Computing an element in the lexicographic kernel of a game

The lexicographic kernel of a game lexicographically maximizes the surplusses $s_{ij}$ (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 $s_{ij}(x)$ corresponding to a given allocation $x$. This approach improves the results in Faigle et al. (in Int J Game Theory 30:79–98, 2001) and allows us to determine a kernel element without appealing to Maschler transfers in the execution of the algorithm.