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The authors 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. As main contributions, they establish the existence, uniqueness and convergence of the NE for the three games. The procedure is distributed and simple to incorporate into the existing IEEE 802.11 MAC protocol.
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