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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] Bondareva O.N., “Nekotorye primeneniya metodov lineinogo programmirovaniya k teorii kooperativnykh igr”, Problemy kibernetiki, 1963, no. 10, 119–140

[2] Morozov V.V., A'zamkhuzhaev M.Kh., “O poiske delezhei diskretnoi kooperativnoi igry”, Primenenie vychislitelnykh sredstv v nauchnykh issledovaniyakh i uchebnom protsesse, Sbornik statei, Izd-vo Mosk. un-ta, M., 1991, 49–62

[3] Morozov V.V., Romanov S.I., “Zadacha ob optimalnom naznachenii kak kooperativnaya igra”, Prikladnaya matematika i informatika, Trudy fakulteta VMK MGU imeni M.V. Lomonosova, 74, MAKS-Press, M., 2023, 19–26

[4] Timokhov A.V., Sukharev A.G., Fedorov V.V., Kurs metodov optimizatsii, Nauka, M., 1986 | MR

[5] Curiel I.J., Cooperative game theory and applications, Ph.D. dissertation, University of Nijmegen, Netherlands, 1988

[6] Kalai E., Zemel E., On totally balanced games and games of flow, Discussion paper No 413, Northwestern University, Illinois, 1980 | MR

[7] Peleg B., Sudhölter P., Introduction to the theory of cooperative games, Springer, Berlin, 2008 | MR

[8] Shapley L.S., On balanced sets and cores, RM-4601-PR, The Rand Corporation, Santa Monica, California, 1965

[9] Shapley L.S., Shubik M., “On Market Games”, Journal of Economic Theory, 1:1 (1969), 9–25 | DOI | MR

[10] Tijs S.H., Parthasarathy T., Potters J.A.M., Rajendra Prasad V., “Permutation games: another class of totally balanced games”, Operations Research Spectrum, 6:2 (1984), 119–123 | DOI | MR | Zbl