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


  • Marina Núñez
  • Carles Rafels


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.

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

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    References listed on IDEAS

    1. 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.
    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.
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    assignment game; core; kernel; nucleolus;


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