Bidding strategy and Nash equilibrium (NE) research are crucial for electricity retailers to increase their profits in a deregulated electricity market. However, traditional game theory and reinforcement learning methods have limitations in solving NE problems due to incomplete information and the curse of dimensionality. In this paper, an agent-based model of electricity retailers that uses the multi-agent deep deterministic policy gradient algorithm has been proposed to approximate the NE under an incomplete information environment. The effectiveness of the proposed model is verified in the 3-bus and IEEE 30-bus system. The numerical results show that the proposed algorithm can converge to the NE of a complete information environment under an incomplete information environment. Compared with the NE obtained through game theory, the proposed the agent-based model owns high accuracy with a tiny error margin.