Geodesic
Dynamic cost-sharing game with spanning arborescence
Contributions to game theory and management, Tome 15 (2022), pp. 287-302

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This paper presents the dynamic Shapley value for cost-sharing game with spanning arborescence. The cooperative behaviour of players is determined, and a two-stage directed network game is considered. At each stage, a cost matrix associated with the directed network is defined by players adopting strategies, and a minimum cost spanning arborescence on the directed network is determined. After the first stage, a particular player will leave the game with a certain probability, which depends on all players' behaviours in the first stage. The characteristic function is defined. Using the Imputation Distribution Procedure (IDP), the dynamic Shapley value in the game is constructed.
Keywords: directed network, cost sharing game, minimum cost spanning arborescences, dynamic Shapley value. 
@article{CGTM_2022_15_a21,
     author = {Peichen Ye and Yin Li and Ovanes Petrosyan},
     title = {Dynamic cost-sharing game with spanning arborescence},
     journal = {Contributions to game theory and management},
     pages = {287--302},
     publisher = {mathdoc},
     volume = {15},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2022_15_a21/}
}
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Peichen Ye; Yin Li; Ovanes Petrosyan. Dynamic cost-sharing game with spanning arborescence. Contributions to game theory and management, Tome 15 (2022), pp. 287-302. http://geodesic.mathdoc.fr/item/CGTM_2022_15_a21/