Characterizing the ELS Values with Fixed-Population Invariance Axioms
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917459782533120 |
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| author | Funaki, Yukihiko Koriyama, Yukio Nakada, Satoshi Tamura, Yuki |
| author_facet | Funaki, Yukihiko Koriyama, Yukio Nakada, Satoshi Tamura, Yuki |
| contents | We study efficient, linear, and symmetric (ELS) values, a central family of allocation rules for cooperative games with transferable-utility (TU-games) that includes the Shapley value, the CIS value, and the ENSC value. We first show that every ELS value can be written as the Shapley value of a suitably transformed TU-game. We then introduce three types of invariance axioms for fixed player populations. The first type consists of composition axioms, and the second type is active-player consistency. Each of these two types yields a characterization of a subclass of the ELS values that contains the family of least-square values. Finally, the third type is nullified-game consistency: we define three such axioms, and each axiom yields a characterization of one of the Shapley, CIS, and ENSC values. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_04996 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterizing the ELS Values with Fixed-Population Invariance Axioms Funaki, Yukihiko Koriyama, Yukio Nakada, Satoshi Tamura, Yuki Theoretical Economics We study efficient, linear, and symmetric (ELS) values, a central family of allocation rules for cooperative games with transferable-utility (TU-games) that includes the Shapley value, the CIS value, and the ENSC value. We first show that every ELS value can be written as the Shapley value of a suitably transformed TU-game. We then introduce three types of invariance axioms for fixed player populations. The first type consists of composition axioms, and the second type is active-player consistency. Each of these two types yields a characterization of a subclass of the ELS values that contains the family of least-square values. Finally, the third type is nullified-game consistency: we define three such axioms, and each axiom yields a characterization of one of the Shapley, CIS, and ENSC values. |
| title | Characterizing the ELS Values with Fixed-Population Invariance Axioms |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2511.04996 |