Pricing telecommunication networks has become a topic of high interest in order to deal with the increasing num- ber of subscribers as well as more and more demanding applications. Users' behavior (or preferences) is usually represented by means of the so-called utility function, but in most cases this function expresses the instantaneous level of satisfaction for the quality of service provided. In this paper, we aim at extending a previous work on auctions for bandwidth to the case where users (or applications) are sensitive to the history of their previous allocations. We introduce a mechanism which takes bids in the form of a fi- nite set of three-(or more)-dimensional points, indicatin g the bidders willingness to pay for a given quantity, con- tingent on a given history of allocations or prices to the bidder. Bids are partial representations of continuous uti l- ity surfaces. The mechanism computes prices and alloca- tions that are approximately (within specified bounds) and myopically incentive compatible and approximately (withi n specified bounds) and myopically efficient. The results are approximate because we use piecewise linear approxima- tions of the unknown true continuous utility functions. Thi s extension also includes a refinement of the scheme previ- ously published by providing a closer approximation of real user demand functions.