The proliferation of technologies such as combined heat and power systems and smart meters has accelerated the multienergy trading. A two-stage game model is built in this paper to analyze the optimal strategy of each player and their interactions. Specifically, in consumer game model, we present an autonomous and distributed micro energy management system among users in which power and heat are traded at the same time. In supplier game model, integrated energy suppliers receive energy demand information and share the market according to the game result. In addition, we present a detailed proof of the existence and uniqueness of the Nash equilibrium, which lays the foundation for researchers to build an effective model using game theory. Further, a distributed algorithm specifically designed for this model is proposed. The players can retain a certain level of anonymity without revealing the details of their energy consumption or generation schedules to other players. Lastly, simulation results confirm the feasibility of two-stage game model and the effectiveness of the proposed distributed algorithm.