  In this paper we relate the Equilibrium Assignment Problem (EAP), which is
underlying in several economics models, to a system of nonlinear equations that
we call the "nonlinear Bernstein-Schr\"odinger system", which is well-known in
the linear case, but whose nonlinear extension does not seem to have been
studied. We apply this connection to derive an existence result for the EAP,
and an efficient computational method.
