Necessary players and values

J. C. Gonçalves-Dosantos, I. García-Jurado, J. Costa and J. M. Alonso-Meijide ()
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J. C. Gonçalves-Dosantos: Universidade da Coruña
I. García-Jurado: Universidade da Coruña
J. Costa: Universidade da Coruña
J. M. Alonso-Meijide: Universidade de Santiago de Compostela

Annals of Operations Research, 2022, vol. 318, issue 2, No 11, 935-961

Abstract: Abstract In this paper we introduce the $$\Gamma $$ Γ value, a new value for cooperative games with transferable utility. We also provide an axiomatic characterization of the $$\Gamma $$ 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 $$\Gamma $$ 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 $$\Gamma $$ Γ value, the equal division value and the Shapley value in two different scenarios. In addition, we propose an extension of the $$\Gamma $$ Γ value for cooperative games with transferable utility and with a coalition structure. Finally, we provide axiomatic characterizations of the coalitional $$\Gamma $$ Γ value and of the Owen and Banzhaf-Owen values using alternative properties concerning necessary players.

Keywords: Cooperative game; Necessary player; Coalition structure; Value (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10479-021-03950-3

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