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We present a game-theoretic study on the power and rate control problem in IEEE 802.11 WLANs where network participants choose appropriate transmission power and data rate to achieve maximum throughput with minimum energy consumption. In such game-theoretic study, the central issues are the existence, uniqueness of the Nash equilibrium (NE), the convergence to the NE and the system performance at the NE. We conduct our study for three specific games: the fixed-rate power control game GNPC, the fixed-power rate control game GNRC and the joint power rate control game GNJPRC. As main contributions, we establish the existence, uniqueness and convergence of the NE for the three games. In GNRC where the NE is inefficient, we provide pricing scheme to improve the efficiency. Based on our analysis on GNJPRC, we propose the joint power and rate control procedure to approach the NE which is proven to be social optimal. The procedure is distributed and simple to incorporate into the existing IEEE 802.11 MAC protocol.