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This paper presents a theoretic framework of optimal resource allocation and admission control for peer-to-peer networks. Peer's behavioral rankings are incorporated into the resource allocation and admission control to provide differentiated services and even to block peers with bad rankings. These peers may be free-riders or suspicious attackers. A peer improves her ranking by contributing resources to the P2P system or deteriorates her ranking by consuming services. Therefore, the ranking-based resource allocation provides necessary incentives for peers to contribute their resources to the P2P systems. We define a utility function which captures the best wish for the source peer to serve competing peers, who request services from the source peer. Although the utility function is convex, Harsanyi-type social welfare functions are devised to obtain a unique optimal resource allocation that achieves max-min fairness. The parameters used in our model can be derived from the nature of the services or chosen by the source peer. No private information is required to reveal from individual peers. This prevents selfish peers to play the system strategically and cheat the resource allocation mechanism for their own benefits. The resource allocation and admission control are fully distributed and linearly scalable.