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We study a setting where a receiver must design a questionnaire to recover a sequence of symbols known to a strategic sender, whose utility may not be incentive compatible. We allow the receiver the possibility of selecting the alternatives presented in the questionnaire, and thereby linking decisions across the components of the sequence. We show that, despite the strategic sender and the noise in the channel, the receiver can recover exponentially many sequences, but also that exponentially many sequences are unrecoverable even by the best strategy. We define the growth rate of the number of recovered sequences as the information extraction capacity. A generalization of the Shannon capacity, it characterizes the optimal amount of communication resources required while communicating with a strategic sender. We derive bounds leading to an exact evaluation of the information extraction capacity in many cases. Our results form the building blocks of a novel, non-cooperative regime of communication involving a strategic sender. • An uninformed receiver aims to recover information from an informed strategic sender • No assumption of incentive compatibility or external incentives • Information-theoretic analysis shows a fundamental limit on recovered information • Real-world setting of screening of travellers using questionnaires can be studied • Novel theory combining Shannon's information theory and Myerson's mechanism design [ABSTRACT FROM AUTHOR]

Alongside the rapid advancement of artificial intelligence technologies, the complexity of society continues to escalate, and the design of multi-agent system rules becomes increasingly crucial, optimize participant engagement and addressing the issue of fairness and equilibrium win rates. The card game Legends of the Three Kingdoms (LTK), as a complex multi-agent system, represents an important abstraction of real-world scenarios, requiring the implementation of proper incentive mechanisms. Based on the mechanism and Stackelberg, this paper optimizes player strategies and system fairness. Firstly, we constructed a multi-agent Stackelberg game model for team battles. Then, we analyzed the impact of decision-making factors on players. Subsequently, we defined three kinds of fairness and improved the incentive mechanism. The results indicate that our mechanism optimizes participants' game behaviors, enhancing fairness among team players. Win rates were improved from 56.2% VS 43.8% to 51.4% VS 48.6%. With three different fairness measures, the win percentage fairness increased by 72 %, and the first elimination fairness increased by about 79 %. Our research provides a reference for understanding and analyzing complex computational models and facilitates the resolution of various resource allocation and system design issues. [ABSTRACT FROM AUTHOR]

The integrated energy system (IES) with hydrogen storage has become one of the most important developments in multi-energy coupling field, where the severe conflict of interests between different entities leads to great challenges to the economy and low-carbon operation. A multi-objective robust dynamic pricing and operation strategy optimization method based on the Stackelberg game is proposed for the hydrogen-containing energy storage (HES) IES. Firstly, the HES-IES trading framework is established based on the introduction of an integrated energy operator (IEO) and a load aggregator (LA). Secondly, a multi-objective robust Stackelberg game model is developed with the IEO as the leader and the LA as the follower, considering the minimization of operating costs and carbon emissions of the IEO and the minimization of integrated energy costs of the LA as the objectives. Finally, the compromise planning and the max-min fuzzy are addressed to solve the multi-objective model, which adopts the adaptive differential evolution (ADE) algorithm. In addition, the robust optimization (RO) with adjustable coefficients is employed to tackle uncertainties of source and load. The results show that this method can effectively balance the operating costs and carbon emissions of the system, improve the benefit of the IEO, reduce the costs of the LA, and avoid the uncertainty risk. Compared with traditional algorithms, the ADE algorithm has significant advantages in the number of iterations and solving time. In summary, the multi-objective robust dynamic pricing and operation strategy optimization proposed in this paper could effectively achieve the benefit balance between the IEO and the LA, also further improve the economy and robustness of the system and reduce carbon emissions. [Display omitted] • A multi-objective robust dynamic pricing and operation strategy optimization method based on Stackelberg game is proposed. • The compromise planning, max-min fuzzy method and adaptive differential evolution algorithm are adopted to solve the model. • The robust optimization with adjustable coefficients is employed to deal with the source-load uncertainty. • The economy and robustness of the system are improved, and carbon emissions are reduced. [ABSTRACT FROM AUTHOR]

This paper researches the impact of different innovation investment modes on the closed-loop supply chain (CLSC) profit and pricing decisions under an uncertain recycling quality background. Furthermore, we construct a battery swapping CLSC under three innovation investment modes. The research results show that: (1) Under the cooperative innovation investment mode, the decision variables and CLSC system profit all reach the optimal level. (2) Increasing the subscription duration can promote the reduction of subscription price, which is beneficial to the improvement of innovation investment level. (3) When the innovation cooperation coefficient is within a certain range, it will promote the increase of profits for the CLSC. (4) The balanced battery ratio is an important factor affecting enterprise decision-making, and it has a more significant impact on the battery swapping operator. (5) The power battery manufacturer can dynamically adjust the echelon utilization quality threshold according to the echelon utilization value to achieve optimal profit. [ABSTRACT FROM AUTHOR]

There is currently a "mother-daughter" model for hydrogen refueling stations (HRS). On-site "mother" stations produce hydrogen from city natural gas or water electrolysis, and off-site "daughter" stations are supplied with hydrogen from nearby on-site stations. This HRS system is a micro hydrogen supply chain that includes hydrogen suppliers, retailers, and end consumers characterized via demand functions. The present paper designs an optimal business model for this distributed HRS system using a multi-level game model, given that on-site and off-site HRS can operate individually or as a coalition to supply hydrogen. Stackelberg game and Shapley value models are constructed to explore how cooperative operation is superior by generating more profits than separate operation. Accordingly, in order to promote cooperation between on-site and off-site operators of HRS, an evolutionary game model is developed to investigate the allocation of profits and coordinated costs on the equilibrium of cooperative operation. The authors conclude that boosting the initial probabilities of actors to choose cooperative strategies and decreasing the coordinated cost can lead the game system to the ideal consequence. The present paper offers recommendations including establishing regulation standards for HRS operation, and advancing the information technology to design a more effective cooperative mechanism. • A business model of the hydrogen distribution is designed by multi-level games. • The centralized cooperation mode is better than the decentralized separation mode. • Reduction in the communication cost can help to achieve the cooperative mode. • Regulation and information technology related to the hydrogen should be enhanced. [ABSTRACT FROM AUTHOR]

A game theory approach is used to study a market-based pollution trading strategy among different point sources. Point sources discharge effluents to the same watershed and participate as rational entities with particular objectives, interacting with each other in a hierarchical organization. Each point source must implement technologies to sell credits to other sources or buy credits to compensate for non-compliance with environmental regulations. The objective function of the formulations proposed considers the minimization of total annual costs for each point source. The participants in the pollutant credit trading are related in a Nash Game by a mixed complementarity problem (MCP) and in a Stackelberg Game by a bilevel optimization problem (BLP). Both systems are solved using the disjunctive constraint method. Different scenarios of interaction among the participants are proposed in order to observe the behavior of each decision strategy. These models should generate more reliable results with respect to non-competitive approaches as the interaction of the participants is considered. [Display omitted] • Optimal pollution trading decisions are found through mathematical programming. • A game theory approach incorporates competition/cooperation among point sources. • Nash equilibrium and a Stackelberg game are used as mathematical scenarios. • Individual rather than overall objectives are considered in the formulation. • The opportunity of forming alliances is studied. [ABSTRACT FROM AUTHOR]

As new energy vehicles continue to advance, the sphere pertaining to power battery recycling is experiencing steady growth. This has sparked widespread discussion and attention regarding the formation of an alliance dedicated to power battery recycling. In order to establish a closed-loop supply chain (CLSC), and faster the amalgamation within the realm of battery recycling, this research examines the influence of the extent of recycling efforts on power battery demand in new energy vehicles. By utilizing a Stackelberg game, the consideration is given to the inclusion of a power battery manufacturer, a new energy vehicle enterprise, and a third-party recycler. The examination revolves around the consequences of various recycling alliance modes about decision-making and profits within the CLSC. The findings indicate that it is more advantageous for the power battery manufacturer to establish a recycling alliance with a new energy enterprise and recycler rather than establishing a separate alliance with a third-party, as this approach enhances the benefits to the battery manufacturer. In other words, the presence of multiple alliance members in the recycling realm positively correlates with the overall profitability of the CLSC. The power battery manufacturer should establish appropriate recycling sensitivity coefficients to incentivize enterprises to intensify recycling efforts and augment the recycled volume of used power batteries. Furthermore, the benefits of CLSC can be amplified by government subsidies, and the distribution ratio of these subsidies can affect the choice of a recycling alliance model for CLSC members. [ABSTRACT FROM AUTHOR]

The construction of the Hainan Free Trade Port (HFTP) is proceeding step by step. With the closing time in 2025, companies from all over the world have begun to notice the importance of the HFTP. Many companies have begun to consider rebuilding their supply chain networks with HFTP as an important node, thus forming a free trade port supply chain. As a result, HFTP has formed a complex system focused on the global supply chain. This paper constructs a dual-channel supply chain networks scenario with a single product manufacturer leading pricing based on complex system perspective. In the context of whether to choose the Free Trade Port Blockchain Platform (FTPBCP), using the traditional distribution channel as a reference, the Stackelberg game strategy is used to analyze the supply chain pricing of online direct sales and online distribution, and the SCN redesign decision. The analysis results show that the construction of the FTPBCP has a very important impact on the redesign of the GSC. Manufacturers need to consider the construction cost of the blockchain technology platform to set an appropriate price or redesign the SCN. [ABSTRACT FROM AUTHOR]

There exist the uncertainties and the inequality constraints in permanent magnet synchronous motor (PMSM) system. In order to meet the safety control requirements in industrial applications, the state transformation is used to meet the inequality constraints for limiting the outputs within desired bounds. Then, fuzzy set theory, which is different from fuzzy logic, is used to describe uncertainty, and the fuzzy PMSM dynamical model is established. Based on that, a robust control with high-order term is proposed to compensate for the time-varying uncertainty. Furthermore, for improving the system performance and decreasing the control cost, the Stackelberg game is introduced into the optimization scheme design, in which the leader plays a more important role than follower. These characteristic corresponds to the influence of the two tunable control parameters on the system. Thus, the optimal parameters are obtained by the rules of Stackelberg game. Finally, experimental results show the effectiveness of the above theories. • A robust control guarantees uniform boundedness and uniform ultimate boundedness. • The uncertainty in PMSM system is described by fuzzy set theory. • The inequality constraints are satisfied by the diffeomorphism principle. • The tunable control parameters are optimized based on Stackelberg game theory. • The intelligent cybernetics method and optimization scheme are established. [ABSTRACT FROM AUTHOR]

The energy consumption of data centers is on a sharp upward trend, and how to achieve joint optimal scheduling and energy management of multiple data centers is the key to the economic and low-carbon operation of data center prosumers (DCPs). This study introduces shared electric-hydrogen energy storage (SEHES) for DCPs, constructs a data center cluster (DCC) framework, and proposes a two-stage energy sharing model for DCC considering the 'Carbon-Green Certificate' coupling mechanism (C-GCCM). First, the DCC framework containing DCC operator (DCCO) and DCPs is established, and the C-GCCM based on conversion coefficients is designed to improve the energy saving and emission reduction level of DCC. In the day-ahead optimization stage, a stochastic multi-objective scheduling model for SEHES considering economy and environmental protection is developed. In the real-time optimization stage, considering the C-GCCM and the difference in on-grid prices, the Stackelberg game model of DCC is constructed according to the internal energy price set by DCCO and the trading strategies of DCPs. Finally, the proposed model is solved using the normal boundary intersection algorithm, the particle swarm algorithm and CPLEX. Simulation results demonstrate that the proposed DCC framework can reduce the daily operating cost of DCPs by 67.05 %. The introduction of C-GCCM has resulted in a shift from negative to positive benefits on carbon emission trading for DCC and a 42.33 % increase in benefits on green certificate trading. • Shared electric hydrogen energy storage is introduced in the data center cluster. • A novel two-stage energy sharing method for the data center cluster is presented. • A novel 'Carbon-Green Certificate' coupled trading mechanism is designed. • The demand response mechanism of data load is constructed. • A pricing mechanism considering the difference of on-grid prices is designed. [ABSTRACT FROM AUTHOR]

Fresh product traceability plays an integral role in ensuring food safety. Recently, many firms have introduced blockchain technology (BCT) for product traceability to guarantee product authenticity and consumer rights. However, introduction of the new technology has also intensified the competition among fresh products. Meanwhile, previous studies on traceability strategies only considered the impact of traceability cost and ignored the issue of increased product competition in blockchain era. Driven by these problems, we build a game-theoretical model to analyze the optimization of traceability schemes for both low-end fresh products (LEFP) and high-end fresh products (HEFP) in a fresh product supply chain (FPSC) in a competitive environment. Moreover, this paper investigates the impact of power structure on traceability schemes and identifies the conditions under which one scheme outperforms the others. We find that the cost per unit of product input has no effect on the traceability decision of the FPSC. Nonetheless, the introduction of BCT increases the number of consumers who choose LEFP and raises the selling price and wholesale price of corresponding products. Finally, from the supply chain perspective, it is best to adopt the same traceability scheme for both products. This study sheds light on the use of BCT in traceability can provide enhanced product authenticity and consumer rights while increasing product competition and demonstrates the significance of traceability schemes in the FPSC. [ABSTRACT FROM AUTHOR]

The hybrid platform is emerging into online retailing market based on reselling and direct selling, forming the dual-channel model composed of third-party operated and platform self-operated channels. To achieve structural matching between channels, this study studies the pricing strategies of suppliers as well as platform under four information-sharing situations: non-sharing information (NS), complete sharing information (CS), sharing information only with supplier of self-operated channel (SS), sharing information only with supplier of third-party operated channel (ST), and derive the equilibrium outcomes. The conclusions show that the retailing price in NS is only affected by levels of competition and transaction fees, while sharing information can raise the retailing price of both channels. Second, the information shared to self-operated supplier can intense competition and bring higher wholesale price, while information not shared to self-operated supplier can enhance co-operation and bring lower wholesale price. Moreover, the self-operated supplier is more inclined to enjoy market information, the third-party supplier prefers to no information shared to self-operated supplier at lower information-sharing level, but the third-party supplier prefers to SS at higher information-sharing level. For equilibrium results, the NS is the equilibrium information-sharing strategy when the information value is high; when the information value is moderate, the equilibrium strategy is ST under small or high transaction fee, and the equilibrium decision is CS under modest transaction fee; when the information value is small, the equilibrium strategy is CS under small or high transaction fee, while the equilibrium decision is ST under modest transaction fee. [ABSTRACT FROM AUTHOR]

Residential air-conditioning load on the power demand side has gradually increased. The air-conditioning loads have thermal storage characteristics, and adjusting their temperature settings will not cause significant negative impacts to users, making them well-suited for demand response. In existing studies, load aggregators usually serve as demand response implementors, and reducing the energy consumption levels of air conditioning loads directly. However, this method often lacks a clear definition of the flexibility of individual air-conditioning units and fails to account for their variations. The absence of well-defined commodity characteristics for the flexible regulation potential complicates pricing, making it difficult to safeguard the interests of the load aggregator and each air-conditioning user. Furthermore, the diversity among residential air-conditioning loads introduces high-dimensional variables into demand response optimization, making it challenging to balance data security with computational efficiency. To address these challenges, this paper proposes a market-based load reduction method for heterogeneous residential air-conditioning loads using cloud-edge collaboration. First, the flexible adjustment capability of air-conditioning loads is defined as a tradable commodity. Then, a cloud-edge collaborative trading scheme is proposed to guarantee the benefits of the load aggregator and each air-conditioning user in a data-neutrality manner. Finally, a hybrid method based on encrypted clustering is developed to compute the optimal trading strategy, ensuring data security and computational efficiency. Simulation results based on data from the Austin area show that Pareto improvement is achieved compared to other load reduction schemes, and the proposed encrypted clustering method reduces computational complexity and data security risks compared to traditional analytical and iterative approaches. [ABSTRACT FROM AUTHOR]

This study introduces an innovative approach that harnesses the Stackelberg differential game framework in combination with advantage actor-critic (A2C) reinforcement learning (RL) to attain adaptive and dynamic control, in the presence of complex faults within spacecraft systems. By reconfiguring the problem of fault tolerance into a strategic interaction involving two pivotal players, specifically, the leader (fault-tolerant control, FTC) and the follower (fault detection observer, FDO), our approach facilitates the dynamic adaptation of their control strategies in response to the system's state, effectively providing a solution for addressing faults within spacecraft systems. This approach overcomes the challenges of cross-optimal indexes commonly found in traditional FTC, resulting in improved efficiency and stability of RL. It harbors substantial potential for applications requiring robust and adaptive FTC strategies. Simulation validation, both the leader and follower can successfully control the spacecraft's velocity before and after a fault occurs, ultimately achieving optimal fault estimation (FE) and FTC objectives. [ABSTRACT FROM AUTHOR]

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. • A Stackelberg game model is developed, motivating EVs and users in demand response. • A multi-stage RO model is proposed to address nonanticipativity issues. • Nash bargaining method is used to realize optimal energy trading and fair benefit distribution among IESs. [ABSTRACT FROM AUTHOR]

With a rising number of buildings being equipped with private distributed energy resources (DERs) such as rooftop PV panels and energy storage devices, an effective energy management method for a building cluster becomes increasingly imperative. This paper proposes a novel decentralized transactive energy management (TEM) method for a hybrid cluster of residential and commercial buildings, which enables peer-to-peer (P2P) energy trading among the DER owners and consumers. The strategic interactions among the DER owners and consumers are modeled as a multi‑leader-multi-follower (MLMF) Stackelberg game and formulated as a bi-level model. The DER owners, the commercial and residential consumers are all autonomous entities, optimizing their individual welfare functions and sharing necessary trading-related information, which are expressed as the upper-level leaders' models and the lower-level followers' models, respectively. To preserve the privacy and autonomy of each entity within the building cluster, a distributed algorithm incorporated with an efficient P2P pricing mechanism is designed for the formulated MLMF Stackelberg game model. Simulation results demonstrate the effectiveness of the proposed method on mitigating the reliance of the building cluster on the power grid, motivating the DERs to actively participate in P2P trading, and reducing the consumers' energy consumption costs • A decentralized transactive energy management framework is designed for a real-world hybrid building cluster. • The strategic interactions among the owners of distributed energy resources (DERs) and the consumers within the building cluster are captured by a multi‑leader-multi-follower Stackelberg game. • A novel distributed algorithm is developed to protect the privacy and autonomy of participants in a large-scale building cluster. [ABSTRACT FROM AUTHOR]

We consider a ride-hail system in which a third-party integrator receives ride requests and allocates them to ride service platforms. The ride allocation problem (RAP) is modeled as a Stackelberg game. The integrator, as the leader, chooses the allocation that maximizes its profit, by pricing the rides such that no platform (i.e., follower) can find a more profitable allocation. In pursuit of self-interest, the integrator may refuse to match as many rides as the platforms are willing to serve, thereby injecting an artificial scarcity into the system. To protect the platforms from over exploitation, an exogenous reserve price is introduced to bound their per capita profit from below. We formulate RAP as a bilevel pricing problem, and convert it to a single-level problem by dualizing the lower level. When artificial scarcity is eliminated and all reserve prices are set to zero, we prove the single-level problem can be turned into a mixed integer-linear program that equals its linear relaxation, thus becoming polynomially solvable. Moreover, this version of RAP is shown to be related to cooperative assignment games. Numerical experiments confirm that artificial scarcity negatively affects matching productivity and social welfare. The integrator is favored to take most profits, and leveraging artificial scarcity strengthens its dominance. Moreover, the tighter the supply, the more the integrator benefit from artificial scarcity. The reserve price helps redistribute benefits from the integrator to the platforms. However, demanding an excessively large reserve price may depress the platforms' profits, while undermining system efficiency. • Third-part integration: Modeled as a Stackelberg game, a ride-hail integrator optimally allocates rides to service platforms. • Artificial Scarcity Dynamics: Integrator's self-interest may limit ride matches, injecting artificial scarcity. • Bilevel Pricing Formulation: The Ride Allocation Problem is formulated as a bilevel pricing problem. • Polynomial Solvability: Eliminating artificial scarcity and setting all reserve prices to zero transform the problem into a polynomially solvable mixed integer-linear program. • Impact of Artificial Scarcity: Numerical experiments highlight negative effects on matching productivity and social welfare. [ABSTRACT FROM AUTHOR]

With the widespread popularity of green and environmental protection concepts, customer satisfaction with green marketing in the green supply chain is particularly important, and channel green marketing is an important part of the green supply chain. Thus, this paper studies competition and cooperation strategies in the pricing and green marketing of a dual-channel supply chain while considering customer satisfaction. Using a two-stage optimization method and the Stackelberg game, we explore two cooperation models. In the first model, two retailers cooperate and compete with the manufacturer; in the second model, retailer 1 cooperates with the manufacturer and competes with retailer 2. It finds that because of the influence of customer satisfaction, the optimal price is not always proportional to green marketing efforts, and retailers with a higher market share may not necessarily have higher profits. The manufacturer, even if it is in competition with retailers, in some cases should actively help retailers improve green marketing to increase profits. Finally, we note that the cooperation strategy in a green supply chain is influenced by the relationship between green marketing and customer satisfaction. [ABSTRACT FROM AUTHOR]

Transportation companies have a significant task in creating resilient public transportation during the pandemic. Observance of health protocols by transportation companies can diminish the spread of the disease. However, adhering to health protocols would put additional economic pressure on them. Consequently, providing safe transportation services will require government support. This study examines governments' support policies for safe transportation companies (STCs) through tax exemptions. In this regard, a three-level Stackelberg game model includes government, safe and unsafe transportation companies (UTCs), travel agencies constructed Equilibrium equations are obtained for the decisions of the government, the transport companies, and the passenger company. Then, a case study was conducted on two transportation companies in Isfahan; the effect of tax rates and tax exemption rates on stakeholders has been investigated using the proposed model. Results show that applying for tax exemptions within certain limits on STCs will strengthen them and increase government benefits. • A three-level Stackelberg game analyzes STCs and UTCs competition. • The government, as the leader, encourages companies to enforce health protocols. • The equilibrium values of the decision variables and players' profits are obtained. • Applying a specific tax exemption to STC will benefit both STC and the government. • By analyzing a real case study, various management insights have been presented. [ABSTRACT FROM AUTHOR]

Integration of a behind-the-meter (BTM) energy storage system (ESS) is a dependable method of reducing electricity costs and improving power quality for industrial users susceptible to voltage sags. However, at present, barriers such as substantial initial investment costs, extended investment return periods, and limited service strategy flexibility are impeding the widespread implementation of BTM ESSs in industrial contexts. Integrated energy service providers (IESPs) supply innovative BTM ESS solutions and have emerged as viable options for navigating these challenges. This study proposes a new two-stage business model designed to advance ESS deployment while considering the needs of both the IESP and users. Herein, the framework of the proposed business model is outlined to delineate the participant roles and responsibilities at different stages. A detailed cost–benefit analysis is conducted to support a scenario analysis based on prospect theory. Then, a Stackelberg game model is constructed to describe the interactive relationship between the participants; using this model, an optimal ESS service strategy can be determined by resolving a simplified Stackelberg game problem. Our findings reveal that this model effectively mitigates long-term income risks for IESPs and substantially lowers initial investment costs for users by 21.93 % to 89.23 %, along with a reduction in lifecycle costs by 2.35 % to 17.12 % for users. A comprehensive analysis of six critical parameters indicates that the ESS lifetime, the disparity between peak and off-peak electricity prices, and power quality management performance exert the most significant influence on the total net benefits for all participants. The proposed model is expected to further the adoption of ESSs among industrial users. • A two-stage business model to promote energy storage-system adoption is designed. • The roles and responsibilities of the participants in each stage are clarified. • The management of voltage sag is regarded as a fundamental element contributing to the ESS revenue. • Based on scenario analysis, the model contributes to user-group expansion. • The model's flexibility and effectiveness are demonstrated by a series of representative service strategies. • The applicability of the proposed two-stage business model in other scenarios has been analyzed and summarized. [ABSTRACT FROM AUTHOR]

With the increased coupling of agriculture and energy, there is a trend to aggregate and manage distributed energy resources in agricultural parks using rural virtual power plants (RVPP). This paper investigates the impact of uncertainties in renewable energy generation and energy usage, as well as the flexibility of energy‑carbon-green certificate (GC) trading, on the planning and operation of RVPP. Firstly, the basic architecture of RVPP is constructed, and a joint trading mechanism for the carbon emission allowance (CEA) and GC is designed. On this basis, a two-stage deterministic optimization model is developed considering capacity configuration in the planning stage and the Stackelberg game in the operation stage of RVPP. Then, several typical scenarios considering the correlation of uncertainties are generated, and the deterministic model is transformed into a distributionally robust optimization (DRO) model in a scenario-driven manner. The confidence intervals of the scenario probability distributions are constrained by a combination of 1-norm and infinity-norm. Finally, the DRO model is decomposed into two problems, solved iteratively using a revised Kriging model and a column-and-constraint generation (C&CG) algorithm. Several cases covering different transaction forms and solution methods are analyzed comparatively to validate the effectiveness of the DRO model. The simulation results indicate that, compared to the energy trading with a fixed price, flexible trading based on the Stackelberg game can reduce the total planning and operating costs by 22.49 %. Compared to the separate trading of GC and CEA, the trading volume of CEA decreases by 44.21 % under the joint trading mechanism, with the increased configuration of renewable energy resources. • A Stackelberg game model is established to achieve a dynamic pricing of RVPP. • Based on an offset method, a joint trading mechanism for GC and CEA is designed. • Based on a R-Vine Copula-based method, a scenario-driven DRO model is developed. • A revised Kriging model is combined with a C&CG algorithm to solve the DRO model. [ABSTRACT FROM AUTHOR]

In recent years, shared energy storage has gained significant attention for mitigating the supply and demand imbalance caused by the intermittency of distributed renewable energy. Considering the subjective perception of prosumers when facing uncertainty, this paper proposes a new dynamic competitive on-demand renting framework for energy storage capacity (ESC) sharing to increase energy storage utilization, increase energy storage operator (ESO) profits, and reduce prosumer costs. In this framework, a demand-based dynamic capacity pricing mechanism is introduced, modeling the relationship between ESO and prosumers as a Stackelberg game while establishing a generalized Nash equilibrium (GNE) problem among prosumers. ESO determines the dynamic capacity pricing mechanism, while prosumers determine the hourly renting capacity based on demand. In capacity sharing, prospect theory is introduced for the first time to describe the subjective perceptions of prosumers when facing the uncertainty of renewable energy. Moreover, the existence of SE and the uniqueness of GNE are analyzed, followed by a summary and proposal of a method to determine the existence of equilibrium in a nested generalized non-cooperative Stackelberg game. Simulations show the effectiveness of the proposed framework on improving the ESC utilization rate, the impact of subjective perceptions on prosumers' decision-making, and the profit favorability of the correct estimation of subjective perceptions on ESO. Specifically, the framework increases ESO utilization by 24.07% and profit by 13.73%. • A new framework for dynamic on-demand energy storage sharing is proposed. • Prospect theory is introduced to describe the subjective uncertainty of prosumers. • A nested generalized non-cooperative Stackelberg game model is constructed. • Proven: Stackelberg equilibrium exists; Generalized Nash equilibrium is unique. [ABSTRACT FROM AUTHOR]

The emergence of vehicular edge computing (VEC) has introduced a new computational paradigm for high-quality processing of computing services in Internet of Vehicles (IoV) scenarios. However, due to the limited computational resources of the VEC server, it is not sufficient to adequately meet the demand for highly concurrent computational services in high-density vehicular communication networks. To address this issue, we consider an idle mobile vehicles assisted vehicular edge computing framework and propose a hybrid Stackelberg-Match cooperative task offloading and resource pricing algorithm (SMOP). The algorithm considers the mobility of vehicles and the duration of channels, coordinating the computational resources of fixed VEC servers and idle mobile vehicles within the vehicular network (VN). This enhances offloading efficiency and maximizes participant benefits. Specifically, the Stackelberg game is used to derive differentiated pricing schemes for idle mobile vehicles and VEC servers for different vehicular tasks, and the stable matching method is employed to determine task offloading strategies. Finally, we conduct experiments on a real Chengdu traffic dataset. The results demonstrate that the proposed solution effectively reduces offloading costs and exhibits strong robustness in handling latency-sensitive and data-intensive service requests. [ABSTRACT FROM AUTHOR]

Rising electricity demand and the swift integration of Distributed Energy Resources (DERs) highlight the imperative for effective voltage regulation (VR) strategies to mitigate voltage violations. Conventional VR methods, plagued by significant operational expenses and slow response times, are increasingly focused on harnessing prosumer flexibility. However, this strategy faces challenges, including uncertainties in VR calculations, designing VR coordination signals, and managing and monitoring prosumer actions. This paper introduces a novel three-step VR coordination scheme to tackle these issues. The first step utilizes a Data-driven Distributionally Robust Optimization (DDRO) algorithm with a Wasserstein metric ambiguity set to calculate the required active and reactive power adjustments for VR. The second step involves generating and disseminating price-based coordination signals via a clustering algorithm, reducing signal complexity. The final step proposes using Virtual Power Plants (VPPs) to aggregate smaller prosumers for VR, applying a bi-level Stackelberg game to account for the impact of distributed coordination signals on VPP member selection. Tested on the IEEE 33-bus system, this framework significantly lowers the computational load by approximately 35 % and cuts VR costs by 5.7 % compared to existing methods. • Voltage regulation framework for DSO-VPP collaboration. • Wasserstein-based distributionally robust uncertainty modeling. • VPP aggregation strategy based on bi-level Stackelberg game. • New distributed price-based voltage regulation coordination signal. • Accuracy and fast coordination of distributed energy resources. [ABSTRACT FROM AUTHOR]

The extended producer responsibility system and government intervention are among the essential requirements for constructing sustainable economies. In a closed-loop supply chain consisting of an original equipment manufacturer (OEM) and a third-party remanufacturer (TPR), this paper develops four Stackelberg game models for four modes of government intervention under patent licensing: no intervention, tax and subsidy, tax and subsidy plus eco-design tax deduction, and eco-design tax deduction only. The impacts of the different government interventions on the optimal production decision, social welfare, and environment are analyzed and compared. The results indicate that, compared with no government intervention, government tax and subsidy decrease the supply of new products, increase supply of remanufactured products, and raise recycling rates of end-of-life products; on top of tax and subsidy, the government's eco-design tax deduction can further increase OEM and TPR profits; the environmental impact under different government intervention depends on the ratio of the environmental impacts of remanufactured to new products and the level of eco-design effort. This study provides decision makers (i.e., OEM and TPR) and policy makers (i.e., governments) with new managerial insights on the benefits of eco-design and effective mechanisms to promote it. [ABSTRACT FROM AUTHOR]

Power to Heat (P2H) technology is seen as an effective solution for integrating stochastic wind power. Particularly in real-time electricity markets, high-precision wind power forecasts enable the load to better accommodate its fluctuations. Nonetheless, the shorter time scales of real-time trading pose challenges for efficiently aggregating a large, heterogeneous, and dispersed loads and fully harnessing the thermal storage capabilities of loads to follow wind power fluctuations across multiple periods. Against this backdrop, this paper proposes an aggregation control approach for P2H loads with considering multi-period Stackelberg game strategy within the framework of a load-oriented virtual power plant (VPP). For multi-period real-time trading, a Stackelberg game model based on a dynamic price ceiling is established with considering dynamic supply-demand balance between wind power and P2H loads; To enhance load aggregation effectiveness, a dynamically updated temperature-power aggregation model is developed by employing model order reduction, variables continuousization, and linear superposition on second-order equivalent thermodynamic model; To improve load decomposition efficiency, a hierarchical and multi-step control strategy encompassing the continuousization of discrete variables is utilized to simplify the problem. Finally, a simulation example is presented using actual data from a power grid in northern China to validate the effectiveness of the proposed method. • Multi-period Stackelberg game model considering dynamic price ceilings. • Dynamic aggregation for P2H loads based on power-temperature feasible domain. • Load decomposition optimization using the continuous model of P2H load. • Enhancing accommodating wind power while ensuring long-term users benefit. • Improved optimization efficiency and speed in load aggregation and decomposition. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Over the past years, game-theoretic modeling for security and public safety issues (also known as security games) have attracted intensive research attention and have been successfully deployed in many real-world applications for fighting, e.g., illegal poaching, fishing and urban crimes. However, few existing works consider how information from local communities would affect the structure of these games. In this paper, we systematically investigate how a new type of players – strategic informants who are from local communities and may observe and report upcoming attacks – affects the classic defender-attacker security interactions. Characterized by a private type, each informant has a utility structure that drives their strategic behaviors. For situations with a single informant, we capture the problem as a 3-player extensive-form game and develop a novel solution concept, Strong Stackelberg-perfect Bayesian equilibrium, for the game. To find an optimal defender strategy, we establish that though the informant can have infinitely many types in general, there always exists an optimal defense plan using only a linear number of patrol strategies; this succinct characterization then enables us to efficiently solve the game via linear programming. For situations with multiple informants, we show that there is also an optimal defense plan with only a linear number of patrol strategies that admits a simple structure based on plurality voting among multiple informants. Finally, we conduct extensive experiments to study the effect of the strategic informants and demonstrate the efficiency of our algorithm. Our experiments show that the existence of such informants significantly increases the defender's utility. Even though the informants exhibit strategic behaviors, the information they supply holds great value as defensive resources. Compared to existing works, our study leads to a deeper understanding on the role of informants in such defender-attacker interactions. [ABSTRACT FROM AUTHOR]

Electric vehicle (EV) load integration and environmental concerns in recent years have motivated energy users to step forward in reducing carbon footprints by promoting energy trading. In the energy trading market, different energy stakeholders participate in trading energy with each other to maximize their utilities and improve trading efficiency. The social welfare (SW) of the energy market plays a significant role in keeping the market going and motivating new users to engage in energy trading. The SW of the energy market depends on its structure, where energy flows from producer to end user in a fair way. This paper introduces a hierarchical energy trading framework, formulated as a three-stage Stackelberg game, to enhance SW. In the first stage of this hierarchy, the retailer, acting as the sole leader, seeks to maximize profits through optimized energy sales to charging stations (CS). Subsequently, in the second stage, each CS operates as a leader for EVs, aiming to maximize profits by minimizing energy trading costs, while also acting as a follower in response to the retailer's strategies. The third and final stage involves EVs collaboratively acting as a unified strategic agent to minimize their trading costs through optimized charging and discharging schedules. This paper also introduces an average price penalty function to further enhance SW in the energy market. The proposed model, addressing the complexities of energy trading interactions, is formulated as a non-linear optimization problem with constraints. It has been implemented in a Python environment and solved using the Gurobi optimization solver, demonstrating its potential to improve the efficiency, fairness, and overall social welfare of the energy trading market. • Introduces a hierarchical energy trading framework using a three-stage Stackelberg game to enhance market social welfare. • Incorporates renewable energy at the retailer level, diversifying energy sources and boosting ecological relevance. • Establishes comprehensive pricing functions across all levels, including reciprocal EV discharge signals, for dynamic market interaction. • Implements an average price penalty at charging stations to preserve social welfare and promote efficient energy use. • Demonstrates model efficiency and practical applicability through tests on the IEEE 33 bus system, showing superior profitability and convergence. [ABSTRACT FROM AUTHOR]

With the rapid development of shared energy storage (SES) and distributed energy resources, the local energy market (LEM) has become a pivotal platform for the interaction between microgrids and distributed energy. In LEM, the challenge of formulating pricing strategies that effectively align with wholesale market prices, and coordinating SES leasing with energy trading, is crucial for the healthy development of the market. This study introduces a real-time floating pricing (FRTP) strategy based on day-ahead market (DAM) prices and establishes a multi-objective, two-level Stackelberg game model between micro-grid operator (MGO) and the photovoltaic prosumer aggregator (PVPA). The model, constrained by a price cap mechanism, employs distributed algorithms to optimize coordinated pricing strategies for trading and SES leasing. Through simulations of various trading modes, this study thoroughly examines the impact of market signals on MGO's pricing strategies within the LEM. Our findings reveal that: (1) Under the two-level trading model, both MGO and PVPA can maximize their economic benefits. (2) The FRTP strategy increases MGO's revenue by 2.86%, 2.35% and 1.55% compared to fixed pricing, time-of-use (TOU) and hybrid pricing strategies, respectively, while also reducing carbon emissions by 3.68%, 1.35%, and 0.8%. (3) Setting price caps plays a crucial role in managing DAM price volatility. This study provides theoretical insights that enhance the market performance of MGO and PVPA, promoting the market-based integration of distributed energy resources crucial for their effective utilization. • Propose a multi-objective two-layer Stackelberg game model for prosumers and MGO. • The proposed FRTP strategy enables the linkage of LEM prices with DAM prices. • Introduce a "price cap" mechanism as the price discipline for LEM transactions. • A synergistic pricing mechanism for electricity trading and SES leasing is designed. • The proposed trading model improve economic and environmental benefits. [ABSTRACT FROM AUTHOR]

• A Stackelberg game-based incentive mechanism embedded with a discharge guidance strategy for Private Electric Vehicles (PREVs) is proposed, enhancing the PREVs participation in load restoration of distribution system. • The V2G Station Operator (VSO)'s discharge guidance strategy for PREVs is modelled as an optimization problem using Huff attraction model, accounting for PREV user destination choice behaviors and preferences. • A Stackelberg game model is constructed to achieve an equilibrium of interests among multi-stakeholder and ultimately achieve load restoration. The uniqueness of the game equilibrium solution is proved. • The restoration results under different strategies, preference coefficients and electric vehicle response rates are investigated. Effectively utilizing large-scale Private Electric Vehicles (PREVs) in load restoration can enhance the capability of Distribution System Operators (DSOs) to respond to accidental power outages. However, the challenge remains in incentivizing and guiding PREVs to participate in load restoration. This paper proposes a Stackelberg game-based incentive mechanism, with a V2G Station Operator (VSO) discharge guidance model based on the Huff attraction model embedded to address this challenge. The VSO is introduced to manage the issue of PREVs having small individual capacities, and not meeting the criteria for direct participation in electricity markets. Firstly, a framework for involving PREVs in load restoration is introduced, clarifying the responsibilities of PREVs, VSO, DSO, and Distribution Market Operator (DMO), as well as the interrelation of incentive mechanism and discharge guidance strategy. Secondly, models for each game participant are established. The VSO encapsulates the discharge guidance strategy into an optimization model using the Huff attraction-based model that captures the destination choice probabilities of PREVs, and the DSO develops a load restoration model. Thirdly, a Stackelberg game model is established with the DMO as the leader and VSO and DSO as followers. The existence and uniqueness of the proposed Stackelberg game's equilibrium solution are proven, and a distributed iterative algorithm is employed for the solution. Finally, numerical simulations are performed with the IEEE 33-bus distribution system and a simplified road network to validate the proposed strategy's effectiveness in guiding PREVs' participation in load restoration, enhancing the restoration capability of the DSO, and improving the economic efficiency of each participant. [ABSTRACT FROM AUTHOR]

Energy and water are interdependent. Water is essential for energy production, and energy is indispensable for water processes. This paper develops a Stackelberg game based bi-level multi-objective model for optimal water allocation under uncertainties from an energy-water nexus perspective, which considers energy-related water consumption and water-related energy production. It handles the hierarchical decision-making problem between the river basin authority and the subareas, as well as the tradeoffs between social equality and ecological damage. The upper level of the model makes schemes on water allocation for multiple subareas, and the lower level decides on water allocation for different types of power generation. To generate reasonable and practical strategies for water allocation, ɛ -constraint method and KKT conditions are used. A case study of Minjiang River, China is given to demonstrate the applicability and practicality. Scenarios analysis is also conducted to demonstrate the effectiveness of the model and the effects of the control parameter changes. The results indicate that the river basin authority would allocate larger water resources to the subareas with higher energy demand. It is concluded that the proposed allocation method is advantageous to the subareas with higher water utilization efficiency. The proposed bi-level model demonstrates its reasonableness and superiority to the single-level model. Policy implications are finally provided to support the sustainable development of energy-water nexus. • A bi-level model for water allocation in energy-water nexus system is proposed. • The hierarchical decision sequence between the river basin and subareas is solved. • The tradeoffs between social equality and ecological damage are made. • Optimal water allocation for multiple subareas and energy resources are quantified. • Uncertainties in decision-making environment are handled by fuzzy set theory. [ABSTRACT FROM AUTHOR]

As the battery recycling market in China is still in an embroynic stage, the mechanisms, channels, pricing, and efficiency of battery recycling are shrouded in opacity. Battery recycling in China is currently dominated by electric vehicle manufacturer, supplemented by other market players such as battery producers and electric vehicle retailers. Due to the lack of information, battery recycling lacks cooperation and communication, and the whole market is dealing with "Information Island." Therefore, based on information sharing and channel competition, this paper designs a Stackelberg game model with an electric vehicle manufacturer, an electric vehicle retailer, and a third-party recycler as the primary participants. This study found that effective information sharing can reduce intensified market competition and promote the transformation of market players into "collaboration state". To promote partnership in the battery recycling market, this paper proposes a revenue-sharing contract incentive for the electric vehicle retailer to share demand information about battery recycling. It finds a revenue-sharing contract based on information sharing can help companies and competitors make appropriate behavioral choices in the battery recycling market. This study demonstrates that information sharing benefits the electric vehicle manufacturer and the third-party recycler while offering no advantages to the electric vehicle retailer. The decreasing accuracy of demand signals results in the diminishing value of information sharing for the electric vehicle manufacturer and the third-party recycler. The revenue-sharing contract can incentivize the electric vehicle retailer to share information. [Display omitted] • A battery recycling mode of electric vehicles is constructed. • Effective information sharing would encourage market players to be more collaborative. • A revenue-sharing contract is designed to incentivize the electric vehicle retailer to share information. • Inaccurate information and channel competition reduce the attractiveness of information sharing. • Inter-firm information sharing is beneficial for building an efficient battery recycling system. [ABSTRACT FROM AUTHOR]

• This paper takes the community electricity trading market with multiple prosumers participating at the distribution network level as the research object, fully considering the impact of the psychological gap effect of prosumers on system operation from a micro-perspective, and proposes a distributed electricity market trading mechanism based on the Stackelberg game, which in order to provide new ideas for the improvement and optimization of the distribution-side electricity market trading system, and the core findings of the paper are as follows:. • The trading mechanism proposed in this paper could better schedule translatable loads and energy storage units, reduce the fluctuation amplitude of the load curve while performing peak cutting and valley filling, stimulate the flexibility of user-side resources, and ensure the stability of system operation. • The trading mechanism proposed in this paper could obtain more evidence-based and reasonable prices for purchasing and selling electricity within the region, ensuring that the distribution network operator could obtain considerable profits while effectively improving the profits of prosumers, which is conducive to improving the economic efficiency of system operation. • In terms of the impact of the gap effect on the energy utility and profits of prosumers, the larger the gap effect coefficient (prosumers are more sensitive to expected deviations), the lower their electricity utility and overall profits, and when the individual electricity utility and overall profits of prosumers are too low, they may withdraw from market transactions. Therefore, government departments could implement policies, such as providing subsidies and adjusting taxes, to further stimulate the enthusiasm of prosumers to participate in distributed market transactions. With the large-scale customer-side development of distributed energy and continuous advancements in power market reform, the market-oriented trading of distributed power generation with the participation of prosumers has gradually become an important solution to promote the consumption of distributed energy. In addition, prosumers exhibit obvious bounded rationality characteristics; therefore, the design of efficient and reasonable trading mechanisms determines the efficiency of the market. From this perspective, a distributed electricity market trading mechanism based on the Stackelberg game is proposed for the community electricity trading market, with multiple prosumers participating in the distribution side. Firstly, the trading architecture of the community electricity market was established under the distribution network level. Secondly, the pricing strategy of the distribution network operator and the quantitative strategy of community prosumers were analysed; on this basis, the characteristics of the bounded rationality of prosumers were considered, and the impact of the psychological gap effect of prosumers on their energy utility was introduced into the objective function of prosumers. This facilitated the construction of a Stackelberg game model in which distribution network operators lead and community prosumers follow. Thirdly, the Stackelberg equilibrium was proven to exist and be unique, which was then solved by the distributed algorithm – combining the evolutionary algorithm and quadratic programming – which improves the solution efficiency and effectively protects the privacy of prosumers. Finally, the effectiveness and feasibility of the proposed trading mechanism were verified through numerical examples. [ABSTRACT FROM AUTHOR]

Prefabricated building systems that take advantage of modern manufacturing, transportation, and assembly approach have attracted great attention as solutions for sustainable cities and urban construction carbon emissions mitigation, especially under the 30% prefabrication of new buildings target in China's development plan of the construction industry. Nevertheless, few research has focused on the carbon reduction/economic costs equilibrium for the integrated traditional and prefabricated construction supply planning (PCSP). Aiming at the sustainable construction for urbanization, this study develops a Stackelberg game-based method for economic and environmental equilibrium under the carbon allocation scheme in an integrated prefabricated construction supply planning. In the bi-level model, the regional authority on the upper level determines the carbon allocations and the enterprises on the lower level develop plans to maximize revenue under the prefabricated rate targets and construction supply logistics limitations. The superiority and practicality of the proposed methodology are then validated through a case study from China. The scenario analyses under different policy control levels indicate that the proposed methodology is capable of systematically controlling the integrated PCSP carbon emissions and promoting the low-carbon transformation and sustainable development of construction industry. Valuable managerial implications are also provided for the policymakers and relevant practitioners. • A Stackelberg game-based model in prefabricated construction supply is developed. • The carbon-economy trade-off of different decision makers is analyzed. • A case study with different control scenarios is demonstrated. • Implications for urban construction industry practitioners are provided. [ABSTRACT FROM AUTHOR]

This study analyzes the scheduling of unpredictable fare inspections in proof-of-payment transit systems, where the transit operator chooses a collection of patrol paths (one for each patrol) every day with some probability in order to avoid any regularity that could be exploited by opportunistic passengers. We use a Stackelberg game approach to represent the hierarchical decision-making process between the transit operator and opportunistic passengers, whose decision on whether to evade the fare depends on the inspection probabilities set by the transit operator. Unlike previous work, we use an exact formulation of the inspection probabilities that allows us to develop new heuristics for the fare inspection scheduling problem, and to assess their solution quality in terms of their optimality gap. • Unpredictable fare inspections in transit systems using a Stackelberg game approach. • Exact formulation of the inspection probabilities. • New heuristics for the fare inspection scheduling problem. • Computational experiments on a full-size transport line. • Computational results show good quality solutions in terms of the optimality gap. [ABSTRACT FROM AUTHOR]

Despite recycling being perceived as essential for sustainable development in the electronics industry, two critical issues have yet to be thoroughly investigated: the role of government intervention and contract design on improving recycling intentions of manufactures. This study employs game-theoretic models to examine the impact of government intervention and various contractual arrangements on the strategic decision-making of electronics manufacturers regarding recycling. Our findings reveal that: 1) the manufacturers' recycling intentions increase when tax rate is within certain range, as their recycling effort, under such a circumstance, contributes to improvements in their profitability; 2) when collaborating with a third-party collector (3 PR), the 3 PR may exhibit passive resistance by reducing recycling efforts upon detecting manufacturers' insufficient incentives for recycling. Intriguingly, the 3 PR will increase the price offered to consumers for recycled materials in order to stimulate greater quantities of recycling; (3) the different designs of recycling contracts can incentivize manufacturers to engage in recycling activities in various ways. Overall, the findings presented herein provide new insights into examining the incentive mechanisms of manufacturers' recycling intentions and identifying potential challenges and opportunities for policy implementation. This study also offers managerial implications for decision-makers to enhance the efficiency of their recycling efforts and contribute to a more sustainable production system. • Manufacturers are reluctant to engage in recycling without strong motivation. • Government intervention and contractual arrangements affect manufacturer's behavior. • Game-theoretic models to analyze recycling intention and recycling strategies. • 3 PR reduces recycling effort responding to low manufacturers' recycling intention. • Findings offer practical implications for building a sustainable production system. [ABSTRACT FROM AUTHOR]

Under the background of sustainable development, the microgrid (MG) has become an important method for energy saving, emission reduction and meeting multiple energy demand. With the continuous promotion of China's carbon emission right market and green certificate market, to further promote the low-carbon development of MG, a multi-level trading optimization strategy is proposed for multi-microgrids (MMG) that considers the coupling of energy-certificate-carbon market. First, a MMG trading framework including a two-level certification-carbon and a three-level electric-thermal coupled trading is proposed. Second, based on the game theory pricing strategy and the elastic price mechanism of the supply-demand ratio, the MMG operation optimization strategy model is constructed considering multi-level energy-certification-carbon coupled trading. Finally, based on the principle of fair benefit allocation, the Shapley value method is utilized to redistribute the comprehensive income among the alliance members. The simulation results show that compared with the MMG baseline scenario, the overall economic efficiency of the proposed trading model is improved by 3.94 % and the carbon emissions are reduced by 11.71 %. In this way, it can effectively release the potential of MMG resource sharing and mutual benefit, so as to optimise the trade-off strategy for joint participation in the energy-certificate-carbon market. [ABSTRACT FROM AUTHOR]

Virtual power plants (VPPs) has been considered as an effective approach to manage internal prosumers participating in market transactions with a jointly clearing of energy markets (EM), reserve ancillary services markets (ASM), and carbon trading markets (CTM). Thus, how to address the problem of energy management for VPP in coupling multiple market trading mechanisms has determined as a technical point. In this paper, a bi-level Stackelberg game pricing strategy for VPP trading on multi-market is devised to incentivize its internal units, especially focusing on electric vehicles (EVs), through distinct price signals. An accurate dispatchable power model for EVs is established based on travel patterns and responsiveness. With the goal of maximizing profits, VPP determines trading prices for heterogeneous prosumers, while prosumers respond consistently with price signals to minimize respective operating costs. The hierarchical model is converted to a unified mixed-integer linear programming problem via duality theory. To overcome the uncertainty of renewable energy during solving, a stochastic programming approach with Conditional-Value-at-Risk (CVaR) is employed to estimate the expected losses. Adopting the proposed pricing method in VPPs increases expected profit by 5.51%, purchase prices being 2.08% higher and selling prices 4.85% lower than unified pricing, benefiting both producers and consumers. • Responsiveness-based available capacity calculation model of aggregated EVs. • A bi-level pricing strategy framework of VPP under trading in multi-market. • The method for acquiring carbon emission quotas for EVs. • A stochastic programming approach with CVaR to describe expected losses. [ABSTRACT FROM AUTHOR]

With the rise of the energy Internet and the reform of the power market, the multi-energy collaborative trading mode plays a fundamental role and acts as the framework in the construction of the integrated energy market. An integrated energy system model and its trading market mechanism are built in this paper. A new transaction strategy in the system is proposed to solve the problem of cascade utilization of thermal energy and flexibility of future market relationships. To facilitate the role transformation of stakeholders, the multiple agents system is used to decouple the complex relationship of the market transaction into two Stackelberg games of "two leaders and one follower". In addition, The Lagrange multiplier method is used to optimize the objective function and the optimal result is obtained by continuous iteration, and the existence and uniqueness of Nash equilibrium are verified. Eventually, The simulation results validate that the model has greater benefits for all stakeholders, new energy consumption and environmental protection. • The trading strategy proposed solves the flexible trading of multiple energies. • Decoupling the multi-energy market transaction into two Stackelberg games models. • The existence and uniqueness of Nash equilibrium in transaction model are verified. [ABSTRACT FROM AUTHOR]

Integrated energy systems within communities play a pivotal role in addressing the diverse energy requirements of the system, emerging as a central focus in contemporary research. This paper contributes to exploring optimal scheduling in a smart community featuring multiple smart buildings equipped with a substantial share of distributed photovoltaic sources, shared energy storage, and controllable loads. The study formulates a two-stage scheduling optimization model incorporating multiple stakeholders, explicitly examining the game dynamics between the smart community operator and the customer load aggregator. The weights assigned to each optimization objective are determined using an analytic hierarchy process-entropy weight method to establish a balanced and nuanced approach. The ensuing optimal scheduling encompasses unit output and energy trading considerations, focusing on enhancing the system's economic viability, safety measures, and environmental sustainability. A comprehensive evaluation is conducted to validate the proposed model by comparing its performance with alternative operational strategies. The results show that the designed strategy can reduce the operating cost by 40.22% and increase the level of PV consumption by 22.57% compared to the traditional heat-based strategy, which is effective in mitigating power fluctuations, smartly responding to dispatch peak demand, enhancing new energy integration, and ensuring the security of grid operation. • Energy optimization dispatch model considering demand side response. • Shared energy storage in smart communities. • Multi-subject game to maximize benefits. • Reduce energy costs and improve operational safety. • Ensure photovoltaic output and realize thermoelectric decoupling. [ABSTRACT FROM AUTHOR]

Virtual Energy Stations (VESs) can aggregate customer-side Integrated Energy Systems (IESs) to participate in electricity and natural gas markets. It helps to promote the synergies among different energies, lower IESs' energy cost, and balance the supply and demand of power systems. This paper proposes an exergy-driven optimal scheduling method of VES based on coordinated cooperative and Stackelberg games to regulate IESs via demand response (DR) effectively and economically. Firstly, the VES operation framework with equal exergy replacement is developed to unify the energy adjustment and conversion of IESs for less energy cost and lower economic loss risk. Secondly, the scheduling models of VES and IESs based on Cooperative and Stackelberg Games are proposed. VES forms a cooperative alliance with IESs to respond to external energy markets' price fluctuations for overall benefit maximization. Then the Stackelberg game theory is employed to characterize the interest-conflict behaviors of VES and IESs. It can maximize the overall interests of VES and IES, achieve more flexibility from IESs, and improve IESs' enthusiasm in DR. Thirdly, the equilibrium solution existence of the VES optimal scheduling model based on game theories is proved. A distributed solution method based on the Alternating Direction Method of Multipliers (ADMM) algorithm is provided to avoid the privacy information leakage of VES and IESs. Simulation results show that VES takes the main risks caused by the energy market prices' fluctuations, which helps to increase the enthusiasm of IESs in DR. And the proposed incentive mechanism has superior properties compared to the sole cooperative game or Stackelberg game. • A exergy-driven VES operation framework is proposed to regulate IESs effectively and economically. • Cooperative game and Stackelberg game is coordinated to tackle the problem of the benefit allocation among different entities. • A distributed solution method based on ADMM algorithm is proposed to solve the VES optimization model in a distributed way. [ABSTRACT FROM AUTHOR]

Hydrogen is called to play a vital role in the decarbonization of the energy sector. Its importance is notable for industries, where it finds multiple applications, but also for electricity generation through fuel-cells. Due to the existence of mature conversion technologies, the electricity‑hydrogen nexus is expected to be frequently present in the future for multiple applications. In this sense, it is very important to develop computational tools that consider both energy vectors and their links. Following this idea, this paper develops a local electricity‑hydrogen market model for industrial parks. The new model is suitable for systems with a notable presence of hydrogen consumers and on-site hydrogen generation through water electrolysis. The proposed market framework is capable to jointly reveal local electricity and hydrogen prices without ignoring the strong physical and financial interactions between systems. The mathematical notation arises from Stackelberg-based models for the electricity and hydrogen pricing sub-problems, which are solved iteratively until reaching convergence, thus resulting in a holistic optimization framework solvable by average machines. A case study is presented with results, which serve to validate the new tool as well as analyse several important aspects such as the role of fuel-cells or local renewable generation. Moreover, the results obtained allows us to show how both sub-systems are capable to cooperate seeking the collective welfare, thus augmenting the possibilities and flexibility of the whole system. • A novel local electricity model for industrial parks is developed. • The different agents involved are properly modelled. • Electricity and hydrogen prices can be calculated. • Electricity and hydrogen systems can cooperate seeking collective welfare. • The presence of photovoltaics or fuel-cells may notably impact on results. [ABSTRACT FROM AUTHOR]

Large-scale congestion can lead to traffic paralysis, which severely hampers the flow of vehicles and disrupts the normal functioning of urban traffic. Traffic optimization strategies can effectively improve the performance of road networks, but often ignore the impact of regional traffic conditions and equity. This paper presents a novel traffic strategy to solve regional traffic congestion in large cities, particularly focusing on mixed traffic scenarios of connected and non-connected vehicles. The proposed method involves monitoring the traffic condition of the congestion warning community and adjusting the internal access flow within each region. The problem is formulated as a Stackelberg game, with traffic policymakers and road users as the key players. The upper layer aims to control traffic access by issuing a community warning index, with the objective of minimizing congestion warning conditions within the community. This information is then disseminated to connected vehicles which utilize it to generate personalized route guidance, while non-connected vehicles remain unaffected. The lower-level objective is to allocate vehicles in the transportation network in a user-optimal manner. To solve the bi-level programming model, the paper introduces a variable neighborhood search approach based on graph theory. The Frank-Wolfe algorithm is used to solve the lower-level model, with a penalty function introduced to transform the constrained traffic assignment problem (TAP) into an unconstrained TAP. The proposed method is applied using the data of Beijing urban road network and a sensitivity analysis is conducted to examine the impacts of critical parameters, such as regional partitioning and mixed traffic proportion. The results show that the method exhibits improved optimization performance across different parameter settings, effectively utilizing idle links and contributing to a reduction in the occurrence of traffic warning regions. • The regional control strategy prevents the emergence of warning communities. • A bi-level model is developed to solve the traffic diversion of mixed traffic. • A variable neighborhood search algorithm is designed to solve the model. • The control strategies under different critical variables scenarios are analyzed. [ABSTRACT FROM AUTHOR]

The Internet of Underwater Things (IoUT), which connects underwater devices, such as sensor clusters and Autonomous Underwater Vehicles (AUVs) to monitor the underwater environment, is an important component of ocean activities. Due to the limited computing resources of Cluster Heads (CHs) of sensor clusters, AUVs can provide additional computing power for CHs. In this paper, an AUV-aided offloading framework is proposed for multi-tier underwater computing, where the Edge Intelligence Service Platform (EISP) manages computing resources. The EISP provides computation services for CHs through multiple AUVs, buoys, and a Low Earth Orbit (LEO) satellite at a certain price. Afterwards, we formulate the game process between CHs and the EISP as a Stackelberg game. Considering the impact of communication energy consumption and communication delay in the process of task offloading, we establish the optimization models of EISP and CHs. Then, the backward induction method is applied to prove that the proposed game has a unique Stackelberg Equilibrium (SE). Furthermore, a Game Solving Algorithm based on Improved Differential Evolution (GSA_IDE) is designed to achieve SE in the proposed game. Finally, the simulation results show that the proposed GSA_IDE can achieve SE and outperform other algorithms. • To satisfy the requirements of IoUT, an AUV-aided offloading framework is proposed. • The Stackelberg Equilibrium of the proposed game has been proved. • The proposed algorithm can achieve Stackelberg equilibrium. • Cluster Heads of IoUT have multiple ways to offload tasks. [ABSTRACT FROM AUTHOR]