Now let formula_167 be the vector of excesses of formula_68, arranged in non-increasing order. In other words, formula_169. Notice that formula_68 is in the core of formula_21 if and only if it is a pre-imputation and formula_172. To define the nucleolus, we consider the lexicographic ordering of vectors in formula_173: For two payoff vectors formula_174, we say formula_175 is lexicographically smaller than formula_176 if for some index formula_177, we have formula_178 and formula_179. (The ordering is called lexicographic because it mimics alphabetical ordering used to arrange words in a dictionary.) The "nucleolus" of formula_21 is the lexicographically minimal imputation, based on this ordering. This solution concept was first introduced in .