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We present FlightPath, a novel peer-to-peer streaming application that provides a highly reliable data stream to a dynamic set of peers. We demonstrate that FlightPath reduces jitter compared to previous works by several orders of magnitude. Furthermore, FlightPath uses a number of run-time adaptations to maintain low jitter despite 10% of the population behaving maliciously and the remaining peers acting selfishly. At the core of FlightPath's success are approximate equilibria. These equilibria allow us to design incentives to limit selfish behavior rigorously, yet they provide sufficient flexibility to build practical systems. We show how to use an Ɛ-Nash equilibrium, instead of a strict Nash, to engineer a live streaming system that uses bandwidth efficiently, absorbs flash crowds, adapts to sudden peer departures, handles churn, and tolerates malicious activity.