Due to environmental concerns, economic issues, and emerging new loads, such as electrical vehicles (EVs), the importance of demand side management (DSM) programs has increased in recent years. DSM programs using a dynamic real-time pricing (RTP) method can help to adaptively control the electricity consumption. However, the existing RTP methods, particularly when they consider the EVs and the power system constraints, have many limitations, such as computational complexity and the need for centralized control. Therefore, a new transactive DSM program is proposed in this paper using an imperfect competition model with high EV penetration levels. In particular, a heuristic two-stage iterative method, considering the influence of decisions made independently by customers to minimize their own costs, is developed to find the market equilibrium quickly in a distributed manner. Simulations in the IEEE 37-bus system with 1141 customers and 670 EVs are performed to demonstrate the effectiveness of the proposed method. The results show that the proposed method can better manage the EVs and elastic appliances than the existing methods in terms of power constraints and cost. Also, the proposed method can solve the optimization problem quick enough to run in real-time.