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.
Lingua originale | English |
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pagine (da-a) | 1051-1062 |
Numero di pagine | 12 |
Rivista | Journal of Optimization Theory and Applications |
Volume | 166 |
DOI | |
Stato di pubblicazione | Pubblicato - 2015 |
Keywords
- Applied Mathematics
- Completely monotonic sequences
- Control and Optimization
- Game theory
- Management Science and Operations Research
- Regular and irregular semivalues
- Unanimity games