Residential flexible resource is attracting much attention in demand response (DR) for peak load shifting. This paper proposes a scenario for multi-stage DR project to schedule energy consumption of residential communities considering the incomplete information. Communities in the scenario can decide whether to participate in DR in each stage, but the decision is the private information that is unknown to other communities. To optimize the energy consumption, a Bayesian game approach is formulated, in which the probability characteristic of the decision-making of residential communities is described with Markov chain considering human behavior of bounded rationality. Simulation results show that the proposed approach can benefit all residential communities and power grid, but the optimization effect is slightly inferior to that in complete information game approach.