In recent years, the interest in electric vehicles (EVs) in the research community has been growing, particularly in the context of decarbonization. Additionally, there is a growing increase in their number, leading to massive energy demand on the charging stations (CSs). Energy trading management for CSs puts great pressure on the power grid and is a stimulating challenge in smart cities. In this paper, we propose an innovative market formulation in which autonomous vehicles and smart charging and discharging stations are motivated to cooperate dynamically with changing roles. In order to mathematically formulate the energy trading market, we adopt a double auction strategy that is repeated in steps. In this strategy, EVs and CSs participate by buying and selling energy. The investigated problem has high complexity, and thus, multi-objective optimization is employed so as to encapsulate the opposing objectives that the EVs and CSs have. Multi-objective optimization leads to a fairer and more efficient market operation. The performance of the presented approach is investigated through analytical and experimental results. More specifically, the proposed algorithm achieves up to 52.5% reduction in energy consumption. The performance evaluation proves that the suggested strategy offers both fairness and significant energy benefits, encouraging both electric vehicles and charging stations to take part in a double auction energy trading system.