Geodesic
A note on cooperative differential games with pairwise interactions
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 20 (2024) no. 1, pp. 91-108

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In this paper, a differential game with pairwise interaction in a network is proposed. For explicitly, the vertices are players, and the edges are connections between them. Meanwhile, we consider the cooperative case. One special characteristic function is introduced and its convexity is proved. The core is used as a cooperative optimality principle. The characteristic function allows the construction of a time-consistent (dynamically stable) solutions, such as the Shapley value and the core. Finally, the results are illustrated by an example.
Keywords: cooperative games, differential network games, pairwise interactions, characteristic function, the Shapley value, time-consistency. 
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     title = {A note on cooperative differential games with pairwise interactions},
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Ya. He; L. A. Petrosyan. A note on cooperative differential games with pairwise interactions. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 20 (2024) no. 1, pp. 91-108. http://geodesic.mathdoc.fr/item/VSPUI_2024_20_1_a7/