The Banzhaf Value and General Semivalues for Differentiable Mixed Games

摘要

We consider semivalues on pM(infinity)-a vector space of games with a continuum of players (among which there may be atoms) that possess a robust differentiability feature. We introduce the notion of a derivative semivalue on pM(infinity) and extend the standard Banzhaf value from the domain of finite games onto pM(infinity) as a certain particularly simple derivative semivalue. Our main result shows that any semivalue on pM(infinity) is a derivative semivalue. It is also shown that the Banzhaf value is the only semivalue on pM(infinity) that satisfies a version of the composition property of Owen and that, in addition, is nonzero for all nonzero monotonic finite games.