Finding Nash equilibrium in bimatrix games in zero-error probabilistic polynomial time
Bibliographic record
Abstract
The computational complexity of computing Nash Equilibrium (NE) in two-player games is in randomized polynomial time (RP). In this paper, we propose a novel algorithm that utilizes fuzzification technique and random number generators to calculate NE in two-player games. We demonstrate that the computational complexity of the new algorithm is in the class of zero-error probabilistic polynomial time (ZPP), and the transformation used in the new algorithm is a polynomial time reduction. Three examples are given and shown that the new algorithm outperforms Lemke-Howson (LH) algorithm from the perspective of discovering more NE points and the variety of NE points in two-player games.
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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 | 0.006 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.004 |
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".