Peer-to-peer (P2P) file sharing networks are an important medium for the distribution of information goods. However, there is little empirical research into the optimal design of these networks under real-world conditions. Early speculation about the behavior of P2P networks has focused on the role that positive network externalities play in improving performance as the network grows. However, negative network externalities also arise in P2P networks because of the consumption of scarce network resources or an increased propensity of users to free ride in larger networks, and the impact of these negative network externalities--while potentially important--has received far less attention. Our research addresses this gap in understanding by measuring the impact of both positive and negative network externalities on the optimal size of P2P networks. Our research uses a unique dataset collected from the six most popular OpenNap P2P networks between December 19, 2000, and April 22, 2001. W find that users contribute additional value to the network at a decreasing rate and impose costs on the network at an increasing rate, while the network increases in size. Our results also suggest that users are less likely to contribute resources to the network as the network size increases. Together, these results suggest that the optimal size of these centralized P2P networks is bounded--at some point the costs that a marginal user imposes on the network will exceed the value they provide to the network. This finding is in contrast to early predictions that larger P2P networks would always provide more value to users than smaller networks. Finally, these results also highlight the importance of considering user incentives--an important determinant of resource sharing in P2P networks--in network design.