We provide a condition guaranteeing when a value defined on the base of the unanimity games and extended by linearity on the space of all games with a fixed, finite set $$N$$N of players is a semivalue. Furthermore, we provide a characterization of the semivalues on the vector space of all finite games, by proving that the coefficients on the base of the unanimity games form a completely monotonic sequence. We also give a characterization of irregular semivalues. In the last part, we remind some results on completely monotonic sequences, which allow one to easily build regular semivalues, with the above procedure.
Bernardi, G., Lucchetti, R., Generating Semivalues via Unanimity Games, <<JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS>>, 2015; 166 (3): 1051-1062. [doi:10.1007/s10957-014-0660-1] [http://hdl.handle.net/10807/133915]
Generating Semivalues via Unanimity Games
Bernardi, Giulia
Writing – Original Draft Preparation
;Lucchetti, RobertoWriting – Original Draft Preparation
2015
Abstract
We provide a condition guaranteeing when a value defined on the base of the unanimity games and extended by linearity on the space of all games with a fixed, finite set $$N$$N of players is a semivalue. Furthermore, we provide a characterization of the semivalues on the vector space of all finite games, by proving that the coefficients on the base of the unanimity games form a completely monotonic sequence. We also give a characterization of irregular semivalues. In the last part, we remind some results on completely monotonic sequences, which allow one to easily build regular semivalues, with the above procedure.
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