Capacity allocation in vertically integrated rail systems: A bargaining approach

This paper presents a game-theoretic bargaining approach to allocating rail line capacity in vertically integrated systems. A passenger rail agency negotiates with the host freight railroad to determine train schedules and the associated payment. The objective on the passenger side is to maximize utility, i.e., revenue minus costs of passenger train operations, passenger schedule delay and en-route delay; the freight side minimizes the costs of train departure delay, en-route delay, loss of demand, and track maintenance. Bargaining in both complete and incomplete information settings are considered; the latter arises because the freight railroad may withhold its private cost information. With complete information, we find that the equilibrium payments proposed by the passenger rail agency and the host freight railroad will each be invariant to who initiates the payment bargaining, although the actual payment does depend on who is the initiator. The equilibrium schedule maximizes system welfare. With incomplete information, the passenger rail agency may choose between pooling and separating equilibrium strategies while proposing a payment, depending on its prior belief about the cost type of the freight railroad; whereas the host freight railroad will adopt strategies that do not reveal its cost type. To identify equilibrium schedules, a pooling equilibrium is constructed along with conditions for the existence of equilibrium schedules. We further conduct numerical experiments to obtain additional policy-relevant insights.