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The authors present a general game-theoretical framework for the resource allocation problem in the downlink scenario of distributed wireless small-cell networks, where multiple Access Points (APs) or small base stations send independent coded network information to multiple Mobile Terminals (MTs) through Orthogonal Frequency Division Multiplexing (OFDM) channels. In such a game-theoretic study, the central question is whether Nash Equilibrium (NE) exists, and if so, whether the network operates efficiently at the NE. For independent continuous fading channels, they prove that the probability of a unique NE existing in the game is equal to 1.
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