We study how secret communication can be effected by the fact that an adversary’s capability to eavesdrop on a collection of communications from a base station to a set of users may be restricted and unknown to the transmitter. In this situation, the eavesdropping adversary might have to choose which user to eavesdrop upon if it cannot eavesdrop upon the full set. Thus, the transmitter must make a decision on how to better maintain secret communication, and to do this it must take into account that the eavesdropper might possibly be passive or could be an active adversary that must actively make a choice about which user to eavesdrop upon. Using an example of a Bayesian game-theoretical model with unknown eavesdropping capacity we show why it is important to incorporate in a secret transmission protocol the possibility of an eavesdropper having restricted eavesdropping capacity. Also, since the equilibrium strategies are obtained explicitly, we establish some interesting properties that can guide deployment o