In this paper, a game-theoretic analysis for the resource allocation policies in fading multiple-access channels (MAC) in the presence of quality of service (QoS) constraints is performed. Effective capacity, which provides the maximum constant arrival rate, or throughput, that a given service process can support while satisfying statistical delay constraints, is considered in a multiuser scenario. We assume that the channel side information (CSI) is available at both the receiver and transmitters, and the transmitters are selfish, rational with certain QoS constraints and average power limitations. Without the aid of the receiver, we prove that there is always a unique admissible Nash equilibrium of the noncooperative power control game. The Nash equilibrium of the power control game is proved to be always inside the rate region where successive decoding techniques are used at the receiver.