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The nucleolus and kernel of veto-rich transferable utility games

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Author Info

  • Arin, J.
  • Feltkamp, V.

    (Tilburg University, Center for Economic Research)

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.

(This abstract was borrowed from another version of this item.)

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1994-40.

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Date of creation: 1994
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Handle: RePEc:dgr:kubcen:199440

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Web page: http://center.uvt.nl

Related research

Keywords: Game Theory;

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References

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  1. Muto, S. & Nakayama, M. & Potters, J.A.M. & Tijs, S.H., 1988. "On big boss games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154246, Tilburg University.
  2. Graham, Daniel A & Marshall, Robert C & Richard, Jean-Francois, 1990. "Differential Payments within a Bidder Coalition and the Shapley Value," American Economic Review, American Economic Association, vol. 80(3), pages 493-510, June.
  3. Maschler, Michael, 1992. "The bargaining set, kernel, and nucleolus," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 18, pages 591-667 Elsevier.
  4. Sankaran, Jayaram K, 1991. "On Finding the Nucleolus of an N-Person Cooperative Game," International Journal of Game Theory, Springer, vol. 19(4), pages 329-38.
  5. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
  6. Potters, Jos & Poos, Rene & Tijs, Stef & Muto, Shigeo, 1989. "Clan games," Games and Economic Behavior, Elsevier, vol. 1(3), pages 275-293, September.
  7. Potters, J.A.M. & Poos, R. & Tijs, S.H. & Muto, S., 1989. "Clan games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154241, Tilburg University.
  8. Sorenson, John R & Tschirhart, John T & Whinston, Andrew B, 1978. "A Theory of Pricing under Decreasing Costs," American Economic Review, American Economic Association, vol. 68(4), pages 614-24, September.
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Citations

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Cited by:
  1. Josep Maria Izquierdo Aznar & Carlos Rafels Pallarola, 2002. "Coalitionally Monotonic Set-solutions for Cooperative TU Games," Working Papers in Economics 75, Universitat de Barcelona. Espai de Recerca en Economia.
  2. René van den Brink & Ilya Katsev & Gerard van der Laan, 2008. "An Algorithm for Computing the Nucleolus of Disjunctive Additive Games with An Acyclic Permission Structure," Tinbergen Institute Discussion Papers 08-104/1, Tinbergen Institute.
  3. Arin Aguirre, Francisco Javier & Katsev, Ilya, 2011. "The SD-prenucleolus for TU games," IKERLANAK 2011-56, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
  4. René van den Brink & Ilya Katsev & Gerard van der Laan, 2008. "Computation of the Nucleolus for a Class of Disjunctive Games with a Permission Structure," Tinbergen Institute Discussion Papers 08-060/1, Tinbergen Institute.
  5. Sylvain Béal & Eric Rémila & Philippe Solal, 2013. "Accessibility and stability of the coalition structure core," Computational Statistics, Springer, vol. 78(2), pages 187-202, October.
  6. Feltkamp, Vicent & Arin Aguirre, Francisco Javier & Montero García, María, 2013. "Coalitional games with veto players: Myopic and farsighted behavior," IKERLANAK Ikerlanak;2013-73, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
  7. F. Grafe & A. Mauleon & E. Iñarra, 1995. "A simple procedure to compute the nucleolus of Γ-component additive games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 3(2), pages 235-245, December.
  8. J Arin & V Feltkamp & M Montero, 2012. "Coalitional Games with Veto Players: Myopic and Rational Behavior," Discussion Papers 2012-11, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  9. Rodica Brânzei & Tamás Solymosi & Stef Tijs, 2005. "Strongly essential coalitions and the nucleolus of peer group games," International Journal of Game Theory, Springer, vol. 33(3), pages 447-460, 09.
  10. J. Arin & V. Feltkamp, 2005. "Monotonicity properties of the nucleolus on the domain of veto balanced games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 13(2), pages 331-341, December.
  11. Brânzei, R. & Fragnelli, V. & Tijs, S.H., 2000. "Tree-connected Peer Group Situations and Peer Group Games," Discussion Paper 2000-117, Tilburg University, Center for Economic Research.
  12. Brânzei, R. & Tijs, S.H. & Timmer, J.B., 2000. "Collecting Information to improve Decision-Making," Discussion Paper 2000-26, Tilburg University, Center for Economic Research.
  13. Yair Tauman & Andriy Zapechelnyuk, 2010. "On (non-) monotonicity of cooperative solutions," International Journal of Game Theory, Springer, vol. 39(1), pages 171-175, March.
  14. Brânzei, R. & Tijs, S.H. & Timmer, J.B., 2000. "Cones of Games arising from Market Entry Problems," Discussion Paper 2000-44, Tilburg University, Center for Economic Research.
  15. René Brink & Ilya Katsev & Gerard Laan, 2011. "A polynomial time algorithm for computing the nucleolus for a class of disjunctive games with a permission structure," International Journal of Game Theory, Springer, vol. 40(3), pages 591-616, August.
  16. Yair Tauman & Andriy Zapechelnyuk, 2006. "Bargaining with a Bureaucrat," Discussion Paper Series dp425, The Center for the Study of Rationality, Hebrew University, Jerusalem.

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