  Matching problems with linearly transferable utility (LTU) generalize the
well-studied transferable utility (TU) case by relaxing the assumption that
utility is transferred one-for-one within matched pairs. We show that LTU
matching problems can be reframed as nonzero-sum games between two players,
thus generalizing a result from von Neumann. The underlying linear programming
structure of TU matching problems, however, is lost when moving to LTU. These
results draw a new bridge between non-TU matching problems and the theory of
bimatrix games, with consequences notably regarding the computation of stable
outcomes.
