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A geometric characterization of the nucleolus of the assignment game

Author

Listed:
  • Francesc Llerena

    () (Universitat Rovira i Virgili)

  • Marina Nunez

    () (University of Barcelona)

Abstract

Maschler et al. (1979) provide a geometrical characterization for the intersection of the kernel and the core of a coalitional game, showing that those allocations that lie in both sets are always the midpoint of certain bargaining range between each pair of players. In the case of the assignment game, this means that the kernel can be determined as those core allocations where the maximum amount, that can be transferred without getting outside the core, from one agent to his/her optimally matched partner equals the maximum amount that he/she can receive from this partner, also remaining inside the core (Rochford, 1984). We now prove that the nucleolus of the assignment game can be characterized by requiring this bisection property be satisfied not only for optimally matched pairs but also for optimally matched coalitions.

Suggested Citation

  • Francesc Llerena & Marina Nunez, 2011. "A geometric characterization of the nucleolus of the assignment game," Economics Bulletin, AccessEcon, vol. 31(4), pages 3275-3285.
  • Handle: RePEc:ebl:ecbull:eb-11-00667
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    File URL: http://www.accessecon.com/Pubs/EB/2011/Volume31/EB-11-V31-I4-P298.pdf
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    References listed on IDEAS

    as
    1. Solymosi, Tamas & Raghavan, Tirukkannamangai E S, 1994. "An Algorithm for Finding the Nucleolus of Asignment Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(2), pages 119-143.
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    Cited by:

    1. van den Brink, René & Pintér, Miklós, 2015. "On axiomatizations of the Shapley value for assignment games," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 110-114.
    2. F. Javier Martínez-de-Albéniz & Carles Rafels & Neus Ybern, 2013. "On the nucleolus of 2 x 2 assignment games," Economics Bulletin, AccessEcon, vol. 33(2), pages 1641-1648.
    3. Nax, Heinrich H. & Pradelski, Bary S. R., 2015. "Evolutionary dynamics and equitable core selection in assignment games," LSE Research Online Documents on Economics 65428, London School of Economics and Political Science, LSE Library.
    4. Francesc Llerena (Universitat Rovira i Virgili - CREIP) & Marina Nunez (Universitat de Barcelona) & Carles Rafels (Universitat de Barcelona), 2012. "An axiomatization of the nucleolus of the assignment game," Working Papers in Economics 286, Universitat de Barcelona. Espai de Recerca en Economia.
    5. F.Javier Martínez-de-Albéniz & Carles Rafels & Neus Ybern, 2015. "Insights into the nucleolus of the assignment game," UB Economics Working Papers 2015/333, Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics.
    6. Francesc Llerena & Marina Núñez & Carles Rafels, 2015. "An axiomatization of the nucleolus of assignment markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 1-15, February.
    7. Heinrich Nax & Bary Pradelski, 2015. "Evolutionary dynamics and equitable core selection in assignment games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 903-932, November.

    More about this item

    Keywords

    assignment game; core; kernel; nucleolus;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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