TY - JOUR

T1 - About One Differential Game on Hypergraph

AU - Тур, Анна Викторовна

AU - Тантлевский, Игорь Романович

N1 - ISSN 1064-5624, Doklady Mathematics, 2025, Vol. 112, No. 4, pp. 698–704. © Pleiades Publishing, Ltd., 2025

PY - 2026/4/16

Y1 - 2026/4/16

N2 - Abstract: A cooperative differential game on a hypergraph is considered. A characteristic function of special type is introduced taking into account the network structure of the game, and its properties are studied. The Shapley value is used as a cooperative optimality principle. For games on hypergraphs with a cycle-free line graph, an explicit formula for the Shapley value is obtained. An illustrative example is considered.

AB - Abstract: A cooperative differential game on a hypergraph is considered. A characteristic function of special type is introduced taking into account the network structure of the game, and its properties are studied. The Shapley value is used as a cooperative optimality principle. For games on hypergraphs with a cycle-free line graph, an explicit formula for the Shapley value is obtained. An illustrative example is considered.

KW - differential games, cooperative games, games on networks, games on hypergraphs, characteristic

KW - differential games, cooperative games, games on networks, games on hypergraphs, characteristic function, Shapley value, network models, Judea

KW - cooperative games

KW - network models

KW - Shapley value

KW - differential games

KW - characteristic function

KW - games on hypergraphs

KW - games on networks

UR - https://www.mendeley.com/catalogue/9cf7b922-7c97-31aa-a43c-1f8aa8611482/

U2 - 10.1134/s1064562425601052

DO - 10.1134/s1064562425601052

M3 - Article

VL - 112

SP - S60-S66

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - Suppl 1

ER -