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.
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This author's research was made possible by grant BFI AE 92/93 of the Department of Education, Universities and Research of the Basque Government.
This author's research was sponsored by the Foundation for the Promotion of Research in Economic Sciences, which is part of the Dutch Organization for Scientific Research (NWO).
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Arin, J., Feltkamp, V. The nucleolus and kernel of veto-rich transferable utility games. Int J Game Theory 26, 61–73 (1997). https://doi.org/10.1007/BF01262513
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DOI: https://doi.org/10.1007/BF01262513