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Resource sharing in peer-to-peer environments with selfish participants suffers from the free-riding phenomenon unless the environment provides appropriate countermeasures. We present a concept for a distributed desktop grid which promotes fairness and inhibits free-riding. It contains a shared-history reputation mechanism designed for use in dynamic peer-to-peer systems. In simulations based on real-world network delay and workload information, we show that our concept offers a considerable speedup over non-distributed computation while effectively thwarting free-riding. Moreover, we assess the benefits of self-organizing super-peer overlays for Desktop Grids.