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We propose a novel wireless radio resource manager to control both the transmission power and the bit rate of mobile devices cooperatively, whereas previous work has focused on handling them separately. The proposed scheme is called Genetic Algorithm for Mobiles Equilibrium (GAME). Based on an evolutionary computational model, GAME assigns optimally both the transmitting power and bit rate values to every mobile device in a given cell. Optimal allocation is in the sense that every mobile unit gets only enough resources necessary for meeting or exceeding its quality of service (QoS) requirements. GAME solves an optimization function that strives to maintain the QoS requirements of the different multimedia streams subject to the physical channel characteristics. Having done that, we gain further benefits as well. In addition to maintaining the QoS requirements, GAME tends to prefer assigning lower levels of transmission power, thus extending the mobile units' battery life, minimizing interference seen by other users, and significantly decreasing the call blocking (or dropping) rates. Furthermore, GAME radio resource allocations reduce infrastructure costs by requiring fewer base stations per square kilometer. In our experiments, we have seen a 70% average expansion in the base station coverage area with 40% decrease in mobile call outage probability among other benefits.