Shapley Mapping and Its Axiomatizations in <i>n</i>-Person Cooperative Interval Games
Interval games are an extension of cooperative coalitional games, in which players are assumed to face payoff uncertainty. Characteristic functions thus assign a closed interval, instead of a real number. In this paper, we first examine the notion of solution mapping, a solution concept applied to i...
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| Format: | Article |
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MDPI AG
2022-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/21/3963 |
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| author | Junnosuke Shino Shinichi Ishihara Shimpei Yamauchi |
| author_facet | Junnosuke Shino Shinichi Ishihara Shimpei Yamauchi |
| author_sort | Junnosuke Shino |
| collection | DOAJ |
| description | Interval games are an extension of cooperative coalitional games, in which players are assumed to face payoff uncertainty. Characteristic functions thus assign a closed interval, instead of a real number. In this paper, we first examine the notion of solution mapping, a solution concept applied to interval games, by comparing it with the existing solution concept called the interval solution concept. Then, we define a Shapley mapping as a specific form of the solution mapping. Finally, it is shown that the Shapley mapping can be characterized by two different axiomatizations, both of which employ interval game versions of standard axioms used in the traditional cooperative game analysis such as efficiency, symmetry, null player property, additivity and separability. |
| first_indexed | 2024-03-09T18:53:03Z |
| format | Article |
| id | doaj.art-9394141b9d724b899689af6d7b7ed0e6 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:53:03Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9394141b9d724b899689af6d7b7ed0e62023-11-24T05:42:47ZengMDPI AGMathematics2227-73902022-10-011021396310.3390/math10213963Shapley Mapping and Its Axiomatizations in <i>n</i>-Person Cooperative Interval GamesJunnosuke Shino0Shinichi Ishihara1Shimpei Yamauchi2School of International Liberal Studies (SILS), Waseda University, 1-6-1 Nishiwaseda, Shinjuku-ku, Tokyo 169-8050, JapanWaseda Institute of Political Economy (WINPEC), Waseda University, 1-6-1 Nishiwaseda, Shinjuku-ku, Tokyo 169-8050, JapanIndependent Researcher, Tokyo 130-0024, JapanInterval games are an extension of cooperative coalitional games, in which players are assumed to face payoff uncertainty. Characteristic functions thus assign a closed interval, instead of a real number. In this paper, we first examine the notion of solution mapping, a solution concept applied to interval games, by comparing it with the existing solution concept called the interval solution concept. Then, we define a Shapley mapping as a specific form of the solution mapping. Finally, it is shown that the Shapley mapping can be characterized by two different axiomatizations, both of which employ interval game versions of standard axioms used in the traditional cooperative game analysis such as efficiency, symmetry, null player property, additivity and separability.https://www.mdpi.com/2227-7390/10/21/3963cooperative interval gamesinterval uncertaintyShapley valuesolution mappingaxiomatization |
| spellingShingle | Junnosuke Shino Shinichi Ishihara Shimpei Yamauchi Shapley Mapping and Its Axiomatizations in <i>n</i>-Person Cooperative Interval Games Mathematics cooperative interval games interval uncertainty Shapley value solution mapping axiomatization |
| title | Shapley Mapping and Its Axiomatizations in <i>n</i>-Person Cooperative Interval Games |
| title_full | Shapley Mapping and Its Axiomatizations in <i>n</i>-Person Cooperative Interval Games |
| title_fullStr | Shapley Mapping and Its Axiomatizations in <i>n</i>-Person Cooperative Interval Games |
| title_full_unstemmed | Shapley Mapping and Its Axiomatizations in <i>n</i>-Person Cooperative Interval Games |
| title_short | Shapley Mapping and Its Axiomatizations in <i>n</i>-Person Cooperative Interval Games |
| title_sort | shapley mapping and its axiomatizations in i n i person cooperative interval games |
| topic | cooperative interval games interval uncertainty Shapley value solution mapping axiomatization |
| url | https://www.mdpi.com/2227-7390/10/21/3963 |
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