Some new results in open and closed-loop linear-quadratic differential games
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Bibliographic record
Abstract
The object of this paper is to revisit the results of P. Bernhard (J. Optim. Theory Appl. 27 (1979), 51-69) on two-person zero-sum linear quadratic differential games and generalize them to utility functions without positivity assumptions on the matrices acting on the state variable in the utility function and to linear dynamics with bounded measurable data matrices. We consider both open and closed loop strategies. We specialize to state feedback via Lebesgue measurable affine closed loop strategies with possible non L2- integrable singularities. We review recent results in the finite dimensional case and provide a classification of closed loop saddle points in terms of the convexity/concavity properties of the utility function and the open loop lower value, upper value, and value of the game. We single out finite dimensional concepts such as normality and normalizability that do not carry over to evolution equations in infinite dimensional spaces.
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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 | 0.000 | 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