Lion and Man Game in Compact Spaces

Olga Yufereva ()
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Olga Yufereva: Krasovskii Institute of Mathematics and Mechanics UrB RAS

Dynamic Games and Applications, 2019, vol. 9, issue 1, No 12, 292 pages

Abstract: Abstract The pursuit-evasion game with two persons is considered. Both players are moving in a metric space, have equal maximum speeds and complete information about the location of each other. We study the sufficient conditions for a capture (with a positive capture radius). We assume that Lion wins if he manages the capture independently of the initial positions of the players and the evader’s strategy. We prove that the discrete-time simple pursuit strategy is a Lion’s winning strategy in a compact geodesic space satisfying the betweenness property. In particular, it means that Lion wins in compact CAT(0)-spaces, Ptolemy spaces, Buseman convex spaces, or any geodesic space with convex metric. We also do not need to use such properties as finite dimension, smoothness, boundary regularity, or contractibility of the loops.

Keywords: Pursuit-evasion game; Lion-and-man game; Simple pursuit; Betweenness; Convex metrics; 91A23; 91A24; 49N75; 53C22 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13235-018-0239-9

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