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Although there are several successful commercial deployments of live P2P streaming systems, the current designs; lack incentives for users to contribute bandwidth resources; lack adaptation to aggregate bandwidth availability; and exhibit poor video quality when bandwidth availability falls below bandwidth supply. In this paper, we propose, prototype, deploy, and validate LayerP2P, a P2P live streaming system that addresses all three of these problems. LayerP2P combines layered video, mesh P2P distribution, and a tit-for-tat-like algorithm, in a manner such that a peer contributing more upload bandwidth receives more layers and consequently better video quality. We implement LayerP2P (including seeds, clients, trackers, and layered codecs), deploy the prototype in PlanetLab, and perform extensive experiments. We also examine a wide range of scenarios using trace-driven simulations. The results show that LayerP2P has high efficiency, provides differentiated service, adapts to bandwidth deficient scenarios, and provides protection against free-riders.