Usage-based or congestion-based charging schemes have been regarded as a relevant way to control congestion and to differentiate services among users in telecommunication networks; auctioning for bandwidth appears as one of several possibilities. In a previous work, the authors designed a multi-bid auction scheme where users compete for bandwidth at a link by submitting several couples (amount of bandwidth asked, associated unit price) so that the link allocates the bandwidth and computes the charge according to the second price principle. They showed that incentive compatibility and efficiency among other properties are verified. We propose in the present paper to extend this scheme to the case of a network, by using the properties/assumptions that the backbone network is overprovisionned and the access networks have a tree structure.