Long-term implementation of the cooperative solution in a multistage multicriteria game
In order to find an optimal and time consistent cooperative path in multicriteria multistage game the minimal sum of relative deviations rule is introduced. Using this rule one can construct a vector-valued characteristic function that is weakly superadditive. The sustainability of the cooperative a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2019-01-01
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| Series: | Operations Research Perspectives |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S221471601830321X |
| _version_ | 1818109673791815680 |
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| author | Denis Kuzyutin Nadezhda Smirnova Ekaterina Gromova |
| author_facet | Denis Kuzyutin Nadezhda Smirnova Ekaterina Gromova |
| author_sort | Denis Kuzyutin |
| collection | DOAJ |
| description | In order to find an optimal and time consistent cooperative path in multicriteria multistage game the minimal sum of relative deviations rule is introduced. Using this rule one can construct a vector-valued characteristic function that is weakly superadditive. The sustainability of the cooperative agreement is ensured by using an imputation distribution procedure (IDP) based approach.We formulate the conditions an IDP should satisfy to guarantee that the core is strongly time consistent (STC). Namely, if the imputation distribution procedure for the Shapley value satisfies the efficiency condition, the strict balance condition and the strong irrational-behavior-proof condition, given that the Shapley value belongs to the core of each subgame along the cooperative path, it can be used as a “supporting imputation” which guarantees that the whole core is STC. We discuss three payment schedules and check whether they can be used as supporting imputation distribution procedures for the considered multicriteria game. Keywords: Dynamic game, Multiple criteria decision making, Multicriteria game, Strong time consistency, Shapley value, Cooperative solution |
| first_indexed | 2024-12-11T02:35:00Z |
| format | Article |
| id | doaj.art-d81f902337ab44b28c9ab393fd0aad56 |
| institution | Directory Open Access Journal |
| issn | 2214-7160 |
| language | English |
| last_indexed | 2024-12-11T02:35:00Z |
| publishDate | 2019-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Operations Research Perspectives |
| spelling | doaj.art-d81f902337ab44b28c9ab393fd0aad562022-12-22T01:23:45ZengElsevierOperations Research Perspectives2214-71602019-01-016Long-term implementation of the cooperative solution in a multistage multicriteria gameDenis Kuzyutin0Nadezhda Smirnova1Ekaterina Gromova2Saint Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg, 199034, Russia; National Research University Higher School of Economics (HSE), Soyuza Pechatnikov ul. 16, St. Petersburg, 190008, RussiaSaint Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg, 199034, Russia; National Research University Higher School of Economics (HSE), Soyuza Pechatnikov ul. 16, St. Petersburg, 190008, Russia; Corresponding author at: National Research University Higher School of Economics (HSE), Soyuza Pechatnikov ul. 16, St. Petersburg, 190008, Russia.Saint Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg, 199034, RussiaIn order to find an optimal and time consistent cooperative path in multicriteria multistage game the minimal sum of relative deviations rule is introduced. Using this rule one can construct a vector-valued characteristic function that is weakly superadditive. The sustainability of the cooperative agreement is ensured by using an imputation distribution procedure (IDP) based approach.We formulate the conditions an IDP should satisfy to guarantee that the core is strongly time consistent (STC). Namely, if the imputation distribution procedure for the Shapley value satisfies the efficiency condition, the strict balance condition and the strong irrational-behavior-proof condition, given that the Shapley value belongs to the core of each subgame along the cooperative path, it can be used as a “supporting imputation” which guarantees that the whole core is STC. We discuss three payment schedules and check whether they can be used as supporting imputation distribution procedures for the considered multicriteria game. Keywords: Dynamic game, Multiple criteria decision making, Multicriteria game, Strong time consistency, Shapley value, Cooperative solutionhttp://www.sciencedirect.com/science/article/pii/S221471601830321X |
| spellingShingle | Denis Kuzyutin Nadezhda Smirnova Ekaterina Gromova Long-term implementation of the cooperative solution in a multistage multicriteria game Operations Research Perspectives |
| title | Long-term implementation of the cooperative solution in a multistage multicriteria game |
| title_full | Long-term implementation of the cooperative solution in a multistage multicriteria game |
| title_fullStr | Long-term implementation of the cooperative solution in a multistage multicriteria game |
| title_full_unstemmed | Long-term implementation of the cooperative solution in a multistage multicriteria game |
| title_short | Long-term implementation of the cooperative solution in a multistage multicriteria game |
| title_sort | long term implementation of the cooperative solution in a multistage multicriteria game |
| url | http://www.sciencedirect.com/science/article/pii/S221471601830321X |
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