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An axiomatization of the nucleolus of the assignment game

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  • Francesc Llerena (Universitat Rovira i Virgili - CREIP)
  • Marina Nunez (Universitat de Barcelona)
  • Carles Rafels (Universitat de Barcelona)

    (Universitat de Barcelona)

Abstract

On the domain of two-sided assignment markets, the nucleolus is axiomatized as the unique solution that satisfies derived consistency (Owen, 1992) and complaint mono- tonicity on sectors size. As a consequence, we obtain a geometric characterization of the nucleolus by means of a strong form of the bisection property that characterizes the inter- section between the core and the kernel of a coalitional game in Maschler et al (1979).

Suggested Citation

  • 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.
    • Handle: RePEc:bar:bedcje:2012286
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    References listed on IDEAS

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    1. Maike Hoffmann & Peter Sudhölter, 2007. "The Shapley value of exact assignment games," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 557-568, April.
    2. Rochford, Sharon C., 1984. "Symmetrically pairwise-bargained allocations in an assignment market," Journal of Economic Theory, Elsevier, vol. 34(2), pages 262-281, December.
    3. Guillermo Owen, 1992. "The Assignment Game : The Reduced Game," Annals of Economics and Statistics, GENES, issue 25-26, pages 71-79.
    4. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
    5. Potters, Jos A M, 1991. "An Axiomatization of the Nucleolus," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 365-373.
    6. Francesc Llerena & Marina Nunez, 2011. "A geometric characterization of the nucleolus of the assignment game," Economics Bulletin, AccessEcon, vol. 31(4), pages 3275-3285.
    7. Sasaki, Hiroo, 1995. "Consistency and Monotonicity in Assignment Problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(4), pages 373-397.
    8. repec:adr:anecst:y:1992:i:25-26:p:03 is not listed on IDEAS
    9. Potters, J.A.M. & Tijs, S.H., 1992. "The nucleolus of a matrix game and other nucleoli," Other publications TiSEM ae3402e7-bd19-494b-b0a1-f, Tilburg University, School of Economics and Management.
    10. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
    12. 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.
    13. Toda, Manabu, 2005. "Axiomatization of the core of assignment games," Games and Economic Behavior, Elsevier, vol. 53(2), pages 248-261, November.
    14. 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.
    15. 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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    Cited by:

    1. 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.

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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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