  A mathematical programming problem with affine equilibrium constraints
(AMPEC) is a bilevel programming problem where the lower one is a parametric
affine variational inequality. We formulate some classes of bilevel programming
in forms of MPEC. Then we use a regularization technique to formulate the
resulting problem as a mathematical program with an additional constraint
defined by the difference of two convex functions (DC function). A main feature
of this DC decomposition is that the second component depends upon only the
parameter in the lower problem. This property allows us to develop
branch-and-bound algorithms for globally solving AMPEC where the adaptive
rectangular bisection takes place only in the space of the parameter. As an
example, we use the proposed algorithm to solve a bilevel Nash-Cournot
equilibrium market model. Computational results show the efficiency of the
proposed algorithm.
