An Isochron-Based Solution to the Target Defense Game Against a Faster Invader
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Bibliographic record
Abstract
This letter studies a target defense game between two defenders and a faster moving invader. We propose a novel approach that solves the saddle point strategy from a family of time-to-capture isochrons. We show that the game can be viewed as a pursuit-evasion game between the invader and the isochrons, where the latter are controlled by the defenders. The optimal defending strategy is the one that forces the invader to isochrons with shorter time-to-capture most efficiently. The proposed method is validated in a special case with zero capture range, where we prove that the saddle point strategy is optimal regardless of other players' behaviors. In addition, the isochrons are shown to be semipermeable, and the barrier of the target defense game is solved.
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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