We present a non-cooperative game-theoretic approach for the distributed resource allocation problem in the context of multiple transmitters communicating with multiple receivers through parallel independent fading channels, which is closely related with small-cell multi-user orthogonal frequency division multiplexing (OFDM) networks, e.g., Wi-Fi hotspots. We assume that all the transmitters are rational, selfish, and each one carries the objective of maximizing its own transmit rate, subject

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... its power constraint. In such a game-theoretic study, the central question is whether a Nash equilibrium (NE) exists, and if so, whether the network operates efficiently at the NE. We show, for independent fading channels, there almost surely exists a unique NE. Finally we present the behavior of average network performance at the NE through numerical results, and we compare the optimal centralized approach with our decentralized approach.