Considering the current commitment to the international community of the“carbon peak, carbon neutral”target, aiming at the demand of multi-interests in the combined operation of electricity and gas, based on the dynamic master-slave game theory and considering carbon emissions and integrated demand response, a game model with a power supply company as the main body and a household load aggregation cluster as the slave body is established. According to the multi-energy combined load characteristics of household load aggregation and the uncertainty of price demand response, the payoff function of the two players in the game is obtained. Considering the carbon emission conversion of the energy structure, a master-slave game model is established with the goal of maximizing the income of the energy supply side and minimizing the payment cost of the demand side. The master party takes price as the strategy set, and the slave party takes demand response as the strategy set. The optimal response function and the non-dominated sorting genetic algorithm are used to solve the master-slave game equilibrium solution. The simulation results show that the proposed model can optimize the social and economic benefits of the subjects and the participants, and provide a reference for the optimal operation of market decision-making under the context of energy interconnection.