Capacity Allocation in Vertically Integrated Railway Systems: A Rubinstein Sequential Bargaining Game Approach

The present paper proposes, for the first time, a game-theoretic bargaining based approach to allocating rail line capacity in the vertically integrated US rail system. A passenger rail agency (PRA) negotiates with a freight railroad (FRR) to obtain appropriate train paths. This market has specific features: FRR charges PRA a fee for access to the railroad; on the other hand, FRR compensates PRA for delayed services. In addition, by US Public Law 110-432 Amtrak passenger trains have priority over all freight trains. Passenger demand is elastic with respect to the service schedule convenience. With these features explicitly taken into account, a multi-step, game-theoretic bargaining model is put forward. We analytically solve this game and show that a schedule that maximizes the sum of utilities of PRA and FRR is the efficient one. We derive the equation yielding the net internal transfer between the two entities, and show that which player initiating the bargaining game does not change the equilibrium schedule, but alters the net internal transfer.