Abstract
The game of degree is analyzed in a surveillance-evasion problem: the evader strives to escape as soon as possible from the pursuer's detection circle, while the pursuer's desire is the opposite. The evader moves with constant speed and is capable of instantaneous direction changes. The pursuer has a minimum turn-radius, independent of speed, and can move forward with any speed not exceeding a maximum greater than the evader's speed.
The solution is surprisingly complex, including regions where the pursuer's speed is optional,switch envelopes, focal lines, as well aschattering by the pursuer to prevent the crossing of certainbarriers.
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References
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Lewin, J., Breakwell, J.V. The surveillance-evasion game of degree. J Optim Theory Appl 16, 339–353 (1975). https://doi.org/10.1007/BF01262940
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DOI: https://doi.org/10.1007/BF01262940