Characterizations, Potential, and an Implementation of the Shapley-Solidarity Value
In this paper, we provide cooperative and non-cooperative interpretations of the Shapley–Solidarity value for cooperative games with coalition structure. Firstly, we present two new characterizations of this value based on intracoalitional quasi-balanced contributions property. Secondly, we study a...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/11/1965 |
| _version_ | 1797548721605443584 |
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| author | Jun Su Yuan Liang Guangmin Wang Genjiu Xu |
| author_facet | Jun Su Yuan Liang Guangmin Wang Genjiu Xu |
| author_sort | Jun Su |
| collection | DOAJ |
| description | In this paper, we provide cooperative and non-cooperative interpretations of the Shapley–Solidarity value for cooperative games with coalition structure. Firstly, we present two new characterizations of this value based on intracoalitional quasi-balanced contributions property. Secondly, we study a potential function of the Shapley–Solidarity value. Finally, we propose a new bidding mechanism for the Solidarity value and then apply the result to the Shapley–Solidarity value. |
| first_indexed | 2024-03-10T15:03:43Z |
| format | Article |
| id | doaj.art-0637f98c9a72493faa71ffac21879f97 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:03:43Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-0637f98c9a72493faa71ffac21879f972023-11-20T19:55:09ZengMDPI AGMathematics2227-73902020-11-01811196510.3390/math8111965Characterizations, Potential, and an Implementation of the Shapley-Solidarity ValueJun Su0Yuan Liang1Guangmin Wang2Genjiu Xu3School of Science, Xi’an University of Science and Technology, Xi’an 710054, Shaanxi, ChinaSchool of Science, Xi’an University of Science and Technology, Xi’an 710054, Shaanxi, ChinaSchool of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, ChinaSchool of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, ChinaIn this paper, we provide cooperative and non-cooperative interpretations of the Shapley–Solidarity value for cooperative games with coalition structure. Firstly, we present two new characterizations of this value based on intracoalitional quasi-balanced contributions property. Secondly, we study a potential function of the Shapley–Solidarity value. Finally, we propose a new bidding mechanism for the Solidarity value and then apply the result to the Shapley–Solidarity value.https://www.mdpi.com/2227-7390/8/11/1965Shapley-Solidarity valuecoalition structurepotentialbidding mechanism |
| spellingShingle | Jun Su Yuan Liang Guangmin Wang Genjiu Xu Characterizations, Potential, and an Implementation of the Shapley-Solidarity Value Mathematics Shapley-Solidarity value coalition structure potential bidding mechanism |
| title | Characterizations, Potential, and an Implementation of the Shapley-Solidarity Value |
| title_full | Characterizations, Potential, and an Implementation of the Shapley-Solidarity Value |
| title_fullStr | Characterizations, Potential, and an Implementation of the Shapley-Solidarity Value |
| title_full_unstemmed | Characterizations, Potential, and an Implementation of the Shapley-Solidarity Value |
| title_short | Characterizations, Potential, and an Implementation of the Shapley-Solidarity Value |
| title_sort | characterizations potential and an implementation of the shapley solidarity value |
| topic | Shapley-Solidarity value coalition structure potential bidding mechanism |
| url | https://www.mdpi.com/2227-7390/8/11/1965 |
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