The Nucleolus and Kernel of Veto-Rich Transferable Utility Games

Vincent Feltkamp and Javier Arin ()

International Journal of Game Theory, 1997, vol. 26, issue 1, 73 pages

Abstract: 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. 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. 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.

Date: 1998-05-19
Note: Received May 1994 Revised version May 1995
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