Intermodal hinterland network design with non-cooperative users

Intermodal hinterland transportation is becoming increasingly critical for global container supply chains and the management of these intermodal hinterland networks is challenging due to the fact that multiple actors often interact in practice. We analyze here the impact of having non-cooperative users in intermodal hinterland networks. To deal with this issue, we make use of non-cooperative game theory. The game we propose falls into the class of network design games but has key distinctive features. We provide some general results for the game and we provide an instance with no Nash equilibrium for the general case. Thus, we focus on the special case with a single intermodal connection available. We show that a Nash equilibrium always exists but that this one is not necessarily unique. We additionally identify key structural properties for this single-hub game. These properties enable us to identify all the Nash equilibria and a system optimal solution in polynomial time. The results enable us to evaluate the impacts having non-cooperative users in intermodal hinterland networks. We illustrate our results with an application related to the development of an extended gate in the Netherland and we derive a series of insights. Overall, the results show that the multiple users feature of intermodal hinterland networks is critical and needs to be accounted for at the network design stage.