Geodesic
Solutions of cooperative differential games with partner sets
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 15 (2023) no. 2, pp. 105-121

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Network differential games with partner sets are considered. The payoff of each player depends on his actions and the actions of the players from his partner set. The article proposes a cooperative version of the game and introduces a special type of characteristic function that takes into account players in partner sets and proves its superadditivity. As a solution, we propose a $C$-core which non-emptiness is proved, as well as a Shapley value and a $\tau$-value.
Keywords: Shapley value, differential network game, partner sets. 
@article{MGTA_2023_15_2_a6,
     author = {Leon A. Petrosyan and Yaroslavna B. Pankratova},
     title = {Solutions of cooperative differential games with partner sets},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {105--121},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2023_15_2_a6/}
}
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Leon A. Petrosyan; Yaroslavna B. Pankratova. Solutions of cooperative differential games with partner sets. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 15 (2023) no. 2, pp. 105-121. http://geodesic.mathdoc.fr/item/MGTA_2023_15_2_a6/