In city integrated energy systems, to reduce the costs of energy production and usage, it is extremely important for different entities to design proper energy management approaches since they have diverse behaviours and benefits. The hierarchy of the system is naturally divided into three layers, and hybrid game theories are employed on the basis of the vertical master–slave and horizontal equal cooperation characteristics among energy providers, aggregators, and users. First, to reflect the interactions between different levels' entities, Stackelberg game theory is adopted vertically, and the model complexity is lessened by the KKT conditions. Then, for energy providers, the asymmetric bargaining game is improved by combining multiple weight allocation factors, which can help reduce renewable energy fluctuations and encourage the consumption of clean energy to reduce the carbon emissions of the system. Also, the results show that the proposed method can enhance the utility of renewable energy generation units by approximately 64 % to 69 %. Finally, the optimality and effectiveness of the proposed game theoretic approaches are verified in case studies and in strict mathematical proofs. In addition, the impact mechanisms on the demand response from the perspectives of the user load and price sensitivity are analysed. To explore pricing methods that are more suitable for user aggregators, two pricing strategies are designed for the user aggregator and compared in terms of computation time and revenue. The results show that a unified pricing strategy can increase the aggregator's revenue by 1.24 % and reduce the computation time by 24.47 %.