## 1 Introduction
The literature [33, 34, 35, 36, 37, 38] mainly focuses on the bidding strategy for the VPPs with distributed renewable energy and energy storage systems. In the literature [33,34], the optimal bidding prices for VPP are studied under the uncertainties of electricity loads and output power of renewable energy. In the optimal solution process, improved heuristic optimization algorithms are used to obtain the optimal bidding strategy. These bidding strategies can improve the VPP earnings under the constraints of renewable energy consumption. In the meantime, there are some consumers installed with distributed renewable energy loads who become photovoltaic producers and marketers (PVP). PVP will operate under the mode of self-use and surplus electricity sales. It is difficult to be fully aggregated by VPP in the short term. In [35], a novel peer-to-peer (P2P) energy trading strategy is proposed among the PVP members under the whole VPP bidding strategy. The results show that VPP with P2P trading can reduce the total operating costs. Similarly, a double-layer energy blockchain framework is proposed for the P2P energy trading strategy among multiple VPPs in [36]. These P2P trading strategies can improve the consumption of renewable energy and reduce reliance on the outer main power grid. In order to enhance the regulatory capability of VPP, energy storage systems are usually aggregated in VPP. A two-stage risk-constrained stochastic model is proposed to reduce the total operation cost of VPP with a number of PVPs, renewable energy resources, and energy storage systems in [37]. Furthermore, in the literature [38], an optimal low-carbon dispatching for a VPP with aggregated distributed energy storage is also proposed to facilitate the development of the multidimensional value of energy storage. The abovementioned achievements have provided effective energy trading energy for VPPs to reduce their costs. Nowadays, carbon markets are also important to embody the environmental value of new energy sources. Hence optimal bidding strategies for VPPs under electricity spot and carbon markets are also discussed in [39; 40]. The simulation results show that the introduction of carbon allowances can increase the proportion of renewable energy in VPP. In fact, due to the different requirements of multiple resources within VPPs, it is a current research hotspot to use master-slave games, cooperative games, and other game theory ideas to construct VPP trading strategies in the electricity market environment [41]. A one-master and multiple-slave game model is proposed in the literature [42], in which distribution system operators are regarded as leaders and multiple VPPs are regarded as followers. The operators' dynamic pricing behavior and VPP energy management model are also discussed in [42]. After adding the power generation side and the power consumption side, the literature [43] takes the VPP operator as the leader, the renewable energy cogeneration operator, and the integrated energy user system operator as the follower, forming a Stackelberg game model of master and slave, optimizing the pricing strategy of VPP operator, energy supply side output plan, and user side demand response strategy. These studies provide a theoretical framework for optimizing VPP operation by aggregating various resources in the electricity market environment. In the actual power market environment, shared energy storage (SES) is an independent market player to participates in the power spot or medium/long-term transactions, which is difficult to aggregate by VPP in the short term [44]. In reality, there is not only a vertical power supply and power consumption interest cooperation relationship among multiple stakeholders, but also a horizontal interest game relationship among the same type of stakeholders. Therefore, the main contribution of our manuscript is given by  
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