Geodesic
On cooperative game in knapsack problem
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 10 (2018) no. 4, pp. 16-29 Cet article a éte moissonné depuis la source Math-Net.Ru

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A knapsack problem with indivisible items as agents is considered. Each agent has certain weight and utility and wants to be in knapsack. Such situation is considered as cooperative game with transferable utility. A characteristic function for such game generalizes bankruptcy problem characteristic function, however, unlike bankruptcy problem case, it is not convex. Nevertheless, it turns out, that the core of such game is not empty. At the end some particular cases are considered. For such cases the Shapley value, $\tau$-value and nucleolus are found in explicit form.
Keywords: knapsack problem, cooperative game, bankruptcy problem, Shapley value, nucleolus
Mots-clés : core, $\tau$-value. 
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     author = {Sergei I. Dotsenko},
     title = {On cooperative game in knapsack problem},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {16--29},
     year = {2018},
     volume = {10},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2018_10_4_a1/}
}
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Sergei I. Dotsenko. On cooperative game in knapsack problem. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 10 (2018) no. 4, pp. 16-29. http://geodesic.mathdoc.fr/item/MGTA_2018_10_4_a1/

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