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On the dimension of the core of the assignment game

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  • Marina Nunez Oliva
  • Carlos Rafels Pallarola

    (Universitat de Barcelona)

Abstract

The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the dimension of the core of the assignment game. This result provides an easy procedure to determine the dimension of the core directly from the entries of the assignment matrix and shows that the dimension of the core is not as much determined by the number of optimal matchings as by their relative position in the assignment matrix.

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Bibliographic Info

Paper provided by Universitat de Barcelona. Espai de Recerca en Economia in its series Working Papers in Economics with number 167.

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Length: 25 pages
Date of creation: 2006
Date of revision:
Handle: RePEc:bar:bedcje:2006167

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Postal: Espai de Recerca en Economia, Facultat de Ciències Econòmiques. Tinent Coronel Valenzuela, Num 1-11 08034 Barcelona. Spain.
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  1. 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, Springer, vol. 27(2), pages 301-303.
  2. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer, Springer, vol. 30(2), pages 177-185.
  3. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 91(3), pages 461-79, June.
  4. Sotomayor, Marilda, 2003. "Some further remark on the core structure of the assignment game," Mathematical Social Sciences, Elsevier, Elsevier, vol. 46(3), pages 261-265, December.
  5. Solymosi, Tamas & Raghavan, Tirukkannamangai E S, 1994. "An Algorithm for Finding the Nucleolus of Asignment Games," International Journal of Game Theory, Springer, Springer, vol. 23(2), pages 119-43.
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Cited by:
  1. Núñez, Marina & Rafels, Carles, 2009. "A glove-market partitioned matrix related to the assignment game," Games and Economic Behavior, Elsevier, Elsevier, vol. 67(2), pages 598-610, November.
  2. F. Javier Martinez-de-Albeniz & Marina Nunez & Carles Rafels, 2010. "Assignment markets with the same core," Working Papers in Economics, Universitat de Barcelona. Espai de Recerca en Economia 239, Universitat de Barcelona. Espai de Recerca en Economia.
  3. Schwarz, Michael & Yenmez, M. Bumin, 2011. "Median stable matching for markets with wages," Journal of Economic Theory, Elsevier, Elsevier, vol. 146(2), pages 619-637, March.

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