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The Nucleolus and Kernel of Veto-Rich Transferable Utility Games

Author

Listed:
  • 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)

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.

Suggested Citation

  • Vincent Feltkamp & Javier Arin, 1997. "The Nucleolus and Kernel of Veto-Rich Transferable Utility Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 61-73.
  • 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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