通过博弈的加权逼近的加权Banzhaf功率和交互指数
Weighted Banzhaf power and interaction indexes through weighted approximations of games
摘要：
在合作对策理论中引入Banzhaf权力指数来衡量博弈中局中人的实际权力。然后提出了Banzhaf互动指数来衡量参与者联盟内部的互动程度。结果表明，功率和相互作用指数可以作为一个标准的最小二乘逼近问题的伪布尔函数的解决方案。考虑到这个近似问题的某些加权版本，我们定义了一类加权的相互作用指数，推广Banzhaf相互作用指数。我们发现，这些指数定义了一个子类的概率相互作用指数的家庭，并研究其最重要的属性。最后，我们给出了一个解释的Banzhaf和Shapley相互作用指数的质量中心的这个子类的相互作用指数。
英文摘要：
The Banzhaf power index was introduced in cooperative game theory to measure the real power of players in a game. The Banzhaf interaction index was then proposed to measure the interaction degree inside coalitions of players. It was shown that the power and interaction indexes can be obtained as solutions of a standard least squares approximation problem for pseudo-Boolean functions. Considering certain weighted versions of this approximation problem, we define a class of weighted interaction indexes that generalize the Banzhaf interaction index. We show that these indexes define a subclass of the family of probabilistic interaction indexes and study their most important properties. Finally, we give an interpretation of the Banzhaf and Shapley interaction indexes as centers of mass of this subclass of interaction indexes.
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