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We devise a model to study the phenomenon of free-riding and free-identities in peer-to-peer systems. At the heart of our model is a user of a certain type, an intrinsic and private parameter that reflects the user's willingness to contribute resources to the system. A user decides whether to contribute or free-ride based on how the current contribution cost in the system compares to her type. We study the impact of mechanisms that exclude low type users or, more realistically, penalize free-riders with degraded service. We also consider dynamic scenarios with arrivals and departures of users, and with whitewashers -users who leave the system and rejoin with new identities to avoid reputational penalties. We find that imposing penalty on all users that join the system is effective under many scenarios. In particular, system performance degrades significantly only when the turnover rate among users is high. Finally, we show that the optimal exclusion or penalty level differs significantly from the level that optimizes the performance of contributors only for a limited range of societal generosity levels.