Geodesic
Lion and Man game and fixed point free maps
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 9 (2017) no. 2, pp. 105-120

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This work is related with pursuit-evasion game where Lion is the pursuer and Man is the evader. We suppose that both players move in a metric space, have equal maximum speeds and complete information about the location of each other. We say that Man wins if he can escape a capture with non-zero radius; more precisely if there exists a positive number p and a non-anticipative strategy for some players' initial positions, that let him always be out of Lion's p-neighbourhood. We study sufficient conditions of the existence of Man's winning strategy. In this way we use the metric properties of space (mainly geodesics' behavior and fixed-point free maps). The technique requires neither convexity nor finite dimension of a space.
Keywords: pursuit-evasion game, lion and man game, fixed point, geodesic loop. 
@article{MGTA_2017_9_2_a3,
     author = {Olga O. Yufereva},
     title = {Lion and {Man} game and fixed point free maps},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {105--120},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2017_9_2_a3/}
}
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Olga O. Yufereva. Lion and Man game and fixed point free maps. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 9 (2017) no. 2, pp. 105-120. http://geodesic.mathdoc.fr/item/MGTA_2017_9_2_a3/