Computing an Element in the Lexicographic Kernel of a Game

The lexicographic kernel of a game lexicographically maximizes the surplusses sij (rather than the excesses as would the nucleolus). We show that an element in the lexicographic kernel can be computed efficiently, provided we can efficiently compute the surplusses sij(x) corresponding to a given allocation x. This approach improves the results in [2] and allows us to determine a kernel element without appealing to Maschler transfers in the execution of the algorithm.