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. <p>We 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. We then provide a fast algorithm which does not use linear programming techniques to compute the nucleolus of these games. <p>Furthermore, we provide a few examples of economic situations which belong to the class of veto-rich games and which are treated in the literature. <!--ID="" Acknowledgements: We gratefully thank Peter Borm, Shigeo Muto and Stef Tijs for their suggestions and help while writing this paper, and Eric van Damme, Gooni Orshan, Hans Reynierse, and Oscar Volij for helpful comments.-->