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Recent research in wireless multimedia streaming has focused on optimizing the multimedia quality in isolation, at each station. However, the cross-layer transmission strategy deployed at one station impacts and is impacted by the other stations, as the wireless network resource is shared among all competing users. Hence, efficient and fair resource management for autonomous wireless multimedia users becomes very important. We consider quality-based fairness schemes based on axiomatic bargaining theory, which can ensure that the autonomous multimedia stations incur the same drop in multimedia quality as compared to a maximum achievable quality for each wireless station. Implementing this quality-based fairness solution in the time-varying channel condition requires high-computational complexity and communication overheads. Hence, we develop solutions that significantly reduce the computational complexity and communication overheads. Our simulations show that the proposed game-theoretic resource management can indeed guarantee desired utility-fair allocations when wireless stations deploy different cross-layer strategies.