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This paper proposes a three-stage multi-energy sharing strategy for a gas-electricity integrated energy system (IES). It aims to solve the multi-energy imbalance problem among energy hubs (EHs) based on the peer-to-peer (P2P) trading mode. First, considering the characteristics of multi-energy coupling and conversion, the quantity of shareable energy is determined for EHs that participate in the P2P trading. Furthermore, EHs conduct multi-bilateral negotiations based on the Raiffa-Kalai-Smorodinsky bargaining solution (RBS) to determine the optimal energy trading price. Finally, the buyer agent and the seller agent will design the optimal energy sharing trading strategy for all EHs. Moreover, the results show that the pricing mechanism improves the fairness of satisfaction obtained by the EHs from the utility distribution, and the social welfare of the system is improved, which proves that the three-stage multi-energy sharing trading strategy is effective.