Matching games: the least core and the nucleolus

  • Authors:
  • Walter Kern;Daniël Paulusma

  • Affiliations:
  • Faculty of Mathematical Sciences, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands;Faculty of Mathematical Sciences, University of Twente, P.O. Box 217, 7500 AE Ebschede, The Netherlands

  • Venue:
  • Mathematics of Operations Research
  • Year:
  • 2003

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Abstract

A matching game is a cooperative game defined by a graph G = (N, E). The player set is N and the value of a coalition S ⊆ N is defined as the size of a maximum matching in the subgraph induced by S. We show that the nucleolus of such games can be computed efficiently. The result is based on an alternative characterization of the least core, which may be of independent interest. The general case of weighted matching games remains unsolved.