We present a Bayesian game-theoretic approach for the distributed resource allocation problem in the context of K-user fading multiple access channels (MAC). We assume that users have incomplete information about the channel state information (CSI), i.e., each user knows his own channel state, but does not know the states of other users. All users (transmitters) are considered to be rational, selfish, and each one carries the objective of maximizing its own achievable data rate. In such a game-theoretic study, the central question is whether a Bayesian equilibrium (BE) exists. Based on the assumption of two channel states, we prove that there exists exactly one BE in this game.