Geodesic
A method for estimating the core of root game
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 2 (2010) no. 1, pp. 3-26

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It is showen that the base of grand (shadow) subcore coincides with the core of the root game in any TU-cooperative game. Comparing definitions of grand subcore and grand shadow subcore with description of aggregate-monotonic core leads to the formal geometrical coincidence of aggregate-monotonic core with either grand subcore or grand shadow subcore. The method for estimating the simplest set of equations and inequalities describing the core of a root game in TU-game with any number of players ($n\ge3$) is proposed. To develop the method dual theory and inductive method by B. Peleg are used.
Keywords: TU-cooperative game, grand (shadow) subcore, root game, aggregate-monotonic core, linear programming, balanced collection of coalitions.
Mots-clés : core 
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     author = {Arina N. Akimova and Viktor V. Zakharov},
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     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
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     number = {1},
     year = {2010},
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Arina N. Akimova; Viktor V. Zakharov. A method for estimating the core of root game. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 2 (2010) no. 1, pp. 3-26. http://geodesic.mathdoc.fr/item/MGTA_2010_2_1_a0/