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The Nucleolus and Kernel of Veto-Rich Transferable Utility Games

  • Vincent Feltkamp

    (CentER and Econometrics Department, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands)

  • Javier Arin

    (Faculty of Economics, Dept. Fundamentos Del Analisis Economico, Universidad de Alicante, 03071 Alicante, Spain)

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.

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Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 26 (1997)
Issue (Month): 1 ()
Pages: 61-73

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Handle: RePEc:spr:jogath:v:26:y:1997:i:1:p:61-73
Note: Received May 1994 Revised version May 1995
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