  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 NP-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 b(v) = 2 as well as an efficient algorithm for
computing the non-simple b-matching nucleolus when b = 2.
