Geodesic
Solutions for cooperative games with a~major player and a~hierarchical structure
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 11 (2019) no. 3, pp. 77-94

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In this paper, we adapt two well-known solutions for cooperative games with an exogenously given cycle-free communication graph structure (the average tree solution and the Myerson value) to the game with a major player. A comparative analysis of such solutions is carried out for special graphs — a star and a complete $k$-ary tree.
Keywords: cooperative game, tree graph, major player, the average tree solution, the Myerson value. 
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     author = {Artem A. Sedakov and Vitaly A. Sorokin},
     title = {Solutions for cooperative games with a~major player and a~hierarchical structure},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {77--94},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2019_11_3_a5/}
}
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Artem A. Sedakov; Vitaly A. Sorokin. Solutions for cooperative games with a~major player and a~hierarchical structure. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 11 (2019) no. 3, pp. 77-94. http://geodesic.mathdoc.fr/item/MGTA_2019_11_3_a5/