On the Toll Setting Problem

We consider the problem of determining a set of optimal prices on a subset of all arcs of a highway network in order to maximize the revenue of the government or private societies. We suppose we have rational clients who want to minimize their cost and so will use the cheapest path from origin to destination, where the cost of a path is determined by all costs and prices on the arcs of the path. A policy of optimal tarification consists in determining prices low enough to favorize the use of toll arcs and on the other hand high enough to get important profits from the used arcs. In order to take into account this interaction between the leader (government or society) and the followers (clients), we formulate this problem as a bilevel problem.