We explore the complexity of nucleolus computation in b-matching games on bipartite graphs. We show that computing the nucleolus of a simple b-matching game is N P-hard even on bipartite graphs of maximum degree 7. We complement this with partial positive results in the special case where b values are bounded by 2. In particular, we describe an efficient algorithm when a constant number of vertices satisfy bv = 2 as well as an efficient algorithm for computing the non-simple b-matching nucleolus when b ≡ 2. * We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC). Cette recherche a été financée par le Conseil de recherches en sciences naturelles et en génie du Canada (CRSNG).

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