Geodesic
New characteristic function for two stage games with spanning tree
Contributions to game theory and management, Tome 14 (2021), pp. 59-71

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Two-stage $n$-player games with spanning tree are considered. The cooperative behaviour of players is defined. After the first stage, a specified player leaves the game with a probability that depends on the actions of all players in the first stage. A new approach to the construction of the characteristic function is proposed. In the game, all players are connected with the source directly or indirectly. Assume that the players in coalition $N\setminus S$ have already connected to the source when the players in coalition $S\subset N$ wish to connect to the source. The players in coalition $S$ could connect to the source with the help of the players in coalition $N\setminus S$. A new characteristic function is defined in the game, and the Shapley value is constructed. Several results based on the new characteristic function in the two-stage stochastic game are given.
Keywords: dynamic game, minimum cost spanning tree, Shapley value. 
@article{CGTM_2021_14_a5,
     author = {Min Cheng and Yin Li},
     title = {New characteristic function for two stage games with spanning tree},
     journal = {Contributions to game theory and management},
     pages = {59--71},
     publisher = {mathdoc},
     volume = {14},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2021_14_a5/}
}
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Min Cheng; Yin Li. New characteristic function for two stage games with spanning tree. Contributions to game theory and management, Tome 14 (2021), pp. 59-71. http://geodesic.mathdoc.fr/item/CGTM_2021_14_a5/