Necessary players and values
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914659262529536 |
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| author | Gonçalves-Dosantos, J. C. García-Jurado, I. Costa, J. Alonso-Meijide, J. M. |
| author_facet | Gonçalves-Dosantos, J. C. García-Jurado, I. Costa, J. Alonso-Meijide, J. M. |
| contents | In this paper we introduce the $Γ$ value, a new value for cooperative games with transferable utility. We also provide an axiomatic characterization of the $Γ$ value based on a property concerning the so-called necessary players. A necessary players of a game is one without which the characteristic function is zero. We illustrate the performance of the $Γ$ value in a particular cost allocation problem that arises when the owners of the apartments in a building plan to install an elevator and share its installation cost; in the resulting example we compare the proposals of the $Γ$ value, the equal division value and the Shapley value in two different scenarios. In addition, we propose an extension of the $Γ$ value for cooperative games with transferable utility and with a coalition structure. Finally, we provide axiomatic characterizations of the coalitional $Γ$ value and of the Owen and Banzhaf-Owen values using alternative properties concerning necessary players. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16930 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Necessary players and values Gonçalves-Dosantos, J. C. García-Jurado, I. Costa, J. Alonso-Meijide, J. M. Computer Science and Game Theory In this paper we introduce the $Γ$ value, a new value for cooperative games with transferable utility. We also provide an axiomatic characterization of the $Γ$ value based on a property concerning the so-called necessary players. A necessary players of a game is one without which the characteristic function is zero. We illustrate the performance of the $Γ$ value in a particular cost allocation problem that arises when the owners of the apartments in a building plan to install an elevator and share its installation cost; in the resulting example we compare the proposals of the $Γ$ value, the equal division value and the Shapley value in two different scenarios. In addition, we propose an extension of the $Γ$ value for cooperative games with transferable utility and with a coalition structure. Finally, we provide axiomatic characterizations of the coalitional $Γ$ value and of the Owen and Banzhaf-Owen values using alternative properties concerning necessary players. |
| title | Necessary players and values |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2401.16930 |