field for a number of seasons, only to fall back in subsequent seasons. Although some clubs achieve consistent success, and a few, consistent failure, most clubs display a cyclical pattern as they ‘‘make a run’’ for success, then take fallback positions. This behavior is difficult to explain using the now standard league model of Fort and Quirk. In this article, the authors discuss the likelihood of this cyclical behavior emerging in the standard model and then develop an extension to the model, which can generate movements between good (team success) and bad (team failure) equilibria. The authors then discuss the stability conditions for each equilibrium and the conditions under which a club might find one of these equilibria unsustainable in the long run.
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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 | 0.001 | 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