We propose a variant of the nucleolus associated with distorted satisfaction of each coalition in TU games. This solution is referred to as the $$\alpha $$ α -nucleolus in which $$\alpha $$ α is a profile of distortion rates of satisfaction of all the coalitions. We apply the $$\alpha $$ α -nucleolus to constant-sum weighted majority games. We show that under assumptions of distortions of satisfaction of winning coalitions the $$\alpha $$ α -nucleolus is the unique normalized homogeneous representation of constant-sum weighted majority games which assigns a zero to each null player. As corollary of this result, we derive the well-known Peleg’s representation theorem.

中文翻译：

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恒定和加权多数博弈上Peleg表示定理的推广

我们提出了核仁的一种变体，与核仁游戏中每个联盟的满意变形有关。该解决方案称为$$ \ alpha $$α-核仁，其中$$ \ alpha $$α是所有联盟的满意失真率的曲线。我们将$$ \ alpha $$α-核仁应用于恒定和加权多数游戏。我们表明，在获胜联盟的满意度失真的假设下，$$ \ alpha $$α-nucleolus是常数和加权多数游戏的唯一归一化均质表示，该游戏将零位参与者分配为零。作为此结果的推论，我们得出了著名的Peleg表示定理。