The Banzhaf Value and General Semivalues for Differentiable Mixed Games
研究连续玩家（含原子）的可微博弈空间上的半值，引入导数半值概念，将有限博弈的Banzhaf值扩展至此空间，并证明任何半值都是导数半值。
We consider semivalues on pM ∞ —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 ∞ and extend the standard Banzhaf value from the domain of finite games onto pM ∞ as a certain particularly simple derivative semivalue. Our main result shows that any semivalue on pM ∞ is a derivative semivalue. It is also shown that the Banzhaf value is the only semivalue on pM ∞ that satisfies a version of the composition property of Owen and that, in addition, is nonzero for all nonzero monotonic finite games.