Necessary players and values
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Necessary players and valuesDate
2022Citation
Gonçalves-Dosantos, J.C., García-Jurado, I., Costa, J. et al. Necessary players and values. Ann Oper Res 318, 935–961 (2022). https://doi.org/10.1007/s10479-021-03950-3
Abstract
[Abstract]: 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 player 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.
Keywords
Cooperative game
Necessary player
Coalition structure
Value
Necessary player
Coalition structure
Value
Description
This version of the article has been accepted for publication, after peer review and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s10479-021-03950-3.
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ISSN
0254-5330
1572-9338
1572-9338