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Due to the increasing popularity of Electric Vehicles (EVs) and infrastructural limitations, it is vital to manage traffic and Charging Stations (CSs) crowdedness. In Bakhshayesh and Kebriaei (2022), the problem of choosing the route and CSs of EVs is modeled as a non-cooperative game of selfish EVs with probabilistic decision strategies. In this paper, we have proposed a linear pricing policy that ensures global efficiency of the obtained Nash strategies of EVs in Bakhshayesh and Kebriaei (2022) for the Smart City Coordinator (SCC). We model the problem as a hierarchical game with a SCC as the leader and EVs as the followers. The leader aims to design optimal price functions of CSs and Traffic Coordinator (TC) and impose them on the EVs to maximize the social profits of CSs and TC. In response, the followers play a non-cooperative game with coupling constraints to optimally decide on their route and charging destination. Thus, we have a Stackelberg Game (SG) between SCC and EVs and also a Nash game among the EVs in the lower level. Compared to the conventional Nash-based pricing policies, our proposed functional SG formulation enables the possibility of simultaneous and global-optimum management of traffic and CSs’ crowdedness. Moreover, we have proposed a two-level decentralized algorithm that preserves the privacy of EVs and have considered a decentralized computation for equilibrium seeking of followers based on the Alternating Direction Method of Multipliers (ADMM) method. Finally, we carry out simulation studies on the transportation network of Sioux Falls City to compare and evaluate the proposed method.