This study proposes a game theoretic approach to assigning freight shipments to a rail network system comprising multiple sub-networks, each of which own and operated by a specific carrier. This setting best represents the freight rail traortation system in the United States. Each player maximizes its benefit, subject to a set of constraints including line capacity, node capacity, demand requirements. A player’s decision variable not only appears in the objective function of its competitors but also in their constraints; therefore, the problem is a Generalized Nash Equilibrium Problem (GNEP) with shared constraints. To solve the problem for equilibrium, we first develop the KKT conditions for each player and then solve a system comprising of KKT conditions of all players. The later system is essentially equivalent to a Nonlinear complementarity problem which can be solved using off-the-shelf software packages. In addition, we analytically show that this problem has a unique global equilibrium solution. To show applicability of the proposed approach, the problem is solved for a small hypothetical rail network as well as an version of US rail network and policy insights are offered. Keywords : Generalized Nash Equilibrium Problem, KKT conditions, game theoretic approach, Nonlinear complementarity problem, Freight assignment.
