Generating Semivalues via Unanimity Games

Giulia Bernardi () and Roberto Lucchetti ()
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Giulia Bernardi: Politecnico di Milano
Roberto Lucchetti: Politecnico di Milano

Journal of Optimization Theory and Applications, 2015, vol. 166, issue 3, No 18, 1062 pages

Abstract: 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.

Keywords: Game theory; Regular and irregular semivalues; Unanimity games; Completely monotonic sequences; Primary 91A12; Secondary 91A70 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10957-014-0660-1

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