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Electric vehicle (EV) load integration and environmental concerns in recent years have motivated energy users to step forward in reducing carbon footprints by promoting energy trading. In the energy trading market, different energy stakeholders participate in trading energy with each other to maximize their utilities and improve trading efficiency. The social welfare (SW) of the energy market plays a significant role in keeping the market going and motivating new users to engage in energy trading. The SW of the energy market depends on its structure, where energy flows from producer to end user in a fair way. This paper introduces a hierarchical energy trading framework, formulated as a three-stage Stackelberg game, to enhance SW. In the first stage of this hierarchy, the retailer, acting as the sole leader, seeks to maximize profits through optimized energy sales to charging stations (CS). Subsequently, in the second stage, each CS operates as a leader for EVs, aiming to maximize profits by minimizing energy trading costs, while also acting as a follower in response to the retailer's strategies. The third and final stage involves EVs collaboratively acting as a unified strategic agent to minimize their trading costs through optimized charging and discharging schedules. This paper also introduces an average price penalty function to further enhance SW in the energy market. The proposed model, addressing the complexities of energy trading interactions, is formulated as a non-linear optimization problem with constraints. It has been implemented in a Python environment and solved using the Gurobi optimization solver, demonstrating its potential to improve the efficiency, fairness, and overall social welfare of the energy trading market. • Introduces a hierarchical energy trading framework using a three-stage Stackelberg game to enhance market social welfare. • Incorporates renewable energy at the retailer level, diversifying energy sources and boosting ecological relevance. • Establishes comprehensive pricing functions across all levels, including reciprocal EV discharge signals, for dynamic market interaction. • Implements an average price penalty at charging stations to preserve social welfare and promote efficient energy use. • Demonstrates model efficiency and practical applicability through tests on the IEEE 33 bus system, showing superior profitability and convergence. [ABSTRACT FROM AUTHOR]