•Two-stage method based on Nash bargaining theory to solve P2P trading is proposed.•The proposed model can incentivize the cooperation among players.•The optimal amounts of exchanged energy among the customers can be obtained.•Obtaining the optimal trading payments by solving the payments bargaining problem.•Social welfare maximization can be achieved through the proposed model. In the traditional power system, the end users are independent individuals without any interaction. While the development of communication and information technology brings many possibilities for the interaction and cooperation among these individuals. This study explores the interaction and cooperative relationship among the prosumers and consumers within a community in the Peer-to-peer (P2P) energy sharing trading. In the community, a customer would like to provide some payoffs to encourage other customers to exchange certain amounts of energy to obtain more profits. We propose a two-stage optimization approach on the optimal strategies to maximize their utilities in the P2P energy sharing trading. In the first-stage optimization model, the decision on whether to participate in the P2P energy sharing trading is obtained based on the maximization of social utility function. Meanwhile, the optimal amounts of exchanged energy also can be obtained. In the second-stage optimization model, we provide an analysis of the optimal associated trading payments based on a payments bargaining model. Both of the above two optimization problems are solved based on a distributed algorithm respectively. Moreover, we demonstrate that the customers who participate in P2P energy sharing trading can improve their utilities compared with an individual optimization method based on a case study.