Cost Allocation Under Competition: How to Reduce Externalities?

Abstract

We consider a setting in which a not-for-profit rail infrastructure provider divides the costs of track maintenance and renewals and the costs of managing track access proportionally among above-rail operators based on their usage. We study a proposed access charge policy aimed at incentivizing the above-rail operators to use long train configurations in order to reduce congestion in the system. The proposed access charge policy sets a target length of a train configuration and gives a discount on an operator's access charge if the operator employs a train configuration of at least the target length. As a result, the access charge of an operator is no longer independent of the actions of other operators, and operators need to be strategic in their decision making. We discuss the different situations that may arise in the induced cost allocation game for two operators for a given discount factor and establish conditions under which a discount factor incentivizes both operators to employ train configurations of at least the target length. If there does not exist a discount factor that incentivizes both operators to employ long train configurations, then we demonstrate that setting a sub-optimal target and a discount factor that incentivizes both train operators to reach that target may be beneficial in terms of reducing congestion.