The Role of Cost Allocation in Locational Models

In facility locational models of public-service systems (for example, fire extinguishment, police and ambulance systems), the allocation of the system's operating cost and the locations of the service stations are in principle very closely related. The farther a user is from the service station, the lower is the cost share he should he willing to defray, and vice versa. We consider in this paper the problem of locating one facility in a tree network, T, and suggest a game theoretic approach for generating the facility location y in T and a corresponding cost allocation scheme q. The pairs (y, q) generated by our game theoretic approach are contained in a least core associated with the locational model, and they are all stable in the sense that they cannot be improved upon by any subset of users.