A vector of balanced weights infers an inequality that games with a nonempty core obey. This paper gives a generalization of the notion 'vector of balanced weights'. Herewith it provides necessary and su?cient conditions to determine whether a TU-game has a population monotonic allocation scheme...

If the excesses of the coalitions in a transferable utility game are weighted, then we show that the arising weighted modifications of the well-known (pre)nucleolus and (pre)kernel satisfy the equal treatment property if and only if the weight system is symmetric in the sense that the weight of...