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Characterization sets for the nucleolus

Author

Listed:
  • D. Granot

    (Faculty of Commerce and Business Administration, The University of British Columbia, Vancouver, B.C., Canada, V6T 1Z2)

  • F. Granot

    (Faculty of Commerce and Business Administration, The University of British Columbia, Vancouver, B.C., Canada, V6T 1Z2)

  • W. R. Zhu

    (Faculty of Commerce and Business Administration, The University of British Columbia, Vancouver, B.C., Canada, V6T 1Z2)

Abstract

We introduce the concept of a characterization set for the nucleolus of a cooperative game and develop sufficient conditions for a collection of coalitions to form a characterization set thereof. Further, we formalize Kopelowitz's method for computing the nucleolus through the notion of a sequential LP process, and derive a general relationship between the size of a characterization set and the complexity of computing the nucleolus.

Suggested Citation

  • D. Granot & F. Granot & W. R. Zhu, 1998. "Characterization sets for the nucleolus," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 359-374.
    • Handle: RePEc:spr:jogath:v:27:y:1998:i:3:p:359-374
    Note: Received May 1994/Revised version May 1997/Final version February 1998
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    Citations

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    Cited by:

    1. Balázs Sziklai & Tamás Fleiner & Tamás Solymosi, 2014. "On the Core of Directed Acyclic Graph Games," CERS-IE WORKING PAPERS 1418, Institute of Economics, Centre for Economic and Regional Studies.
    2. 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.
    3. Tamas Solymosi & Balazs Sziklai, 2015. "Universal Characterization Sets for the Nucleolus in Balanced Games," CERS-IE WORKING PAPERS 1512, Institute of Economics, Centre for Economic and Regional Studies.
    4. Olivier Massol & Stéphane Tchung-Ming, 2009. "Stratégies coopératives dans l'industrie du GNL : l'argument de la rationalisation est-il fondé ?," Working Papers hal-02469480, HAL.
    5. Xiaotie Deng & Qizhi Fang & Xiaoxun Sun, 2009. "Finding nucleolus of flow game," Journal of Combinatorial Optimization, Springer, vol. 18(1), pages 64-86, July.
    6. repec:has:discpr:1321 is not listed on IDEAS
    7. Walter Kern & Daniël Paulusma, 2003. "Matching Games: The Least Core and the Nucleolus," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 294-308, May.
    8. D. Granot & H. Hamers & J. Kuipers & M. Maschler, 2004. "Chinese Postman Games on a Class of Eulerian Graphs," Discussion Paper Series dp366, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    9. Massol, Olivier & Tchung-Ming, Stéphane, 2010. "Cooperation among liquefied natural gas suppliers: Is rationalization the sole objective?," Energy Economics, Elsevier, vol. 32(4), pages 933-947, July.
    10. Márton Benedek & Jörg Fliege & Tri-Dung Nguyen, 2020. "Finding and verifying the nucleolus of cooperative games," CERS-IE WORKING PAPERS 2021, Institute of Economics, Centre for Economic and Regional Studies.

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