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Data, audio and video services over 3G networks possess certain requirements in QoS and thus in resources. Accommodating such service requests constitutes a challenge for UMTS networks. To this end, 3GPP Release 5 introduces the high speed downlink packet access (HSDPA). In this paper, we propose: i) an auction-based HSDPA resource allocation mechanism, which consists of a series of Generalized Vickrey Auctions that are conducted in the short time-scale over which the network resources are allocated and ii) a set of innovative user utility functions. These functions provide a quantification of both the user's willingness to pay for reserving resources in the short time-scale auctions and his attained utility from the pattern of resources allocated during his long time-scale service session. The utility functions are additive and are used as bidding functions in the series of auctions the user participates. Each user selects one of these functions, which is scaled by his total willingness to pay. Then, the network runs the auctions by bidding on behalf of each user. The effectiveness of our mechanism has been assessed experimentally and it appears that most of the users either are served very satisfactorily or are allocated very limited quantities of resources (if at all) at a low total charge.