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We develop a novel design framework for dynamic distributed spectrum sharing among secondary users (SUs), who adjust their power levels to compete for spectrum opportunities while satisfying the interference temperature (IT) constraints imposed by primary users. The considered interaction among the SUs is characterized by the following three unique features. First, the SUs are interacting with each other repeatedly and they can coexist in the system for a long time. Second, the SUs have limited and imperfect monitoring ability: they only observe whether the IT constraints are violated, and their observation is imperfect due to the erroneous measurements. Third, since the SUs are decentralized, they are selfish and aim to maximize their own long-term payoffs from utilizing the network rather than obeying the prescribed allocation of a centralized controller. To capture these unique features, we model the interaction of the SUs as a repeated game with imperfect monitoring. We first characterize the set of Pareto optimal operating points that can be achieved by deviation-proof spectrum sharing policies, which are policies that the selfish users find it in their interest to comply with. Next, for any given operating point in this set, we show how to construct a deviation-proof policy to achieve it. The constructed deviation-proof policy is amenable to distributed implementation, and allows users to transmit in a time-division multiple-access (TDMA) fashion. In the presence of strong multi-user interference, our policy outperforms existing spectrum sharing policies that dictate users to transmit at constant power levels simultaneously. Moreover, our policy can achieve Pareto optimality even when the SUs have limited and imperfect monitoring ability, as opposed to existing solutions based on repeated game models, which require perfect monitoring abilities. Simulation results validate our analytical results and quantify the performance gains enabled by the proposed spectr- m sharing policies.