IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v26y1997i1p61-73.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Yair Tauman & Andriy Zapechelnyuk, 2006. "Bargaining with a Bureaucrat," Levine's Bibliography 321307000000000108, UCLA Department of Economics.
    3. Arin Aguirre, Francisco Javier & Feltkamp, Vincent, 2005. "Implementing with veto players: a simple non cooperative game," IKERLANAK 2005-17, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    4. 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.
    5. repec:spr:compst:v:78:y:2013:i:2:p:187-202 is not listed on IDEAS
    6. Rodica Brânzei & Vito Fragnelli & Stef Tijs, 2002. "Tree-connected peer group situations and peer group games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(1), pages 93-106, March.
    7. 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.
    8. Yair Tauman & Andriy Zapechelnyuk, 2010. "On (non-) monotonicity of cooperative solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 171-175, March.
    9. Rodica Brânzei & Tamás Solymosi & Stef Tijs, 2005. "Strongly essential coalitions and the nucleolus of peer group games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 447-460, September.
    10. 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;Sociedad de Estadística e Investigación Operativa, vol. 3(2), pages 235-245, December.
    11. Arin, J. & Feltkamp, V., 2007. "Coalitional games with veto players: Consistency, monotonicity and Nash outcomes," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 855-870, September.
    12. 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;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 331-341, December.
    13. 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;Game Theory Society, vol. 40(3), pages 591-616, August.
    14. Katsev, Ilya & Arin Aguirre, Francisco Javier, 2011. "The SD-prenucleolus for TU games," IKERLANAK 2011-56, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    15. Sylvain Béal & Eric Rémila & Philippe Solal, 2013. "Accessibility and stability of the coalition structure core," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 187-202, October.
    16. Arin Aguirre, Francisco Javier & Katsev, Ilya, 2016. "The SD-prekernel for TU games," IKERLANAK Ikerlanak;2016-96, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    17. Driessen, Theo S.H. & Fragnelli, Vito & Katsev, Ilya V. & Khmelnitskaya, Anna B., 2011. "On 1-convexity and nucleolus of co-insurance games," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 217-225, March.
    18. Izquierdo, Josep M. & Rafels, Carles, 2001. "Average Monotonic Cooperative Games," Games and Economic Behavior, Elsevier, vol. 36(2), pages 174-192, August.
    19. 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.
    20. 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.
    21. 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.
    22. Arin Aguirre, Francisco Javier & Feltkamp, Vicent & 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.
    23. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jogath:v:26:y:1997:i:1:p:61-73. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: http://www.springer.com .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.