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One of the key issues in cognitive transmission is for secondary users to dynamically acquire spare spectrum from the primary user and then select appropriate transmission schemes. The existing spectrum sharing scheme adopts a deterministic Cournot game to formulate this problem, of which the solution is Nash equilibrium. This formulation implicitly assumes that each secondary user is willing to fully exchange transmission parameters with all other users and hence knows the complete information of all others. However, this assumption may not be true in general. To remedy this, the present paper considers a more realistic assumption of incomplete information, i.e., each secondary user may choose to conceal its private information for achieving higher transmission benefit. Following this assumption, we adopt a probabilistic Cournot game to propose an opportunistic transmission scheme to maximize the transmission benefit of all secondary users. Bayesian equilibrium is considered as the solution of this game. Moreover, we rigorously prove that a secondary user can improve its expected transmission benefit by actively hiding its private transmission parameters and increasing the variance of its allocated spectrum.