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We present the first peer-to-peer data streaming application that guarantees predictable throughput and low latency in the BAR (Byzantine/Altruistic/Rational) model, in which non-altruistic nodes can behave in ways that are self-serving (rational) or arbitrarily malicious (Byzantine). At the core of our solution is a BAR-tolerant version of gossip, a well-known technique for scalable and reliable data dissemination. BAR Gossip relies on verifiable pseudo-random partner selection to eliminate non-determinism that can be used to game the system while maintaining the robustness and rapid convergence of traditional gossip. A novel fair enough exchange primitive entices cooperation among selfish nodes on short timescales, avoiding the need for long-term node reputations. Our initial experience provides evidence for BAR Gossip's robustness. Our BAR-tolerant streaming application provides over 99% convergence for broadcast updates when all clients are selfish but not colluding, and over 95% convergence when up to 40% of clients collude while the rest follow the protocol. BAR Gossip also performs well when the client population consists of both selfish and Byzantine nodes, achieving over 93% convergence even when 20% of the nodes are Byzantine.