Stackelberg Game Theory Research Articles

A low-carbon supply chain pricing mechanism considering CSR under carbon cap-and-trade policy.

In the context of environmental deterioration and people's growing environmental protection awareness, governments or regions have put forward corresponding carbon emission reduction policies. Among them, the carbon trading mechanism, as an effective means to promote enterprises to implement emission reduction measures, plays a crucial role in regulating enterprise behavior and promoting social sustainable development. Since various industries and sectors support each other in social and economic development, it is more reasonable to study the carbon emission reduction optimization decisions of society and enterprises from the perspective of the supply chain. To achieve the carbon reduction target of the supply chain system, manufacturing enterprises usually need to incur additional costs to invest in emission reduction technologies, and retail enterprises also need to conduct low-carbon publicity to increase product market share. On one hand, considering the impact of the government's emission reduction constraints and consumers' low-carbon preferences, manufacturers will take corporate social responsibility (CSR) into consideration to enhance product competitiveness. On the other hand, smaller retailers are more concerned about being treated fairly than about their own profits due to the extra cost of low-carbon advertising. In this paper, considering the background of carbon trading, the manufacturer's CSR and retailer's fairness concern behavior are introduced into the decision-making process of the low-carbon supply chain (LCSC), and the relevant emission reduction decision-making model is constructed by using Stackelberg game theory and backward derivation method. Through comparative analysis of relevant parameters, members' profits and utilities, this paper focuses on the influence of CSR and fairness concerns on system decision-making. The results show that the optimal way for LCSC decision-making is to cooperate with fair-concerned retailers and manufacturers with CSR. When manufacturers consider social responsibility within a certain range and retailers bear part of the cost of social responsibility as followers, it can not only effectively improve the emission reduction level of the supply chain and the profits of each entity, but also help to increase the enthusiasm of each entity for carbon emission reduction and the overall social welfare.

Transactive energy management for CIES considering tri-level hybrid game-theoretic approaches with multiple weight allocation factors

In city integrated energy systems, to reduce the costs of energy production and usage, it is extremely important for different entities to design proper energy management approaches since they have diverse behaviours and benefits. The hierarchy of the system is naturally divided into three layers, and hybrid game theories are employed on the basis of the vertical master–slave and horizontal equal cooperation characteristics among energy providers, aggregators, and users. First, to reflect the interactions between different levels' entities, Stackelberg game theory is adopted vertically, and the model complexity is lessened by the KKT conditions. Then, for energy providers, the asymmetric bargaining game is improved by combining multiple weight allocation factors, which can help reduce renewable energy fluctuations and encourage the consumption of clean energy to reduce the carbon emissions of the system. Also, the results show that the proposed method can enhance the utility of renewable energy generation units by approximately 64 % to 69 %. Finally, the optimality and effectiveness of the proposed game theoretic approaches are verified in case studies and in strict mathematical proofs. In addition, the impact mechanisms on the demand response from the perspectives of the user load and price sensitivity are analysed. To explore pricing methods that are more suitable for user aggregators, two pricing strategies are designed for the user aggregator and compared in terms of computation time and revenue. The results show that a unified pricing strategy can increase the aggregator's revenue by 1.24 % and reduce the computation time by 24.47 %.

Optimization of Organic Rankine Cycle for Hot Dry Rock Power System: A Stackelberg Game Approach

Due to its simple structure and stable operation, the Organic Rankine Cycle (ORC) has gained significant attention as a primary solution for low-grade thermal power generation. However, the economic challenges associated with development difficulties in hot dry rock (HDR) geothermal power systems have necessitated a better balance between performance and cost effectiveness within ORC systems. This paper establishes a game pattern of the Organic Rankine Cycle with performance as the master layer and economy as the slave layer, based on the Stackelberg game theory. The optimal working fluid for the ORC is identified as R600. At the R600 mass flow rate of 50 kg/s, the net system cycle work is 4186 kW, the generation efficiency is 14.52%, and the levelized cost of energy is 0.0176 USD/kWh. The research establishes an optimization method for the Organic Rankine Cycle based on the Stackelberg game framework, where the network of the system is the primary optimization objective, and the heat transfer areas of the evaporator and condenser serve as the secondary optimization objective. An iterative solving method is utilized to achieve equilibrium between the performance and economy of the ORC system. The proposed method is validated through a case study utilizing hot dry rock data from Qinghai Gonghe, allowing for a thorough analysis of the working fluid and system parameters. The findings indicate that the proposed approach effectively balances ORC performance with economic considerations, thereby enhancing the overall revenue of the HDR power system.

Solutions to insufficient incentives for developing green tourism by travel agencies: government intervention

PurposeThis research aims to develop an improved model with government intervention and find the government policy for developing green tourism to induce the travel agencies have incentives to produce green tourism products.Design/methodology/approachThis research employs Stackelberg game theory to study two travel agencies in the horizontal direction of the tourism supply chain. Two deterministic, price-sensitive linear demand functions are utilized for these two different tourism products to derive possible analytical solutions.FindingsNo travel agency is willing to produce green tourism products without government intervention. The solution proposed in this paper is that a government should subsidize green travel agencies for their production of green tourism products, and create a tax for non-green traditional travel agencies for the production of non-green traditional tourism products. The amount of government subsidies for green tourism products plus the tax on non-green traditional tourism products equals the difference in unit cost of the two products. The travel agency that produces green tourism products has incentive to produce if there is government intervention.Practical implicationsThis paper provides the stakeholders with three practical implications. The first one is that the amount of subsidy for green travel agencies can be paid by taxing non-green ones. This is the optimal solution. The second one for both the tourism sector and government is that technological innovation in cooperation between government and tourism industry such as low-carbon technology is critical to reduce the cost difference between green travel agency products and non-green ones. The third one is that green travel agencies that produce green tourism products can also fulfill their corporate social responsibilities and enhance their social image.Originality/valueThis paper is unique in that it develops a model to resolve the problem of insufficient incentives. In terms of government intervention, this article also considers tax policy in addition to subsidy policy which is different from previous literature.

Optimization of offshore wind farm cluster transmission system topology based on Stackelberg game

Offshore wind energy is pivotal in the global energy transition, with a global installed capacity reaching 64.3 GW by 2022 and an expected annual increase of 60.2 GW over the next decade. This study aims to optimize the topology of transmission systems (TS) for offshore wind farm (OWF) clusters using Stackelberg game theory. The OWF investor (OWFI) acts as the leader, optimizing investment returns while considering wake effects, and the offshore TS operator (OTSO) follows by adjusting transmission strategies to reduce costs. The analysis includes the wake effects within OWF clusters and their impact on power generation efficiency. Simulation results demonstrate that the proposed model can balance stakeholder interests and enhance the economic viability of OWF clusters, showing a potential increase in net present value (NPV) by up to 30 %. This study validates the practical application of the Stackelberg game model in optimizing OWF cluster TS topology, contributing to more efficient and cost-effective renewable energy integration.

Game theoretic operation optimization of photovoltaic storage charging station considering uncertainty and carbon trading

With the advancement of energy conservation and emission reduction efforts, the orderly charging of electric vehicles and the operation of photovoltaic-storage-charging stations associated with electric vehicles have become increasingly important topics. This study constructs an optimization model for the operation of stations under the synergy of electricity and carbon markets from a game theory perspective. Firstly, Latin hypercube sampling and Monte Carlo sampling are employed to handle the uncertainties in photovoltaic output and the stochastic nature of electric vehicles charging. Secondly, a ladder-type carbon trading mechanism is introduced, and a charging optimization model based on Stackelberg game theory is developed to describe the benefit interaction between charging stations and electric vehicles users. In this model, the upper level represents the charging station operator aiming to maximize joint electricity and carbon revenue while minimizing load fluctuations, whereas the lower level represents electric vehicles users aiming to maximize consumer surplus. Finally, a genetic algorithm nested with mixed-integer linear programming is used to solve the optimization model. The simulation results validate the model's effectiveness and superiority. The results indicate that, compared to centralized optimization methods, the Stackelberg game mechanism can increase consumer surplus by 119.40 %, reduce carbon emissions by 217.92 %, and achieve a win-win situation for both parties. Compared to a fixed carbon trading value, the ladder-type carbon trading mechanism can reduce carbon emissions by 23.84 % and smooth load fluctuations.

A stackelberg game-based programming approach for industrial steam systems incorporating renewable energy considering demand response

Fossil fuels account for 37 % of industrial combustion, primarily used for steam production. Given the significant role of steam in industrial processes, industrial steam systems (ISS) offer a critical opportunity to accelerate the transition from fossil fuels to renewable energy by integrating renewable sources. Currently, ISS optimization focuses mainly on internal improvements, often neglecting stakeholder interactions and the inherent unpredictability of renewable energy sources. This paper introduces a novel bi-level programming approach based on Stackelberg game theory to address the balance between ISS and user interests. A new ISS model is proposed that integrates multiple renewable energy sources while accounting for their intermittency. Revenue models for energy servers (ES) and consumers (EC) are developed, and demand response mechanisms and real-time pricing are incorporated into the bi-level programming model. In the designed bi-level ISS (B-L-ISS) model, the upper level optimizes energy conversion equipment and pricing, while the lower level aims to minimize users' energy costs. The Karush-Kuhn-Tucker (KKT) conditions are used to reformulate the bi-level problem into a single-level programming problem with equilibrium constraints. Validation on a real coastal industrial steam system shows that the proposed method integrates renewable energy four times more effectively than traditional methods, reducing CO2 emissions by 15,790 tons annually, while balancing the interests of both the steam system and its users.

Design methodology of permanent magnet eddy current brake and optimization based on the Stackelberg game theory

Design methodology of permanent magnet eddy current brake and optimization based on the Stackelberg game theory

Research on low-carbon supply chain emission reduction strategies based on blockchain technology

The difficulty of regulating carbon trading due to information asymmetry and low consumer trust in low-carbon products are key factors hindering companies from reducing emissions. This paper examines a manufacturer-led secondary low-carbon supply chain consisting of a single supplier and a retailer, focusing on the impact of blockchain technology on carbon transaction costs and consumers' low-carbon preferences. Utilizing Stackelberg game theory, the paper constructs a supply chain decision model for emission reduction, determining the payment matrix and analyzing the stable strategy for blockchain adoption through evolutionary game theory. The findings indicate that retailers' adoption of blockchain technology significantly promotes emission reduction within the supply chain, whereas manufacturers' adoption has minimal impact. Additionally, the study reveals that variations in blockchain adoption costs and carbon quotas result in multiple evolutionary stable strategies. Specifically, when blockchain adoption costs and carbon quotas are below certain thresholds, the system reaches a unique equilibrium where both parties adopt blockchain technology.

Optimizing carbon emission reduction strategies in power batteries: Ensuring compliance with the EU battery regulation's carbon labeling initiatives

Reducing carbon emissions from power batteries is essential for the low-carbon development of electric vehicles (EVs). In response to the carbon labeling requirements of the EU battery regulation, this study developed a three-tiered supply chain model incorporating the battery material supplier, the power battery manufacturer, and the EV company. Using Stackelberg game theory, the research evaluated four carbon emission reduction strategies and analyzed the impact of consumer environmental awareness on carbon emissions. The results reveal that for batteries with lower initial carbon footprints, increased consumer environmental awareness is associated with a reduction in carbon emissions. For batteries with higher initial carbon footprints, the relationship between consumer environmental awareness and carbon emissions is more complex. Below a certain threshold, higher environmental awareness leads to carbon emission reduction; however, beyond this threshold, increased environmental awareness can elevate carbon emissions. Moreover, under low consumer environmental awareness, a strategy of comprehensive collaboration among all supply chain tiers yields the highest economic benefits, albeit with higher emissions. As environmental awareness rises, the strategy where the material supplier independently reduces emissions and the battery manufacturer and EV company collaborate on emission reductions emerges as the most effective, striking an optimal balance between economic and environmental interests.

Financing a Capital-Constrained Supply Chain under Risk Regulations: Traditional Finance versus Platform Finance

Small- and medium-sized enterprises (SMEs) frequently face challenges in obtaining financial assistance from traditional banks. Platform Supply Chain Finance (PSCF) has emerged as a promising solution for financing issues among SMEs, with an added focus on integrating sustainability aspects. This study focused on a two-tier supply chain as its primary research topic to find strategies to enhance supplier financial viability and improve the efficiency and profitability of the main manufacturing enterprise. In this study, we establish three distinct hypotheses corresponding to the three models involving supplier and manufacturer participation, encompassing parameters such as production batch size, pricing, and supply chain profit. First, it examined financing decisions through the lens of core enterprise-led platform finance. Second, it applied the Stackelberg game theory to investigate financing decisions in three distinct modes: traditional finance, platform internal finance, and external platform finance. Suppliers, manufacturers, and banks can be seen as participants in a Stackelberg game. In this game, suppliers act as leaders, making production and procurement decisions first, while manufacturers and banks act as followers, adjusting their behavior based on the suppliers’ decisions. Finally, it performed a comparative analysis of decisions and supply chain efficiency across these modes. When the risk regulation cost coefficient falls below a certain threshold, suppliers are willing to set up their own PSCF and there is an optimal level of risk regulation effort within the interval (0, 1). We compare platform finance with traditional finance and find that the traditional finance model maximizes profits for suppliers, while the external financing model maximizes profits for manufacturers and the overall supply chain profit. Findings provide insights for platforms, suppliers, manufacturers, and banks to implement optimal financing and channel structures to increase their profits and promote the sustainable development of the financial supply chain. In addition, future research on blockchain platform models would be highly meaningful.

Optimal recycling model selection in a closed-loop supply chain for electric vehicle batteries under carbon cap-trade and reward-penalty policies using the Stackelberg game

In recent years, a large number of electric vehicle (EV) batteries have retired owing to the significant growth of EVs. Developing an efficient closed-loop recycling system and effective management of retired EV batteries have become crucial. Motivated by this challenge, a closed-loop supply chain for the EV battery is formulated with four mixed-channel recycling models under the carbon cap-trade and reward-penalty mechanism. In the forward supply chain, the retailer purchases EV batteries from the manufacturer and then sells the batteries to the customers. In the reverse supply chain, the collection of retired EV batteries is carried out by either the retailer, third-party recycler, echelon firm, or a combination of these members. These collected EV batteries are classified into echelon utilizable or non-echelon utilizable batteries. The echelon-utilizable batteries are modified into echelon products, while the non-echelon batteries are recycled for extraction of raw materials to manufacture new EV batteries. The findings are derived by using actual market data and Stackelberg game theory. The influence of carbon trading prices, reward penalty intensity, costs associated with the firms, and competition coefficients are studied to provide a detailed and comprehensive analysis. A comparison of optimal profits pertaining to different models is also conducted. The results indicate that (i) different models of recycling EV batteries do not influence the optimal decisions in the forward supply chain; (ii) it is beneficial for the members to participate in the reverse chain; (iii) manufacturer’s profit increases when the carbon quota rises and decreases when the price of carbon trading increases; (iv) the involvement of echelon firms in the recycling sector has a positive effect on reducing the recycling load and increasing the profitability of the manufacturer. Managerial insights and concluding remarks are provided to guide manufacturers and recyclers in selecting the most suitable recycling model based on their specific requirements.

Game-Theoretic Adversarial Interaction-Based Critical Scenario Generation for Autonomous Vehicles

Ensuring safety and efficiency in the rapidly advancing autonomous vehicle (AV) industry presents a significant engineering challenge. Comprehensive performance evaluations and critical scenario testing are essential for identifying situations that AVs cannot handle. Thus, generating critical scenarios is a key problem in AV testing system design. This paper proposes a game-theoretic adversarial interaction method to efficiently generate critical scenarios that challenge AV systems. Initial motion prediction for adversarial and surrounding vehicles is based on kinematic models and road constraints, establishing interaction action spaces to determine possible driving domains. A novel evaluation approach combines reachability sets with adversarial intensity to assess collision risks and adversarial strength for any state, used to solve behavior values for each interaction action state. Further, equilibrium action strategies for the vehicles are derived using Stackelberg game theory, yielding optimal actions considering adversarial interactions in the current traffic environment. Simulation results show that the adversarial scenarios generated by this method significantly increase incident rates by 158% to 1313% compared to natural driving scenarios, while ride comfort and driving efficiency decrease, and risk significantly increases. These findings provide critical insights for model improvement and demonstrate the proposed method’s suitability for assessing AV performance in dynamic traffic environments.

Optimal Operation of Virtual Power Plants Based on Stackelberg Game Theory

As the scale of units within virtual power plants (VPPs) continues to expand, establishing an effective operational game model for these internal units has become a pressing issue for enhancing management and operations. This paper integrates photovoltaic generation, wind power, energy storage, and constant-temperature responsive loads, and it also considers micro gas turbines as auxiliary units, collectively forming a typical VPP case study. An operational optimization model was developed for the VPP control center and the micro gas turbines, and the game relationship between them was analyzed. A Stackelberg game model between the VPP control center and the micro gas turbines was proposed. Lastly, an improved D3QN (Dueling Double Deep Q-network) algorithm was employed to compute the VPP’s optimal operational strategy based on Stackelberg game theory. The results demonstrate that the proposed model can balance the energy complementarity between the VPP control center and the micro gas turbines, thereby enhancing the overall economic efficiency of operations.

A Study of Electronic Product Supply Chain Decisions Considering Extended Warranty Services and Manufacturer Misreporting Behavior

In the supply chain management of electronic products, asymmetric cost information is a prevalent issue that can lead manufacturer to misreport costs, thereby exacerbating supply chain imbalances. This study focuses on the electronic product supply chain with an extended warranty service, where the manufacturer bears the after-sales responsibility during the extended warranty period. It explores the decision-making (DM) issues within the supply chain under different information environments and power structures. The Stackelberg game theory is employed to solve and analyze these models, and the main findings are as follows: (1) When supply chain information is symmetrical, centralized DM is the best choice. However, in cases where the supply chain adopts decentralized DM, it is more beneficial for the retailer and the supply chain if the retailer assumes the role of DM leader. Additionally, when the retail price sensitivity coefficient is low, the manufacturer will compete with the retailer for DM priority. Conversely, when the retail price sensitivity coefficient is higher, the manufacturer is better off as a follower in DM; (2) When the supply chain information is asymmetric, the manufacturer may engage in misreporting, which benefits the manufacturer but is detrimental to both the supply chain and the retailer. Moreover, if the price sensitivity coefficient is low, the manufacturer should lead the supply chain DM. Otherwise, the retailer should take the lead in supply chain DM. Adopting such a flexible strategy will prove advantageous for all parties involved in the supply chain. (3) The strategy of “reducing the retail price and increasing the extended warranty price” is a favorable strategy for the supply chain.

Two-stage data-driven optimal energy management and dynamic real-time operation in networked microgrid based on a deep reinforcement learning approach

Given the significant challenges posed by the vast and diverse data in energy management, this study introduces a two-stage approach: optimal energy management system (OEMS) and dynamic real-time operation (DRTOP). These stages employ a multi-agent policy-oriented deep reinforcement learning (DRL) approach, aiming to minimize operating and energy exchange costs through interactions in the networked microgrid (NMG) energy market. The primary objectives include minimizing the distribution system operator (DSO) cost and optimizing the exchanged power between DSO and NMG, and the power transmission losses and the secondary include minimizing MG’s operating cost, optimal use of renewable energy resources (RER) and energy storage systems (ESS), minimizing the exchanged power cost with the main grid and, risk analysis. The OEMS&DRTOP model is developed based on the Stackelberg game theory and the DRL structure. The DRL model is developed in two offline learning and online distributed operation phases to minimize the computational burden, time, and DRL operation process. This study’s results show the high efficiency of the presented approach to minimizing the operating cost, the exchanged power based on the price uncertainty, power transmission losses, and, RER and ESSs optimal participation. In addition, regarding computational load, the proposed concept demonstrates a 12.9% reduction compared to the dueling deep Q-network method and a 17% reduction compared to the deep Q-network method. Also regarding computational time, the proposed concept demonstrates a 17.13% reduction compared to the dueling deep Q-network method and a 25.6% reduction compared to the deep Q-network method.

The Green Paradox in NEV Manufacturing: Regulatory Impacts on Innovation from a Stakeholder Perspective

This paper explores the paradoxical impact of environmental regulations on green innovation in the manufacturing of new energy vehicles (NEVs) from a stakeholder perspective. We address the dual challenge of accelerating green innovation across various diffusion stages and refining environmental regulations for effective stakeholder engagement, including the central government, upstream suppliers, and internal operations teams. First, we utilize Stackelberg game theory to analyze the strategic interaction and behavioral rationale between local governments and NEV manufacturers at different stages of innovation diffusion, represented by specific parameter sets. Second, we examine the roles of four key stakeholders, exploring their unique impact mechanisms and potential to influence the game’s Nash equilibrium. Finally, the game models’ validity and primary conclusions are corroborated with real-world case studies, prominently including the ongoing shift of Chinese automakers towards NEVs. Results demonstrate that: (1) environmental regulations should be calibrated according to the diffusion stages of green innovation, and (2) misaligned stakeholder interests can lead to environmental regulations that inadvertently hinder, rather than promote, NEV manufacturers’ green innovation efforts.

A multi-stage techno-economic model for harnessing flexibility from IoT-enabled appliances and smart charging systems: Developing a competitive local flexibility market using Stackelberg game theory

The increasing integration of renewable energy sources with power systems has led to greater uncertainties, heightening the need for more flexible services. Demand-side resources can provide significant flexibility cost-effectively, making it crucial to design new business models to harness their flexible capacities. Hence, this paper introduces a three-stage techno-economic framework designed to enhance the exploitation of flexible capacities from demand-side resources such as Internet-of-Things (IoT)-Enabled Appliances (IEAs), Battery-Integrated Rooftop Solar Panels (BIRSPs), and Electric Vehicle (EV) smart charging systems in the local flexibility market. The proposed framework operates in three stages. First, smart homes with IEAs, BIRSPs, and smart charging systems assess their flexibility and report it to their Microgrid (MG) operators. Next, MG operators optimize strategies to maximize market returns and report capacities to the Distribution System Operator (DSO). Finally, the DSO manages flexibility transactions based on MG inputs. A Stackelberg game theory model using a gradient-based method updates the coupling variables between market parties, ensuring convergence in the second and third stages within a decentralized space with limited information sharing. Implemented on a modified IEEE 69-node distribution system, the model fully utilizes the potential of smart homes, including IEAs, BIRSPs, and smart charging systems in the local flexibility market. It reduces the Upstream Network (UN) share in the local flexibility market by 56.86% and decreases DSO costs for energy balancing by 22.36%.

Optimal supply chain performance: risk aversion to green innovation

PurposeAlthough many countries are focusing on the management of construction and demolition waste (CDW) resource utilization, the effect of risk aversion of the green innovation-led enterprise on the performance of the CDW resource utilization supply chain is unclear when considering different green innovation contexts (green innovation led by the building materials remanufacturer or by the construction waste recycler). This study aims to investigate how the level of risk aversion of the green innovation-led enterprise affects CDW resource utilization under different green innovation contexts based on contingency theory.Design/methodology/approachUsing Stackelberg game theory, this study establishes a decision model consisting of a building materials remanufacturer, construction waste recycler and CDW production unit and investigates how the level of risk aversion of the green innovation-led enterprise under different green innovation contexts influences the performance level of the supply chain.FindingsThe conclusions are as follows. (1) For the green innovation-led enterprise, the risk-averse behaviour is always detrimental to his own profits. (2) For the follower, the profits of the construction waste recycler are negatively correlated with the level of risk aversion of the green innovation-led enterprise in the case of a small green innovation investment coefficient. If the green innovation investment coefficient is high, the opposite result is obtained. (3) When the green innovation investment coefficient is low, the total supply chain profits decrease as the level of risk aversion of the green innovation-led enterprise increases. When the green innovation investment coefficient is high, total supply chain profit shows an inverted U-shaped trend with respect to the degree of risk aversion of the green innovation-led enterprise.Originality/value(1) This study is the first to construct a green innovation context led by different enterprises in the CDW resource utilization supply chain, which provides a new perspective on green management and operation. (2) This study is the first to explore the operation mechanism of the CDW resource utilization supply chain based on contingency theory, which provides new evidence from the CDW resource utilization supply chain to prove contingency theory. At the same time, this study examines the interactive effects of the green innovation cost coefficient and the degree of risk aversion of green innovation-led enterprises on the performance of supply chain members, expanding the contingency theory research on contingencies affecting enterprise performance. (3) This study will guide members of the CDW resource utilization supply chain to rationally face risks and achieve optimal supply chain performance.

Cooperative operation optimization for rural multi-microgrid and county-integrated energy operators considering typical energy scenarios

Despite being rich in renewable energy, China's rural areas are backwards in terms of energy use. Rural multi-microgrid cooperative operation optimization can effectively promote renewable energy use in rural areas. Many different microgrid energy scenarios have been developed for rural areas of China, and they have different resource endowments and unit compositions. Moreover, frequent power-related interactions occur between counties and villages. This study analyzes four typical microgrid energy scenarios in rural areas of China and optimizes their synergistic operation based on county-integrated energy operators. First, a mathematical model of rural microgrids for four energy scenarios and a trading mechanism between rural multi-microgrid and county-integrated energy operators were constructed. Subsequently, an upper-level optimization model that minimizes operating costs was developed for the county-integrated energy operator. A low-level optimization model was developed for rural multi-microgrid usage, and it minimized the operating costs. Finally, Stackelberg game theory was utilized to resolve the optimization issue. The results showed that the cooperative optimization of rural multi-microgrid and county-integrated energy operations can reduce the operating costs of both parties compared to that when each subject is operating alone. This optimization reduced the rural multi-microgrid cost from 12 773.64 yuan to 11 508.67 yuan and county-integrated energy operator cost from 3898.37 yuan to 1581.79 yuan. Moreover, it reduced both parties' dependence on external power grids; increased the self-balancing capacity of the rural multi-microgrid and county-integrated energy operator from 0.424 to 0.715 and 0.694 to 0.852, respectively; substantially increased the capacity of renewable energy consumption through power interaction; and reduced the risk of fluctuations in system operating costs.