In the context of the vigorous promotion of energy Internet, the formation of cooperation alliances among multiple micro grids in the region has become an important trend to improve the efficiency of regional energy utilization. A microgrid group cooperative game model under incomplete information is proposed to address the challenges of energy exchange, information asymmetry, and profit distribution during the operation of cooperative alliances. Firstly a cooperative game model for integrated energy microgrids considering energy storage sharing is established. Bayesian games are further to characterize incomplete information, are combined with cooperative games to improve the model, and operating costs are minimized while considering uncertain information risks. Finally, in the income distribution, electricity sharing indicators are design to improve the traditional Shapley value method and form a differentiated distribution strategy. Simulation results show that shared energy storage can support energy exchange between integrated energy microgrids and improve energy utilization efficiency；The Bayesian cooperative game model for microgrid group collaborative operation can be used to reduce overall external energy dependence, achieve risk return balance while incomplete information scenarios are considered, and the operating costs of participants are reduced；the improved allocation method based on the electricity sharing index can effectively enhance the benefits of contributors in the alliance and optimize the distribution of alliance benefits.