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In the recent years, the demand for video streaming and multimedia communications over a mobile terminal has grown tremendously. These services require data rate of the order of hundreds of megabits per second (Mbps). However, a wireless terminal is an energy constrained device, and hence, a lot of attention is given to power control and link adaptation in a wireless network. Lately, game theory has emerged as a very promising method to tackle the power control issue in next generation cellular networks. A novel game-theoretic method is investigated for a third generation (3G) Universal Mobile Telecommunication System (UMTS) cellular architecture, wherein, the transmitter power and the adaptable code rate constitute the action set of players. The utility function for this action set aims to achieve the dual goal of maximizing the system throughput and minimizing the power consumption. It has been found that the game-theoretic model with a modified cost function leads to a much better solution than the one with fair scheduling or a greedy approach.