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While peer-to-peer (P2P) video streaming systems have achieved promising results, they introduce a large number of unnecessary traverse links, which consequently leads to substantial network inefficiency. To address this problem and achieve better streaming performance, we propose to enable cooperation among “group peers,” which are geographically neighboring peers with large intra-group upload and download bandwidths. Considering the peers' selfish nature, we formulate the cooperative streaming problem as an evolutionary game and derive, for every peer, the evolutionarily stable strategy (ESS), which is the stable Nash equilibrium and no one will deviate from. Moreover, we propose a simple and distributed learning algorithm for the peers to converge to the ESSs. With the proposed algorithm, each peer decides whether to be an agent who downloads data from the peers outside the group or a free-rider who downloads data from the agents by simply tossing a coin, where the probability of being a head for the coin is learned from the peer's own past payoff history. Simulation results show that the strategy of a peer converges to the ESS. Compared to the traditional non-cooperative P2P schemes, the proposed cooperative scheme achieves much better performance in terms of social welfare, probability of real-time streaming, and video quality (source rate).