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Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2018, Volume 10, Issue 4, Pages 16–29
(Mi mgta225)
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On cooperative game in knapsack problem
Sergei I. Dotsenko National Taras Shevchenko University of Kyiv, Faculty of Computer Science and Cybernetics
Abstract:
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, τ-value and nucleolus are found in explicit form.
Keywords:
knapsack problem, cooperative game, bankruptcy problem, core, Shapley value, nucleolus, τ-value.
Citation:
Sergei I. Dotsenko, “On cooperative game in knapsack problem”, Mat. Teor. Igr Pril., 10:4 (2018), 16–29; Automation and Remote Control, 80:9 (2019), 1734–1744
Linking options:
https://www.mathnet.ru/eng/mgta225 https://www.mathnet.ru/eng/mgta/v10/i4/p16
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Statistics & downloads: |
Abstract page: | 250 | Full-text PDF : | 317 | References: | 30 |
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