Stackelberg Game Research Articles

Robust optimization for integrated energy systems based on multi-energy trading

Amid rising energy demands and environmental concerns, integrated energy systems (IESs) face conflicting interests. Conventional strategies of interest distribution face issues such as irrational resource allocation. Accordingly, establishing energy trading strategies with multiple stakeholders becomes essential. This paper proposes a robust optimization (RO) for IESs based on multi-energy trading to reduce energy trading cost. In this regard, a single-leader-multi-follower Stackelberg game is first modeled where IES acts as the leader, and the users and the electric vehicles (EVs) act as the followers. Secondly, this model is transformed into a single-layer linear model and integrated into the multi-stage RO. With this, the nonanticipativity in the two-stage RO can be effectively handled. Besides, by constructing multi-interval uncertainty sets for renewable energy, load, and electricity prices, the conservatism of the model is reduced, making the optimization results closer to actual condition. Noteworthy that the Nash bargaining method ensures a fair distribution of benefits among IESs and encourages them to participate in energy trading. Finally, the multi-energy trading model is solved using the prediction-correction-based alternating direction method with multipliers (PCB-ADMM) algorithm. The PCB-ADMM not only protects each IES’s privacy but also has less execution time than the ADMM algorithm. The effectiveness of the proposed strategy is validated through simulation using Matlab.

PP-LEM: Efficient and Privacy-Preserving Clearance Mechanism for Local Energy Markets

In this paper, we propose a novel Privacy-Preserving clearance mechanism for Local Energy Markets (PP-LEM), designed for computational efficiency and social welfare. PP-LEM incorporates a novel competitive game-theoretical clearance mechanism, modelled as a Stackelberg Game. Based on this mechanism, a privacy-preserving market model is developed using a partially homomorphic cryptosystem, allowing buyers’ reaction function calculations to be executed over encrypted data without exposing sensitive information of both buyers and sellers. The comprehensive performance evaluation demonstrates that PP-LEM is highly effective in delivering an incentive clearance mechanism with computational efficiency, enabling it to clear the market for 200 users within the order of seconds while concurrently protecting user privacy. Compared to the state of the art, PP-LEM achieves improved computational efficiency without compromising social welfare while still providing user privacy protection.

Equilibrium Interaction Strategies for Integrated Energy System Incorporating Demand-Side Management Based on Stackelberg Game Approach

This paper analyzes the balanced interaction strategy of an integrated energy system (IES) operator and an industrial user in the operation process of the IES under the demand-side management (DSM) based on game theory. Firstly, we establish an electric–thermal IES, which includes a power grid, a heat grid and a natural gas grid. Secondly, a two-stage Stackelberg dynamic game model is proposed to describe the game behavior of IES operators and industrial users in the process of participating in DSM. The interactions between the IES operator (leader) and the user (follower) are formulated into a one-leader–one-follower Stackelberg game, where optimization problems are formed for each player to help select the optimal strategy. A pricing function is adopted for regulating time-of-use (TOU), which acts as a coordinator, inducing users to join the game. Then, for the complex two-stage dynamic game model established, the lower user-side constraint optimization problem is replaced by its KKT condition, so that the two-stage hierarchical optimization problem is transformed into a single-stage mixed-integer nonlinear optimization model, and the branch-and-bound method is introduced to solve it. Finally, the equilibrium strategies and income values of both sides of the game are obtained through a case simulation, and the dynamic equilibrium strategy curves under different capacity configurations are obtained through the sensitivity analysis of key parameters. The equilibrium income of the IES is USD 93.859, while the equilibrium income of industrial users in the park is USD 92.720. The simulation results show that the proposed method and model are effective.

Research on Coordination of Fresh Supply Chain Considering Supplier Misreporting and Consumer Return

Misreporting is prevalent in supply chain characterized by asymmetric information, and its impact on the supply chain is substantial and cannot be overlooked. In order to explore the impact of fresh supplier’s misreporting decisions on fresh supply chain, this paper takes the fresh supply chain with a single fresh supplier and a single e-commerce enterprise as the research object, and constructs five Stackelberg game models based on the differences of supply chain information transparency and power structure. Particularly, the effect of fresh-keeping level on the after-sales rate and market demand of the product is incorporated into the model, and the following conclusions are drawn by solving and analyzing the decision results of the different models: (1) When the supplier has the decision advantage, it will not choose to misreport. But when it loses the decision advantage, it will produce the misreporting behavior. Supplier misreporting is detrimental to the retailer and the supply chain; specifically, it can lead to lower fresh-keeping level and higher after-sales rates. (2) In the decentralized decision-making model, it is more beneficial for the supply chain that the supplier has the leading right of decision-making. In the absence of misreporting, the leader’s profit is always higher than that of the follower. When there is misreporting, even if the retailer is the dominant player, its profit is still lower than the manufacturer’s. (3) Both supply chain profit and fresh-keeping level are positively correlated with the coefficient of consumer perception of freshness and the coefficient of sensitivity to fresh-keeping technology, and are more significant under the centralized decision-making model. Furthermore, in response to supplier misreporting behavior, this paper achieves coordination in the fresh supply chain by designing a joint contract and confirms the effectiveness of this contract through an arithmetic analysis.

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.

Optimizing Operational and Sustainable Decisions for GASC

This study delves into the operational decision-making and sustainability dynamics within a two-tier green agricultural supply chain (GASC), comprising a manufacturer and a retailer. By developing decision models for the manufacturer, both with and without outward altruism, we explore the intricate interplay of government subsidies, consumer green preferences, and manufacturers' altruistic behavior influencing operational efficiency and sustainability within the GASC based on the Stackelberg Game. Our findings underscore the intricate relationship between these factors and the retail pricing of green agricultural products. Specifically, we demonstrate that while the manufacturer's outward altruism is significant, the combined effects of government subsidies and consumer preferences exert substantial influence on pricing strategies. Moreover, we reveal that government subsidies, consumer preferences for sustainability, and manufacturers' altruistic actions collectively bolster the economic, environmental, and social dimensions of sustainability within the GASC.

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.

Analysis of green supply chains under fairness concern and differential power structure

PurposeThis study aims to examine how fairness concerns and power structure in dyadic green supply chains impact retail price, supply chain profits and greening level decisions.Design/methodology/approachThis study develops game-theoretic models considering fairness concerns and asymmetric power structures under an iso-elastic demand setting. The research paper employs the Stackelberg game approach, taking into consideration the fairness concern of the channel leader.FindingsThe findings indicate that under fairness, there is an increase in both wholesale and retail prices, as well as greening expenditures. Notably, when comparing the two models (manufacturer Stackelberg and retailer Stackelberg), double marginalization is more pronounced in the retailer Stackelberg setup than in the manufacturer Stackelberg setup. In a traditional supply chain with iso-elastic demand, the follower typically extracts higher profit compared to the leader; however, our results show that, under fairness conditions, the leader achieves higher profit than the follower. Additionally, our study suggests that supply chain coordination is unattainable in a fairness setup. This paper provides insights for managers on the optimal supply chain structure and the level of fairness to maximize profit.Originality/valueThis paper investigates the impact of a leader's fairness on the optimal decisions within a green supply chain, an area that has received limited attention previously. Additionally, the study investigates how fairness concerns manifest in distinct power dynamics, specifically, in the contexts of manufacturer Stackelberg and retailer Stackelberg.

Game theory-based electricity pricing decisions incorporating prosumer energy preferences and renewable portfolio standard

The implementation of renewable energy-based power generation substantially enhances the greenness of the energy market. Concerns about pricing policies and widespread renewable energy (RE) industries have resulted in ongoing economic conflicts among stakeholders, including power companies (PCs) and different prosumer groups. This study proposes a game theory framework embedded in a pricing model to examine the influences of three-part tariff (3 PT) and renewable portfolio standard (RPS) on electricity pricing. Employing a Stackelberg game, the objective is to maximize stakeholders' profits through a sequential decision-making relationship between PCs (as the leader), and residential and industrial prosumers (as the followers). The findings reveal that the PC can maximize profit by coordinating the 3 PT and RPS, regardless of environmental awareness. Furthermore, given the prosumers’ preference for peer-to-peer (P2P) energy trading, the PC should employ a comprehensive approach encompassing 3 PT, P2P, and buy-back to maximize the total profit. On the energy trading platform, the relationship between residential and industrial prosumers is mutually beneficial, with the P2P scheme allowing residents to sell electricity while the industry approaches a lower electricity price from peer channels. Overall, understanding the energy preferences of prosumers should provide flexible and reliable power supply options for different groups of prosumers.

An exact method for trilevel hub location problem with interdiction

In this paper, we study the problem of designing a hub network that is robust against deliberate attacks (interdictions). The problem is modeled as a three-level, two-player Stackelberg game, in which the network designer (defender) acts first to locate hubs to route a set of flows through the network. The attacker (interdictor) acts next to interdict a subset of the located hubs in the designer’s network, followed again by the defender who routes the flows through the remaining hubs in the network. We model the defender’s problem as a trilevel optimization problem, wherein the attacker’s response is modeled as a bilevel hub interdiction problem. We study such a trilevel problem on three variants of hub location problems studied in the literature namely: p-hub median problem, p-hub center, and p-hub maximal covering problems. We present a cutting plane based exact method to solve the problem. The cutting plane method uses supervalid inequalities, which is obtained from the solution of the lower level interdiction problem. To solve the lower level hub interdiction problem efficiently, we propose a penalty-based reformulation of the problem. Using the reformulation, we present a branch-and-cut based exact approach to solve the problem efficiently. We conduct experiments to show the computational advantages of the above algorithm. To the best of our knowledge, the cutting plane approach proposed in this paper is among the first exact method to solve trilevel location–interdiction problems. Our computational results show interesting implications of incorporating interdiction risks in the hub location problem.

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%.

Blockchain and game theory enable high-efficiency data sharing in the IIoT

The rapid development of intelligent manufacturing is inseparable from collaboration among smart factories (SFs). In the real unmanned intelligent collaborative production process, each SF exists as an independent individual peer. However, due to the selfishness of SFs and intelligent manufacturing equipment (IME), they do not actively participate in data sharing, which brings serious obstacles to the collaborative development of SF. In order to solve the above problems, this paper combines blockchain technology and game theory technology to propose a high-efficiency data sharing incentive method based on the Stackelberg game. Specifically, We first take the SF as the leader and the IME as the follower, and we define the data sharing incentive problem among SFs as the master–slave game problem. Then, the lower game problem and the upper game problem are solved, respectively, and finally the Nash equilibrium is derived. Then, a high-efficiency data sharing incentive method based on the Stackelberg game is designed and implemented. Finally, we conducted simulation experiments on the method proposed in this paper. Through theoretical and simulation experiments, it has been proven that the proposed method effectively reduces the impact of the selfishness of SFs and IME and improves the efficiency of data sharing among SFs.

Multistage supply chain inventory model for controllable deterioration and imperfect production with carbon emissions regulations under Stackelberg game approach

Multistage supply chain inventory model for controllable deterioration and imperfect production with carbon emissions regulations under Stackelberg game approach

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.

Climate and geopolitical risk correlations and response decisions for semiconductor global supply chains

Threats from climate risk (CR) and geopolitical risk (GR) undermine the resilience of the Semiconductor Global Supply Chain (SGSC). Plenty of company profit has plummeted due to the chip supply disruptions and delays. Particularly, the complex risk correlations (RCs) in a multi-project environment, and the inter-entity relationships, render the risk analysis and risk response decisions (RRDs) within CR and GR challenging. To address the problem, this study proposes a novel three-stage approach to explore the impact of CR and GR and obtain RRDs. First, based on the actual operation of SGSC, a system dynamics model of the RCs is conducted to analyze the effects of CR and GR. Second, a Stackelberg game model is formed based on the project interdependencies to find the optimal response resources and profit considering the inter-entity relationships. Third, a binary optimization model constrained in the optimal response resources is developed to determine RRDs. From the simulation results and the numerical example, the proposed approach is a powerful tool for risk managers of SGSCs. The actionable recommendations on managing and responding to CR and GR are summarized. This study provides theoretical and managerial insights for resilient supply chain management.

Low-carbon optimal scheduling of park-integrated energy system based on bidirectional Stackelberg-Nash game theory

Multi-stakeholder participation is crucial in facilitating the development of park-integrated energy systems (PIES). Balancing the diverse interests of various stakeholders, each with its distinct requirements presents a notable challenge. Concurrently, the model's complexity increases due to the engagement of various stakeholders, posing challenges to its resolution through traditional methods. In this context, this paper aims to investigate an optimal scheduling model that incorporates shared energy storage (SES) system, microgrids operator (MGO), electric vehicles station (EVS), and user aggregator (UA) with multiple prosumers. To comprehensively address the interests of all stakeholders, this study introduces a tri-level optimization model. The proposed model integrates a bidirectional Stackelberg-Nash game framework, in which the SES acts as the leader, the MGO acts as the secondary leader, and the UA-EVS acts as the followers while allocating benefits based on the asymmetric Nash bargaining theory. The Stackelberg game model between MGO and UA-EVS is analyzed using the Karush-Kuhn-Tucker (KKT) condition, while the Stackelberg game model between SES and MGO is resolved using the bisection method. Meanwhile, the Nash bargaining method among users is solved using the alternating direction method of multipliers (ADMM) technique. The analysis indicates that the proposed strategy can reduce PIES's costs and carbon emissions, yielding a win-win situation for all stakeholders.

Blockchain technology embedded in the power battery for echelon recycling selection under the mechanism of traceability

This paper examines the use of blockchain technology in power battery echelon recycling. The technology helps to improve battery capacity identification and market transaction trust. The study focuses on power battery manufacturers and recycling participants. Two recycling modes are constructed using the Stackelberg game method, and the optimal decision-making of the participating subjects in the two modes of power battery echelon recycling under the embedding of blockchain technology is compared. The influence of each parameter on the optimal decision-making is analyzed. The research findings indicate that the degree of blockchain technology integration rises as the preference coefficient for traceability information increases. When recycling competition is intense and the sensitivity of recycling prices is low, the optimal recycling model for the number of spent power batteries (SPBs) to be recycled is the model in which echelon utilizers do not participate in recycling if the level of cost optimization coefficient embedded in blockchain technology is high, otherwise, it is the model in which echelon utilizers participate in recycling. The profit of power battery manufacturers and echelon utilizers decreases with the increase of the intensity of power battery recycling competition, the cost optimization coefficient of echelon utilizers and the cost optimization coefficient of manufacturers.

Optimal strategies for supply chain with credit guarantee using CVaR

In this paper, we explore optimal strategies of a supply chain consisting of one manufacturer, one capital-constrained retailer and one bank, where the bank provides loans to the retailer due to credit guarantees. However, there are default risks if the retailer can not repay the loans. Using conditional value-at-risk (CVaR) to describe risk aversion of the retailer, optimal order quantities of the retailer and optimal wholesale prices of the manufacturer are obtained by solving a Stackelberg game model, where the manufacturer is a leader and the retailer is a follower, respectively. Our numerical results show that the default probability of the retailer are proportional to optimal wholesale prices of the manufacturer. It implies that when the default probability of the retailer is high, the manufacturer should reduce the default risk by setting higher wholesale prices to avoid a burden of a substantial guarantee. Thus, our results can serve as insights for decision-makers of supply chain management.

Cost-sharing incentive for collaborative innovation between main manufacturer-core supplier based on risk factors

This paper considers the “main manufacturer-supplier” model in collaborative cooperation among firms which requires the leader to invest significant resources and bear huge risks. However, few scholars simultaneously consider innovation risks and incentive issues under the model. We construct a Stackelberg game incentive model with different cost-sharing ratios under the risk of technological innovation. We characterize the equilibrium of the model and highlight the key role played by the main manufacturer and supplier. The results are as follows: (a) Main manufacturer can implement the cost-sharing incentive strategy under certain conditions, which is, its profit coefficient is greater than 0.75 times that of supplier and the cost-sharing ratios expected coefficient is greater than the minimum threshold. (b) The optimal cost-sharing ratio is directly proportional to the profit coefficient of the main manufacturer, inversely proportional to that of the supplier, and shows an inverted U-shape function with the probability of successful technological innovation. (c)This strategy can motivate suppliers to invest more resources, reduce the investment of the main manufacturer, simultaneously increase the profits of the main manufacturer and supplier in the certain ranges of innovation success probability and profit coefficients, with significant incentive effects.