This article aims to establish a Bayesian Stackelberg game framework for analyzing the incomplete information demand response management with overlapping electricity sales areas, and further provide the corresponding equilibrium strategies. Considering that the satisfaction parameters of power users are private, a Bayesian game model is constructed among these power users, and a non-cooperative game model is established due to the price competition of microgrids. To ensure the sequential interactions of demand response, a Stackelberg game is developed by assuming that the microgrids are leaders and the power users are followers, and the Bayesian Nash equilibrium and Stackelberg equilibrium are proved to exist and are unique under some conditions. In addition, the Bayesian Nash equilibrium for power users is obtained using the fictitious play method in the symmetrical case, and an iterative algorithm is presented for determining the Stackelberg equilibrium. Finally, the numerical simulations are provided showing the effectiveness and convergence of the iterative algorithm, which indicates that our approach can enhance profits for microgrids while ensuring power supply and demand balance.