半值和最小平方值的人均公式及其相互关系

证明了半值和最小平方值的人均公式,与早期从Shapley值的平均种数公式发展而得到的算法相似,这些公式允许用一种算法来进行计算.同时发现最小平方值是一种通过对给定对策的赎买得到的对策的沙普利值,并且用算法证明了Ruiz/Valenciano/Zarzuelo所提出的定理中一个半值的效率正常化是一个最小平方值.

On Semivalues and Least Square Values,Average per Capita Formulas and Relationships

Average per capita formulas for Semivalues and the Least Square Values are proved, which allow to use an algorithm for computing, similar to the algorithm developed for the Shapley value derived earlier from the Average per capita formula for the Shapley value. As byproducts we show that any Least Square Value is a Shapley value for a game obtained by rescaling from the given game, and we prove algebraically the theorem of Ruiz/Valenciano/Zarzuelo saying that the efficient normalization of a Semivalue is a Least Square Value.