On cost allocation in networks with threshold based discounting

We consider network design in which each pair of nodes can communicate via a direct link and the communication flow can be delivered through any path in the network. The cost of flow through each link is discounted if and only if the amount of flow exceeds a certain threshold. This exploitation of economies of scale encourages the concentration of flows and use of a relatively small number of links. We will call such networks hub-like networks. Applications include telecommunications, airline traffic flow, and mail delivery networks. The cost of services delivered through a hub-like network is distributed among its users who may be individuals or organizations with possibly conflicting interests. The cooperation of these users is essential for the exploitation of economies of scale. Consequently, there is a need to find a fair distribution of the cost of providing the service among users of such a network. In order to describe this cost allocation problem we formulate the associated cooperative game, to be referred to as the hub-like game. In this game special attention is paid to users' contribution to economies of scale. We then demonstrate that a certain cost allocation solution (the core of hub-like game), which provide users with the incentive to cooperate, can be efficiently characterized.