The Shapley value for arbitrary families of coalitions

We address the problem of finding a suitable definition of a value similar to that of Shapley’s, when the games are defined on a subfamily of coalitions with no structure. We present two frameworks: one based on the familiar efficiency, linearity and null player axioms, and the other on linearity an...

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Bibliographic Details
Published in:European journal of operational research 2010-07, Vol.204 (1), p.125-138
Main Authors: Aguilera, Néstor E., Di Marco, Silvia C., Escalante, Mariana S.
Format: Article
Language:English
Subjects:
Applied sciences
Coalitions
Cooperative game
Exact sciences and technology
Game theory
Game theory Cooperative game Shapley value
Operational research and scientific management
Operational research. Management science
Shapley value
Studies
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Summary:We address the problem of finding a suitable definition of a value similar to that of Shapley’s, when the games are defined on a subfamily of coalitions with no structure. We present two frameworks: one based on the familiar efficiency, linearity and null player axioms, and the other on linearity and the behavior on unanimity games. We give several properties and examples in each case, and give necessary and sufficient conditions on the family of coalitions for the approaches to coincide.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2009.09.031