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In this paper we present an open multi-agent based Desktop Grid System that improves the performance of cooperative clients while decreasing the performance of non-cooperative clients as an incentive for good conduct. This is achieved by trust-based job client and worker algorithms that take into account the local and global history of the credibility and reliability experiences between agents, as well as their current state. We show with simulation results that the algorithms provide performance increases by applying standard Desktop Grid performance metrics and evaluating the system in several scenarios with a varying number of disturbances to the system. In this paper, we focus on the task of minimising wasteful computation and thus increasing the benefit of grid participation for the agents.