The Lexicographic Kernel of a Cooperative Game

The purpose of this paper is to compare the nucleolus and the lexicographic kernel, and find analogous properties. It is shown that the lexicographic kernal has, like the nucleolus, the following properties: It lies in the intersection of the kernel and the least core, and has a converging dynamic procedure similar to Justman's procedure for the nucleolus. The lexicographic kernel does not always consist of a unique point as the nucleolus. However it is continuous as a set valued function. On the other hand, the lexicographic kernel is a “geometrical locus” in the nonempty ϵ-core, whereas the nucleolus is not.