The nucleolus and kernel of veto-rich transferable utility games

The process of computing the nucleolus of arbitrary transferable utility games is notoriously hard. A number of papers have appeared in which the nucleolus is computed by an algorithm in which either one or a huge number of huge linear programs have to be solved. The authors show that on the class of veto-rich games, the nucleolus is the unique kernel element. Veto-rich games are games in which one of the players is needed by coalitions in order to obtain a non-zero payoff. The authors then provide a fast algorithm which does not use linear programming techniques to compute the nucleolus of these games. Furthermore, they provide a few examples of economic situations which belong to the class of veto-rich games and which are treated in the literature.