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Universal Characterization Sets for the Nucleolus in Balanced Games

Author

Listed:
  • Tamas Solymosi

    (Momentum Game Theory Research Group, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences)

  • Balazs Sziklai

    (Momentum Game Theory Research Group, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences)

Abstract

We provide a new modus operandi for the computation of the nucleolus in cooperative games with transferable utility. Using the concept of dual game we extend the theory of characterization sets. Dually essential and dually saturated coalitions determine both the core and the nucleolus in monotonic games whenever the core is non-empty. We show how these two sets are related with the existing characterization sets. In particular we prove that if the grand coalition is vital then the intersection of essential and dually essential coalitions forms a characterization set itself. We conclude with a sample computation of the nucleolus of bankruptcy games - the shortest of its kind.

Suggested Citation

  • 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.
    • Handle: RePEc:has:discpr:1512
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    References listed on IDEAS

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    Cited by:

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    2. Hougaard, Jens Leth & Smilgins, Aleksandrs, 2016. "Risk capital allocation with autonomous subunits: The Lorenz set," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 151-157.
    3. Bruce C. Hartman, 2018. "Sharing Loading Costs for Multi Compartment Vehicles," Games, MDPI, vol. 9(2), pages 1-21, May.

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    More about this item

    Keywords

    Cooperative game theory; Nucleolus; Characterization sets;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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