The proportional coalitional Shapley value

Authors:
José MaríA Alonso-Meijide;Francesc Carreras
Affiliations:
Department of Statistics and Operations Research, Faculty of Sciences of Lugo, University of Santiago de Compostela, Spain;Department of Applied Mathematics II, Industrial and Aeronautical Engineering School, Technical University of Catalonia, Spain
Venue:
Expert Systems with Applications: An International Journal
Year:
2011

Citing 4
Cited 0

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Abstract

We propose a modification of the Shapley value for monotonic games with a coalition structure. The resulting coalitional value is a twofold extension of the Shapley value in the following sense: (1) the amount obtained by any union coincides with the Shapley value of the union in the quotient game; and (2) the players of the union share this amount proportionally to their Shapley value in the original game (i.e., without unions). We provide axiomatic characterizations of this value close to those existing in the literature for the Owen value and include applications to coalition formation in bankruptcy and voting problems.