In this paper we study the interaction between two wireless communication systems in interference Rayleigh fading channel with incomplete information. This is modelled as a game with incomplete information where players choose between frequency division multiplexing (FDM) and full spread (FS) of their transmit power. Previously, a closed form expression for an FDM equilibrium point was derived. This point was shown to be Pareto dominant (i.e. component wise larger payoff) over the pure-FS NE point in which both players use the entire band and interfere with each other. This quality makes the FDM equilibrium a desirable operating point to which distributed algorithms for spectrum management may converge to. In this paper, we show that the previously derived FDM equilibrium point exists and is unique in Rayleigh fading channels. This is important for its future implementation. We conclude with numerical evaluation of FDM equilibrium points in Rayleigh fading channels with incomplete information and study the effect of averaged received power on the behavior of selfish users in such channels.