Although the definition of the nucleolus seems abstract, gave a more intuitive description: Starting with the least-core, record the coalitions for which the right-hand side of the inequality in the definition of formula_181 cannot be further reduced without making the set empty. Continue decreasing the right-hand side for the remaining coalitions, until it cannot be reduced without making the set empty. Record the new set of coalitions for which the inequalities hold at equality; continue decreasing the right-hand side of remaining coalitions and repeat this process as many times as necessary until all coalitions have been recorded. The resulting payoff vector is the nucleolus.