A reduction method for local sensitivity analyses of network equilibrium arc flows

A reduction method is proposed which allows standard sensitivity techniques for variational inequalities to applied to equilibrium network flow problems without additional assumptions on either the underlying network or the numbers of active paths. In particular it is shown that under mild regularity conditions, small perturbations of equilibria can be given an explicit arc-flow representation which is free of path-flow variables. It is also shown that this reduced form allows the differentiability of perturbations to be studied by standard methods. These results are illustrated by a small numerical example.