Polynomial-time Computation of Exact Correlated Equilibrium in Compact\n Games
Bibliographic record
Abstract
In a landmark paper, Papadimitriou and Roughgarden described a\npolynomial-time algorithm ("Ellipsoid Against Hope") for computing sample\ncorrelated equilibria of concisely-represented games. Recently, Stein, Parrilo\nand Ozdaglar showed that this algorithm can fail to find an exact correlated\nequilibrium, but can be easily modified to efficiently compute approximate\ncorrelated equilibria. Currently, it remains unresolved whether the algorithm\ncan be modified to compute an exact correlated equilibrium. We show that it\ncan, presenting a variant of the Ellipsoid Against Hope algorithm that\nguarantees the polynomial-time identification of exact correlated equilibrium.\nOur new algorithm differs from the original primarily in its use of a\nseparation oracle that produces cuts corresponding to pure-strategy profiles.\nAs a result, we no longer face the numerical precision issues encountered by\nthe original approach, and both the resulting algorithm and its analysis are\nconsiderably simplified. Our new separation oracle can be understood as a\nderandomization of Papadimitriou and Roughgarden's original separation oracle\nvia the method of conditional probabilities. Also, the equilibria returned by\nour algorithm are distributions with polynomial-sized supports, which are\nsimpler (in the sense of being representable in fewer bits) than the mixtures\nof product distributions produced previously; no tractable algorithm has\npreviously been proposed for identifying such equilibria.\n
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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".