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For the isolated island micro grid, a safe and reliable energy supply system is indispensable. Generally speaking, the power generation modules of an small and medium-sized isolated island energy system with off-grid power supply mode mainly include diesel generator(DIG) and distributed power supply. In order to smooth the power output fluctuation of wind and solar, coordinate the output of multiple energy generation technologies, and increase the penetration rate of distributed energy, it is necessary to develop a flexible and reliable energy system, and an efficient and smart scheduling strategy. In this paper, the power-to-gas (P2G) technology is introduced to construct a multi-energy complementary integrated energy system with deep coupling of power-gas network. Four possible game planning models are proposed by using game theory analysis method, and the energy scheduling strategies under each game mode are obtained by particle swarm optimization(PSO). By comparing the scheduling strategies under the four game modes, it can be found that the synergistic response of hydrogen and methane in the alliance cooperative game mode has absolute advantages in reducing the curtailment rate of wind and solar energy, balancing the income of each participant, improving the total income of the system, and saving energy and environmental protection. • A multi-energy complementary electric-gas coupled model containing five kinds of generators is established. • Four possible game modes are proposed. • Optimization of electrical load and gas load scheduling strategies for an isolated island microgrid. • Uninterrupted electricity and gas supply assured from the analysis. • The penetration rate of distributed renewable energy are improved and the share of diesel generator power is reduced. [ABSTRACT FROM AUTHOR]