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Insights into the nucleolus of the assignment game

Author

Listed:
  • F.Javier Martínez-de-Albéniz

    (Universitat de Barcelona)

  • Carles Rafels

    (Universitat de Barcelona)

  • Neus Ybern

    (Universitat Politècnica de Catalunya)

Abstract

We show that the family of assignment matrices which give rise to the same nucleolus form a compact join-semilattice with one maximal element, which is always a valuation (see p.43, Topkis (1998)). We give an explicit form of this valuation matrix. The above family is in general not a convex set, but path-connected, and we construct minimal elements of this family. We also analyze the conditions to ensure that a given vector is the nucleolus of some assignment game.

Suggested Citation

  • F.Javier Martínez-de-Albéniz & Carles Rafels & Neus Ybern, 2015. "Insights into the nucleolus of the assignment game," UB School of Economics Working Papers 2015/333, University of Barcelona School of Economics.
    • Handle: RePEc:ewp:wpaper:333web
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    References listed on IDEAS

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    More about this item

    Keywords

    Assignment game; core; nucleolus; semilattice.;
    All these keywords.

    JEL classification:

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

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