We generalize the notion of convexity and average-convexity to the notion of weighted average-convexity. We show several results on the relation between weighted average-convexity and cooperative games. First, we prove that if a game is weighted average-convex, then the corresponding weighted Shapley value is in the core. Second, we exhibit necessary conditions for a communication TU-game to preserve the weighted average-convexity. Finally, we provide a complete characterization when the underlying graph is a priority decreasing tree.
翻译：我们把顺差和平均顺差的概念概括为加权平均顺差的概念。 我们在加权平均顺差与合作游戏之间的关系上展示了几项结果。 首先,我们证明如果游戏是加权平均顺差,那么相应的加权色素值就在核心。 其次,我们展示了通信TU游戏的必要条件,以保持加权平均顺差。 最后,当底图是优先减速的树时,我们提供了完整的定性。
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