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We investigate the circumstances under which it is possible to discourage free-riding in a peer-to-peer system for resource-sharing by prioritizing resource allocation to peers with higher reputation. We use a model to predict conditions necessary for any reputation scheme to succeed in discouraging free-riding by this method. We show with simulations that for representative cases, a very simple autonomous reputation scheme works nearly as well at discouraging free-riding as an ideal reputation scheme. Finally, we investigate the expected dynamic behavior of the system.