To address urban traffic congestion, researchers have made various efforts to mitigate issues such as prolonged travel time, fuel wastage, and pollutant emissions. These efforts primarily involve microscopic route selection from the vehicle perspective, multi-vehicle route optimization based on traffic flow information and historical data, and coordinated route optimization that models vehicle interaction as a game behavior. However, existing route selection algorithms suffer from limitations such as a lack of heuristic, low dynamicity, lengthy learning cycles, and vulnerability to multi-vehicle route conflicts. To further alleviate traffic congestion, this paper presents a Period-Stage-Round Route Selection Model (PSRRSM), which utilizes a population game between vehicles at each intersection to solve the Nash equilibrium. Additionally, a Period Learning Algorithm for Route Selection (PLA-RS) is proposed, which is based on a multi-agent deep deterministic policy gradient. The algorithm allows the agents to learn from the population game and eventually transition into autonomous learning, adapting to different decision-making roles in different periods. The PSRRSM is experimentally validated using the traffic simulation platform SUMO (Simulation of Urban Mobility) in both artificial and real road networks. The experimental results demonstrate that PSRRSM outperforms several comparative algorithms in terms of network throughput and average travel cost. This is achieved through the coordination of multi vehicle route optimization, facilitated by inter-vehicle population games and communication among road agents during training, enabling the vehicle strategies to reach a Nash equilibrium.