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We consider a peer-to-peer network where nodes can send and receive files amongst their peers. File requests are generated randomly, and each new file can correspond to a different subset of peers that already have the file and hence can assist in the download. Nodes that help others are rewarded by being able to download more. The goal is to design a control algorithm that allocates requests and schedules transmissions to maximize overall throughput-utility, subject to meeting “tit-for-tat” constraints that incentivize participation. Our algorithm is shown to operate efficiently on networks with arbitrary traffic and channel sample paths, including wireless networks whose capacity can be significantly extended by the peer-to-peer functionality.