We 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 a Nash equilibrium (NE) exists, and if so, whether the network operates efficiently at the NE. For independent continuous fading channels, we prove that the probability of a unique NE existing in the game is equal to 1. We show that this resource allocation problem can be studied as a potential game, and hence efficiently solved. We discuss the convergence of waterfilling based best-response algorithm. Finally, numerical results are provided to investigate the inefficiency of NE.