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Prior theory and empirical work emphasize the enormous free-riding problem facing peer-to-peer (P2P) sharing networks. Nonetheless, many P2P networks thrive. We explore two possible explanations that do not rely on altruism or explicit mechanisms imposed on the network: direct and indirect private incentives for the provision of public goods. The direct incentive is a traffic redistribution effect that advantages the sharing peer. We find this incentive is likely insufficient to motivate equilibrium content sharing in large networks. We then approach P2P networks as a graph-theoretic problem and present sufficient conditions for sharing and free-riding to co-exist due to indirect incentives we call generalized reciprocity.