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Peer-to-peer (P2P) systems are flexible, robust, and self-organizing resource sharing infrastructures which are typically designed in a fully decentralized manner. However, a key problem of such systems are peers overusing a resource. This paper presents a fully decentralized scheme to achieve fair use in P2P systems, which does not require a priori information about a peer. The approach developed is based on a scarce resource trading scheme (SRTCPU), which utilizes CPU time as a form of payment. SRTCPU provides an incentive to offer CPU time in return of consuming a scarce resource. A distributed DNS has been implemented as an example application that uses SRTCPU.