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Hidden information is a critical issue for the successful delivery of services in grid systems. It arises when the agents (hardware and software resources) employed to serve a task belong to multiple administrative domains, thus rendering monitoring of remote resource provision absent or unreliable. Therefore, the grid service broker can often observe only the outcome of the collective effort of groups of agents rather than their individual efforts, which makes it hard to identify cases of free-riding or low-performing agents. In this paper, we first identify cases of hidden information in grid systems and explain why they cannot be handled satisfactorily by the existing accounting systems. Second, we develop and evaluate a reputation-based mechanism enabling the grid service broker to deal effectively with hidden information. Our mechanism maintains a reputation metric for each agent; we propose and evaluate several approaches on how to update this metric based only on the observations of collective outcomes. We also provide recommendation on which such approach is preferable for a grid service broker in collaborative or competitive environments.