Incentives for resource sharing are crucial for the proper operation of P2P networks. The principle of the incen- tive mechanisms in current content sharing P2P networks such as BitTorrent is to have peers exchange content of mu- tual interest. As a consequence, a peer can actively par- ticipate in the system only if it shares content that is of immediate interest to other peers. In this paper we pro- pose to lift this restriction by using bandwidth rather than content as the resource upon which incentives are based. Bandwidth, in contrast to content, is independent of peer interests and so can be exchanged between any two peers. We present the design of a protocol called amortized tit- for-tat (ATFT) based on the bandwidth-exchange concept. This protocol defines mechanisms for bandwidth exchange corresponding to those in BitTorrent for content exchange, in particular for finding bandwidth borrowers that amortize the bandwidth borrowed in the past with their currently idle bandwidth. In addition to the formally proven incentives for bandwidth contributions, ATFT provides natural solu- tions to the problems of peer bootstrapping, seeding incen- tive, peer link asymmetry, and anonymity, which have previ- ously been addressed with much more complex designs. Ex- periments with a real-world dataset confirm that ATFT is efficient in enforcing bandwidth contributions and results in download performance better than provided by incentive mechanisms based on content exchange.