As an important part of demand side, residential users have the characteristics of imperfect rationality and strong randomness, which are rarely considered in the existing study. Moreover, to effectively improve the energy efficiency, integrated demand response (IDR) is proposed as an effective measure to reduce the local energy supply pressure. This paper focuses on a scenario for IDR programs, in which the intelligent building aggregator (IBA) wants to encourage residential users to participate in IDR according to a proper contract price policy. To analyze how the participation degree tendency evolves over time, an evolutionary game approach is proposed considering residential users’ bounded-rationality. A symmetric evolutionary game model and an asymmetric evolutionary game model are established, and the stability of equilibrium points in the above models is proven. Simulation results show that different contract price policies will obviously influence residential users’ strategy, and affect the stable equilibrium points of the evolutionary game. The simulation results provide an effective reference for IBA to set proper and effective price incentives.