A Bayesian game-theoretic model is developed to design and analyze the resource allocation problem in K-user fading multiple access channels (MAC), where users are assumed to selfishly maximize their average achievable rates with incomplete information about the fading channel gains. In such a game-theoretic study, the central question is whether a Bayesian equilibrium exists, and if so, whether the network operates efficiently at the equilibrium point. We prove that there exists exactly one Bayesian equilibrium in our game. Furthermore, we study the network sum-rate maximization problem by assuming that users coordinate to the symmetric strategy profile. This result also serves as an upper bound for the Bayesian equilibrium. Finally, simulation results are provided to show the network efficiency at the unique Bayesian equilibrium, and compare it with other strategies.