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A geometric chracterization of the nucleolus of the assignment game

Author

Listed:
  • Francesc Llerena
  • Marina Nunez
  • Carles Rafels

    (Universitat de 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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Francesc Llerena & Marina Nunez & Carles Rafels, 2011. "A geometric chracterization of the nucleolus of the assignment game," Working Papers in Economics 260, Universitat de Barcelona. Espai de Recerca en Economia.
  • Handle: RePEc:bar:bedcje:2011260
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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.
    2. Theo S. H. Driessen, 1998. "A note on the inclusion of the kernel in the core of the bilateral assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 301-303.
    3. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. F. Javier Martínez-de-Albéniz & Carlos Rafels & Neus Ybern, 2018. "Solving Becker's assortative assignments and extensions," UB School of Economics Working Papers 2018/376, University of Barcelona School of Economics.
    5. 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.
    6. 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.
    7. R. Branzei & E. Gutiérrez & N. Llorca & J. Sánchez-Soriano, 2021. "Does it make sense to analyse a two-sided market as a multi-choice game?," Annals of Operations Research, Springer, vol. 301(1), pages 17-40, June.
    8. F. Javier Martínez-de-Albéniz & Carlos Rafels & Neus Ybern, 2019. "A note on assignment games with the same nucleolus," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 187-198, July.
    9. Martínez-de-Albéniz, F. Javier & Rafels, Carlos & Ybern, Neus, 2019. "Solving Becker's assortative assignments and extensions," Games and Economic Behavior, Elsevier, vol. 113(C), pages 248-261.
    10. 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.
    11. 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.

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    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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