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In this paper, we propose a new resource allocation framework for multimedia systems that perform multiple simultaneous video decoding tasks. We jointly consider the available system resources (e.g., processor cycles) and the video decoding task's characteristics such as the sequence's content, the bit-rate, and the group of pictures (GOP) structure, in order to determine a fair and optimal resource allocation. To this end, we derive a quality-complexity model that determines the quality [in terms of peak signal-to-noise ratio (PSNR)] that a task can achieve given a certain system resource allocation. We use these quality-complexity models to determine a quality-fair and Pareto-optimal resource allocation using the Kalai-Smorodinski Bargaining Solution (KSBS) from axiomatic bargaining theory. The KSBS explicitly considers the resulting multimedia quality when performing a resource allocation and distributes quality-domain penalties proportional to the difference between each video decoding task's maximum and minimum quality requirements. We compare the KSBS with other fairness policies in the literature and find that, because it explicitly considers multimedia quality, it provides significantly fairer resource allocations in terms of the resulting PSNR compared with policies that operate solely in the resource domain. To weight the quality impact of the resource allocations to the different decoding tasks depending on application-specific requirements or user preferences, we generalize the existing KSBS solution by introducing bargaining powers based on each video sequence's motion and texture characteristics.