In this paper an order on the set of embedded coalitions is studied in detail. This allows us to define new notions of superaddivity and convexity of games in partition function form which are compared to other proposals in the literature. The main results are two characterizations of convexity. The first one uses non-decreasing contributions to coalitions of increasing size and can thus be considered parallel to the classic result for cooperative games without externalities. The second one is based on the standard convexity of associated games without externalities that we define using a partition of the player set. Using the later result, we can conclude that some of the generalizations of the Shapley value to games in partition function form lie within the cores of specific classic games when the original game is convex.

本文详细研究了嵌入式联盟集的顺序。这使我们能够以分区函数形式定义博弈的超可加性和凸性的新概念，与文献中的其他提议进行比较。主要结果是凸性的两个特征。第一个使用对规模不断增加的联盟的非递减贡献，因此可以认为与没有外部性的合作博弈的经典结果相似。第二个是基于没有外部性的相关游戏的标准凸性，我们使用玩家集的分区来定义。使用后面的结果，我们可以得出结论，当原始游戏是凸的时，Shapley 值对分区函数形式的游戏的一些推广位于特定经典游戏的核心内。