In this paper we generalise marginal vectors and permutational convexity. We show that if a game is generalised permutationally convex, then the corresponding generalised marginal vector is a core element. Furthermore we refine the concept of permutational convexity and show that this refinement...

An assignment situation can be considered as a two-sided market consisting of two disjoint sets of objects. A non-negative reward matrix describes the profit if an object of one group is assigned to an object of the other group. Assuming that each object is owned by a different agent, Shapley...