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With the emergence of shared overlay network infrastructures and the recent deregularization of spectrum policies, a new, more dynamic network resource "market" is emerging. To effectively operate this new market, resource management becomes of paramount importance. This is especially important for multimedia streaming applications that require a large amount of resources to guarantee an acceptable level of multimedia quality to the end users. However, providing the necessary resources to various networked multimedia users is challenging since they have different requirements in terms of multimedia characteristics, delay, or network constraints. To simplify this problem, we propose a novel utility-based resource management scheme for multi-user multimedia transmission over networks. To manage the available resources, the resource manager deploys bargaining solutions from economics in order to explicitly consider the utility impact for different resource allocation schemes. We focus on the Kalai-Smorodinsky bargaining solution (KSBS) because it can successfully model relevant noncollaborative utility-aware fairness policies for multimedia users. The KSBS explicitly considers the application-specific utility domain (i.e., resulting multimedia quality) when performing the resource allocation. The proposed KSBS allocates the resources in such a way that the achieved utility of every participating station incurs the same quality penalty, i.e., the same decrease in video quality as opposed to their maximum achievable qualities. Our simulations show that the proposed game-theoretic resource management provides a fairer and more efficient allocation of resources in terms of derived multimedia quality.