A NEW SEQUENCE FORM APPROACH FOR THE ENUMERATION AND REFINEMENT OF ALL EXTREME NASH EQUILIBRIA FOR EXTENSIVE FORM GAMES
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Bibliographic record
Abstract
This paper presents two new results on the enumeration of all extreme equilibria of the sequence form of a two person extensive game. The sequence form of an extensive game is expressed, for the first time to our knowledge, as a parametric linear 0 - 1 program. Considering Ext(P) as the set of all of the sequence form extreme Nash equilibria and Ext(Q) as the set of all the parametric linear 0 - 1 program extreme points, we show that Ext(P) ⊆ Ext(Q). Using exact arithmetics classes, the algorithm EχMIP Belhaiza (2002); Audet et al. (2006) is extended to enumerate all elements of Ext(Q). A small procedure is then applied in order to obtain all elements of Ext(P).
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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 | 0.004 | 0.002 |
| 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 | 0.001 | 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