Cost Sharing in Chains and Other Fixed Trees

We consider a cost sharing problem among agents on a line. The problem is closely related to the classic airport game, but in our model agents are characterized by their location, rather than their needed runway length. We characterize a family of cost allocation rules in which agents pay a share of the incremental costs as well as any debt from upstream agents, with the Bird rule (where agents pay their full incremental cost) and the ‘free rider’ rule (where the terminal agent pays everything) as the two extreme cases. We also extend the analysis to cost sharing among agents located on a fixed tree structure.