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One of the fundamental challenges for peer-to-peer (P2P) systems is the ability to manage risks involved in interacting and collaborating with priorly unknown and potentially malicious parties. Reputation-based trust management can mitigate this risk by deriving the trustworthiness of a certain peer from that peer's behavior history. However, the existing reputation systems do not provide adequate reaction to quick changes in peers' behavior, raising serious concerns regarding their effectiveness in coping with dynamic malicious peers. In this paper we investigate the requirements on the dynamics of trust in P2P systems and propose a versatile trust metric which satisfies these requirements. In particular, our proposed metric is capable to detect and penalize both the sudden changes in peers' behavior and their potential oscillatory malicious behavior. Moreover, our metric is flexible to implement different types of trust dynamics. We evaluate our metric through simulation and show its unique features and advantages over the existing metrics.