Cooperative Games Based on Coalition Functions in Biform Games
In this paper, we try to study a class of biform games with the coalition function from the cooperation of players. For this purpose, we interpret the biform games as cooperative games by defining a characteristic function of minimax representation based on the coalition function and giving the core...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/3/296 |
| _version_ | 1797613477314953216 |
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| author | Chenwei Liu Shuwen Xiang Yanlong Yang Enquan Luo |
| author_facet | Chenwei Liu Shuwen Xiang Yanlong Yang Enquan Luo |
| author_sort | Chenwei Liu |
| collection | DOAJ |
| description | In this paper, we try to study a class of biform games with the coalition function from the cooperation of players. For this purpose, we interpret the biform games as cooperative games by defining a characteristic function of minimax representation based on the coalition function and giving the core and Shapley value as cooperative solutions. The relations between the coalition function and the characteristic function are investigated in terms of additivity and convexity, and the properties associated with the characteristic function, such as individual rationalities and cores, are compared with the corresponding results. The relations among the solutions of the normal-form game, biform game, and cooperative game are discussed with several examples. |
| first_indexed | 2024-03-11T06:56:22Z |
| format | Article |
| id | doaj.art-4994e934290241beaf6396785a22bbea |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T06:56:22Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-4994e934290241beaf6396785a22bbea2023-11-17T09:35:31ZengMDPI AGAxioms2075-16802023-03-0112329610.3390/axioms12030296Cooperative Games Based on Coalition Functions in Biform GamesChenwei Liu0Shuwen Xiang1Yanlong Yang2Enquan Luo3School of Mathematics and Statistics, Guizhou University, Guiyang 550025, ChinaSchool of Mathematics and Statistics, Guizhou University, Guiyang 550025, ChinaSchool of Mathematics and Statistics, Guizhou University, Guiyang 550025, ChinaSchool of Management, Guizhou University, Guiyang 550025, ChinaIn this paper, we try to study a class of biform games with the coalition function from the cooperation of players. For this purpose, we interpret the biform games as cooperative games by defining a characteristic function of minimax representation based on the coalition function and giving the core and Shapley value as cooperative solutions. The relations between the coalition function and the characteristic function are investigated in terms of additivity and convexity, and the properties associated with the characteristic function, such as individual rationalities and cores, are compared with the corresponding results. The relations among the solutions of the normal-form game, biform game, and cooperative game are discussed with several examples.https://www.mdpi.com/2075-1680/12/3/296cooperative gamesShapley valuecorecharacteristic functionsadditivity |
| spellingShingle | Chenwei Liu Shuwen Xiang Yanlong Yang Enquan Luo Cooperative Games Based on Coalition Functions in Biform Games Axioms cooperative games Shapley value core characteristic functions additivity |
| title | Cooperative Games Based on Coalition Functions in Biform Games |
| title_full | Cooperative Games Based on Coalition Functions in Biform Games |
| title_fullStr | Cooperative Games Based on Coalition Functions in Biform Games |
| title_full_unstemmed | Cooperative Games Based on Coalition Functions in Biform Games |
| title_short | Cooperative Games Based on Coalition Functions in Biform Games |
| title_sort | cooperative games based on coalition functions in biform games |
| topic | cooperative games Shapley value core characteristic functions additivity |
| url | https://www.mdpi.com/2075-1680/12/3/296 |
| work_keys_str_mv | AT chenweiliu cooperativegamesbasedoncoalitionfunctionsinbiformgames AT shuwenxiang cooperativegamesbasedoncoalitionfunctionsinbiformgames AT yanlongyang cooperativegamesbasedoncoalitionfunctionsinbiformgames AT enquanluo cooperativegamesbasedoncoalitionfunctionsinbiformgames |