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A Canonical Representation for the Assignment Game: the Kernel and the Nucleolus

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  • Marina Núñez
  • Carles Rafels

Abstract

The core of an assignment market is the translation, by the vector of minimum core payoffs, of the core of another better positioned market, the matrix of which has the properties of being dominant diagonal and doubly dominant diagonal. This new matrix is defined as the canonical form of the original assignment situation, and it is uniquely characterized by these three properties. The behavior of some well-known cooperative solutions in relation with the canonical form is analyzed. The kernel and the nucleolus of the assignment game, are proved to be the translation of the kernel and the nucleolus of the canonical representative by the vector of minimal core payoffs.

Suggested Citation

  • Marina Núñez & Carles Rafels, 2006. "A Canonical Representation for the Assignment Game: the Kernel and the Nucleolus," Working Papers 279, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:279
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    References listed on IDEAS

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    1. 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).
    2. 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.
    3. 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.
    4. 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.
    5. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 177-185.
    6. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 461-479, June.
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    Cited by:

    1. Trudeau, Christian, 2018. "From the bankruptcy problem and its Concede-and-Divide solution to the assignment problem and its Fair Division solution," Games and Economic Behavior, Elsevier, vol. 108(C), pages 225-238.

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