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- W1991783184 abstract "In the cookie-cutter game, there is a trapping circle, of radius 1, in which an evader hides. A searcher has a “cookie-cutter”, a disk of radius r < 1. If, when he places the cookie-cutter on the trapping circle, the evader is within it, the evader is caught and the searcher wins. Otherwise the evader wins. If r = √2/2, the problem is trivial. The evader should choose a point from the uniform distribution on the outer circumference of the trapping circle, and the searcher a point from the uniform distribution on the circle of radius r * = (1 − r 2 ) 1/2 concentric to that circle; this choice gives him maximum coverage of the outer circumference. For the case r ≧ 1/2, an easy and elegant solution was given by Gale and Glassey in 1974. Both players should go to the center with probability 1/7. The minimizer should go to the outer circumference, and the maximizer to r * = √3/2, both with probability 6/7. For other r the problem is difficult. This paper proves that there are no solutions based on finitely many radii if r < r 0 ≐ 0.476, where r 0 solves a cubic equation, finds two-point solutions on [r 0 , r 1 ], where r 1 ≐ 0.515 solves a trigonometric equation, and proves qualitative facts for r ∈ (r 1 , √2/2)." @default.
- W1991783184 created "2016-06-24" @default.
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- W1991783184 date "1990-11-01" @default.
- W1991783184 modified "2023-09-23" @default.
- W1991783184 title "On the Cookie-Cutter Game: Search and Evasion on a Disc" @default.
- W1991783184 cites W2061620049 @default.
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- W1991783184 doi "https://doi.org/10.1287/moor.15.4.573" @default.
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