In this paper, we investigate equilibrium states of incomplete information model of control. The formal description of the model of control is a Bayesian game with two decision-makers. Determination of equilibrium states is performed with consideration of this model to be in the form of static and dynamic games with incomplete information. We study various types of game-theoretic models with incomplete knowledge of the first player about possible types of the second player and vice versa, and models with bilateral incomplete knowledge of players about possible types of each other. Labor cost function coefficients and control cost function coefficients are treated as uncontrolled information parameters. We consider the Bayesian Nash equilibrium for static games, as well as the perfect Bayesian Nash equilibrium for dynamic games. Also, we demonstrate the influence of players various awareness types on strategies and objective functions chosen by each game participant. The player awareness is defined by player subjective representation of possible types of other players.