The Banzhaf interaction index in game with coalition structure

Based on cooperative games with coalition structure, Owen introduced the modified Banzhaf value as an extension of Banzhaf value. Spired by the conclusion of interaction phenomena among players in cooperative games, In this paper, a concept of derivative to measure interaction for games with coalition structure is established. Furthermore, the Banzhaf index of interation among players in games with coalition structure is proposed. This index can be viewed as the extension of modified Banzhaf value. Some properties of the indices are researched as well.