鉴于 Shapley 值和 Winter 值都是局中人边际贡献的平均值,探究了它们之 间的解析关系.证明了 Shapley 值是 Winter 值在层次结构集上对称概率分布下的期望均值. 作为这一结论的一个推论, 证明了 Shapley 值是 Winter 值在层次结构集的任意相似类中的平均值. 最后,还指出了这一结 论与推论的等价性.研究结果不仅扩展了 Shapley 值和 Owen 值与此对应的解析关系, 还大大简化了这些关系的已有证明.

As both the Shapley and Winter values are averages of players' marginal contributions, this paper explores their analytic relationship. Specifically, the result that Shapley value is Winter value's expectation with respect to symmetric probability distributions on level structure set is proved. As a corollary, the argument that
Shapley value is Winter value's average with respect to any similar class in level structure set is also attested. Finally, the equivalence of this result and corollary is presented. The research results not only expand corresponding relationship between Shapley and Owen values, but also simplify the proofs of these correspondingrelationship enormously.