Geodesic
A pursuit-evasion differential game with slow pursuers on the edge graph of simplexes.~I
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 12 (2020) no. 4, pp. 7-23

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We consider the differential game between several pursuing points and one evading point moving along the graph of edges of a simplex when maximal quantities of velocities are given. The normalization of the game in the sense of J. von Neumann including the description of classes of admissible strategies is exposed. In the present part of the paper the qualitative problem for the full graph of three dimensional simplex is solved using the strategy of parallel pursuit for a slower pursuer and some numerical coefficient of a simplex characterizing its proximity to the regular one. Next part will be devoted to higher dimensional cases.
Keywords: differential game, game on a graph, pursuit problem, evasion problem, П-strategy, coefficient of regularity of a simplex, full graph. 
@article{MGTA_2020_12_4_a1,
     author = {Abdulla A. Azamov and Tolanbay T. Ibaydullayev},
     title = {A pursuit-evasion differential game with slow pursuers on the edge graph of {simplexes.~I}},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {7--23},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2020_12_4_a1/}
}
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Abdulla A. Azamov; Tolanbay T. Ibaydullayev. A pursuit-evasion differential game with slow pursuers on the edge graph of simplexes.~I. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 12 (2020) no. 4, pp. 7-23. http://geodesic.mathdoc.fr/item/MGTA_2020_12_4_a1/