Marginality and convexity in partition function form games

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