In leased line services used by ISPs (Internet service providers) the bandwidth is fixed, but the traffic changes dynamically. To address this, we propose an auction method for the dynamic allocation of bandwidth to ISPs sharing backbone networks. By the method, backbone networks can be used effectively as each ISP is able to secure bandwidth according to its own policy. The Internet users can also be expected to receive good services, as it has been made possible for them to get all information about all ISPs, such as access fee and QoS provided, and to select their congenial ISPs among all ISPs according to this information. We compare a dynamic bandwidth allocation service (dynamic allocation of bandwidth to ISPs) with a leased line service (fixed allocation of bandwidth to ISPs) by using the users' utility to estimate the effectiveness of the proposed method.