On the dimension of the core of the assignment game
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.
|Date of creation:||2006|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://www.ere.ub.es
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Solymosi, Tamas & Raghavan, Tirukkannamangai E S, 1994. "An Algorithm for Finding the Nucleolus of Asignment Games," International Journal of Game Theory, Springer, vol. 23(2), pages 119-43.
- Sotomayor, Marilda, 2003. "Some further remark on the core structure of the assignment game," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 261-265, December.
- 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, vol. 27(2), pages 301-303.
- 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 461-79, June.
- T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer, vol. 30(2), pages 177-185.
When requesting a correction, please mention this item's handle: RePEc:bar:bedcje:2006167. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Espai de Recerca en Economia)
If references are entirely missing, you can add them using this form.