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In this paper, we study both positive and negative scale effects on the operations of peer-to-peer (P2P) file sharing networks and propose the optimal sizing (number of peers) and grouping (number of directory intermediary) decisions. Using analytical models and simulation, we evaluate various performance metrics to investigate the characteristics of a P2P network. Our results show that increasing network scale has a positive effect on the expected content availability and transmission cost, but a negative effect on the expected provision and search costs. We propose an explicit expression for the overall utility of a content sharing P2P community that incorporates tradeoffs among all of the performance measures. This utility function is maximized numerically to obtain the optimal network size (or scale). We also investigate the impact of various P2P network parameters on the performance measures as well as optimal scaling decisions. Furthermore, we extend the model to examine the grouping decision in networks with symmetric interconnection structures and compare the performance between random- and location-based grouping policies.