Universal characterization sets for the nucleolus in balanced games

We provide a new mo dus op erandi for the computation of the nucleolus in co op- erative games with transferable utility. Using the concept of dual game we extend the theory of characterization sets. Dually essential and dually saturated coalitions determine b oth the core and the nucleolus in monotonic games whenever the core is non-empty. We show how these two sets are related with the existing charac- terization sets. In particular we prove that if the grand coalition is vital then the intersection of essential and dually essential coalitions forms a characterization set itself. We conclude with a sample computation of the nucleolus of bankruptcy games - the shortest of its kind