Peer-to-peer (P2P) networks are becoming an important medium for the distribution of consumer information goods. However, there is little academic research into the behavior of these networks. We analyze the impact of positive and negative network externalities on the optimal size of P2P networks. Using data collected from the six most popular OpenNap P2P music-sharing networks between December 19, 2000, and April 22, 2001, we find that additional users contribute value in terms of additional network content at a diminishing rate, while they impose costs in terms of congestion on shared resources at an increasing rate. Using an analytic model, we explore technical solutions to the congestion problem, for example, by increasing network capacity. This model suggests that although increasing capacity will allow more users to participate on the network, there may be little incentive for network operators to do so. This is because diminishing positive network externalities imply decreasing content benefits to adding more users. Together these results suggest that the optimal size of a P2P network may be bounded in many common implementations. We conclude by discussing various options to improve network performance including network membership rules and usage- based pricing.