Pricing traffic in a spanning network

Users need to connect a pair of target nodes in the network. They share the fixed connection costs of the edge. The system manager elicits target pairs from users, builds the cheapest forest meeting all demands, and choose a cost sharing rule satisfying:Routing-proofness: a user cannot lower his cost by reporting as several users along an alternative path connecting his target nodes;Stand Alone core stability: no group of users pay more than the cost of a subnetwork meeting all connection needs of the group.We construct two such rules. When all connecting costs are 0 or 1, one is derived from the random spanning tree weighted by the volume of traffic on each edge; the other is the weighted Shapley value of the Stand Alone cooperative game. Both rules are then extended by the familiar piecewise-linear technique. The former is computable in polynomial time, the latter is not.