Geodesic
On integer imputations of the core of totally balanced cooperative games
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 16 (2024) no. 2, pp. 29-44

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We consider totally balanced cooperative games in which the characteristic function takes integer values. It has been proven that any three- and four-person game has an integer imputation from the core. A similar result, with the exception of one degenerated case, was obtained for five-person game. The method of construction of mentioned integer imputation is indicated. An example of a five-person game is given in which the core consists of a single non-integer imputation.
Keywords: totally balanced cooperative game, core of a cooperative game, balanced collection, characteristic function with integer values
Mots-clés : integer imputation. 
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     author = {Vladimir V. Morozov and Saryal I. Romanov},
     title = {On integer imputations of the core of totally balanced cooperative games},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {29--44},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2024_16_2_a2/}
}
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Vladimir V. Morozov; Saryal I. Romanov. On integer imputations of the core of totally balanced cooperative games. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 16 (2024) no. 2, pp. 29-44. http://geodesic.mathdoc.fr/item/MGTA_2024_16_2_a2/