  This paper is concerned with an optimization problem that is constrained by
the Kantorovich optimal transportation problem. This bilevel optimization
problem can be reformulated as a mathematical problem with complementarity
constraints in the space of regular Borel measures. Because of the
non-smoothness induced by the complementarity relations, problems of this type
are frequently regularized. Here we apply a quadratic regularization of the
Kantorovich problem. As the title indicates, this is the second part in a
series of three papers. While the existence of optimal solutions to both the
bilevel Kantorovich problem and its regularized counterpart were shown in the
first part, this paper deals with the (weak-*) convergence of solutions to the
regularized bilevel problem to solutions of the original bilevel Kantorovich
problem.
