Abstract: Considering the subjectivity in multi-objective optimization for existing integrated energy systems, this paper proposes a multi-objective cooperative optimization method of single entity based on the non-cooperative game theory. First, an integrated electricity-gas system model coupling the distribution network, gas distribution network, and energy station is established. To make the optimization dispatch results closer to reality, a compressor model with variable compression ratio is employed in the model of gas distribution network. Its nonlinear consumption characteristic is considered. Then, based on the non-cooperative game theory, the economic objective and environmental objective of the energy station with a single stakeholder are treated as completely equal and rational virtual gamers. The strategy space is composed of the constraints of various devices in the system.Moreover, to ensure the existence of Nash equilibrium solutions in the game model, auxiliary variables and constraints are used to transform the payoff functions（objective functions） into pseudo-convex and differentiable functions. The method of convex relaxation is applied to handle non-convex and nonlinear constraints in the model, and a non-linear iterative strategy is proposed to accelerate the relaxation tightening process. In order to facilitate the solving of Nash equilibrium, the Nikaido-Isoda function is used to reformulate the payoff function, transforming the original model into a global optimization problem. Finally, the validity of the proposed method is verified by cases.