基于分量差的线性及匿名合作对策值的简化算法

通过给出Shapley值、均分Shapley值、贴现Shapley值、Solidarity值、广义Solidarity值、合意值、 Banzhaf值及最小二乘预核仁分量差的显式解析表达式,本文提出了一种同时计算这些线性及匿名效用可转移合作对策值的简化算法.特别地,这一算法也适用于同时计算这些值中的两种及以上.为了详细说明简化算法的计算过程及优越性,文中给出了具体的数值算例,并将其与传统算法进行了比较分析,结果表明简化算法确实能显著降低同时计算多个值的时间复杂度.

A component differences based simplified algorithm for linear and anonymous values of cooperative games

By giving explicit analytic expressions for the component differences of the Shapley value, egalitarian Shapley value, discounted Shapley value, Solidarity value, generalized Solidarity value, consensus value, Banzhaf value, and least square prenucleolus, this paper proposes a simplified algorithm for simultaneous calculation of these linear and anonymous values of transferable utility cooperative games.Specially, the algorithm is also suitable for calculating more than one of them.So as to illustrate the computational process and the advantages of the algorithm, a numerical example, as well as comparison between the simplified and traditional algorithms, is provided.Results show that the simplified algorithm can decrease the time complexity of calculating more than one values contemporaneously.