Generating Semivalues via Unanimity Games
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 \(N\) 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.
unanimity games completely monotonic sequences game theory regular and irregular semivalues primary 91a12 secondary 91a70