Matching Games: The Least Core and the Nucleolus

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.