The bipolar Möbius transform is an extension of dividends of cooperative games to that of bi-cooperative games. In this paper, we introduce the bipolar co-Möbius transform as an extension of co-Möbius transform of the cooperative game to that of bi-cooperative game. Then, we propose the Banzhaf interaction index among players in bi-cooperative games (or among criteria in bi-capacities ). Lastly, we give the expression of the Banzhaf interaction index in terms of each of the bipolar Möbius transform and bipolar co-Möbius transform as it was done for a cooperative game.

中文翻译：

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双向合作博弈的 Banzhaf 交互指数

双极莫比乌斯变换是合作博弈红利对双合作博弈红利的扩展。在本文中，我们引入了双极共莫比乌斯变换作为合作博弈的共莫比乌斯变换对双合作博弈的扩展。然后，我们提出了双合作博弈中玩家之间（或双能力中的标准之间）的 Banzhaf 互动指数。最后，我们根据合作博弈中的双极莫比乌斯变换和双极共莫比乌斯变换给出 Banzhaf 交互指数的表达式。