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To enhance the interests of all stakeholders in the multi-microgrid integrated energy system and to promote photovoltaic consumption, this paper proposes a master–slave game operation optimization strategy for a multi-microgrid system considering photovoltaic consumption and integrated demand response. Initially, an energy interaction model was established to delineate the relationships between each microgrid and the distribution network, as well as the interactions among the microgrids. Additionally, an integrated demand response model for end-users was developed. This framework leads to the formulation of a one-leader multi-follower interaction equilibrium model, wherein the multi-microgrid system acts as the leader and the users of the multi-microgrid serve as followers. It is proven that a unique equilibrium solution for the Stackelberg game exists. The upper level iteratively optimizes variables such as energy-selling prices, equipment output, and energy interactions among microgrids, subsequently announcing the energy-selling prices to the lower level. The lower level is responsible for optimizing energy load and returning the actual load demand to the upper level. Finally, the rationality and effectiveness of the proposed strategy are demonstrated through the case analysis. Thus, the profitability of the multi-microgrid system is enhanced, along with the overall benefits for each microgrid user, and the amount of photovoltaic curtailment is significantly reduced. [ABSTRACT FROM AUTHOR]

The distributed generation of new energy can effectively use the local endemic clean new energy and provide green power. However, due to the small scale and scattered layout of distributed generation resources, it is difficult to participate in the economic dispatch of power systems and even the competition of the power market. Virtual Power Plant (VPP) can act as a carrier of Distributed Energy Resource (DER) to manage its internal energy, to carry out combined bidding in the day‐ahead energy market and the regulation market. When virtual power plants coordinate multiple distributed energy resources to participate in electricity market transactions, the degree of disclosure of their internal privacy information will produce different trading strategies. A Stackelberg game model between multiple virtual power plant aggregators and virtual power plant operators is constructed, and the Kriging model is combined to protect the privacy information in the transactions of virtual power plant operators. Energy management for distributed generation is carried out, and the profit situation of virtual power plant operators under different strategies is analyzed. [ABSTRACT FROM AUTHOR]

In view of the uncertainty regarding consumers' perceived value of remanufactured products, a remanufacturing supply chain system with the manufacturer as the Stackelberg leader is constructed, in which the manufacturer faces three modes, namely the manufacturer recycling mode (M), the retailer recycling mode (R), and the entrusted third-party recycling mode (3P). The remanufacturing supply chain is analyzed using the game theory approach in these three recycling modes. Using game theory to analyze the optimal pricing and profits of each supply chain participant, we also discuss the impact of consumers' perceived value uncertainty on the profits of each party under the different recycling modes, and we then explore the selection of recycling channels in the remanufacturing supply chain. The results show that when the perceived value uncertainty is at a medium or low level, retailers are responsible for recycling used products and producing remanufactured products, which brings higher profits to the supply chain system; when the perceived value uncertainty is high, the demand for remanufactured products in the market decreases, and the recycling revenue of remanufactured products is lower. Finally, the validity of the theoretical model is verified by a numerical simulation. [ABSTRACT FROM AUTHOR]

Purpose: Although 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/approach: Using 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. Findings: The 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. [ABSTRACT FROM AUTHOR]

We study a reinsurer who faces multiple sources of model uncertainty. The reinsurer offers contracts to n insurers whose claims follow compound Poisson processes representing both idiosyncratic and systemic sources of loss. As the reinsurer is uncertain about the insurers' claim severity distributions and frequencies, they design reinsurance contracts that maximise their expected wealth subject to an entropy penalty. Insurers meanwhile seek to maximise their expected utility without ambiguity. We solve this continuous-time Stackelberg game for general reinsurance contracts and find that the reinsurer prices under a distortion of the barycentre of the insurers' models. We apply our results to proportional reinsurance and excess-of-loss reinsurance contracts, and illustrate the solutions numerically. Furthermore, we solve the related problem where the reinsurer maximises, still under ambiguity, their expected utility and compare the solutions. [ABSTRACT FROM AUTHOR]

With the prevalence of green supply chains, the government has basic requirements for companies' green investments and outcomes while consumers increasingly favor green products. Thus, green degree decision has garnered significant attention from manufacturers. This paper incorporates green degree decisions into a dual-channel supply chain and adopts a Stackelberg model to analyze the green degree and pricing strategies under centralized and decentralized decisions. We find that, when the manufacturer only decides on price, dual-channel choice is always the optimal strategy under centralized decision-making; however, under decentralized decision-making, the dual-channel choice will be chosen only when the wholesale price is low. Considering green degree decision, both direct and indirect channel prices increase with the green degree, and the indirect channel price is more sensitive to changes in the green degree under centralized decision-making; and higher green degrees are always advantageous for the retailer, but the manufacturer's profit initially decreases and then increases as the green degree rises under decentralized decision-making. Moreover, the wholesale price is used as a strategic tool for the manufacturer to control the distribution channel, particularly when the green degree is not introduced, the manufacturer can always ensure the introduction of dual channels. Besides, higher consumers' environmental awareness is always beneficial to channel members, as it promotes channel prices and green degree. This study provides strategic insights for optimizing pricing and green degree decisions in dual-channel supply chains to achieve better economic and environmental outcomes. [ABSTRACT FROM AUTHOR]

In the era of big data, breaking down data silos to enable efficient data transactions has become essential, with the fairness and transparency of pricing mechanisms being paramount. This study addresses these challenges by introducing a novel tripartite pricing model for customized data products that integrates the Stackelberg and bargaining game frameworks. By designing distinct utility functions for buyers, sellers, and the platform, the model effectively aligns the varying objectives of each participant. A dynamic adjustment mechanism further enhances this model by adaptively recalibrating the guidance price and pricing range based on real-time updates to buyer budgets and seller offers, thus ensuring fairness and responsiveness throughout the negotiation process. Experimental simulations comprising 100 transaction rounds across diverse buyer–seller profiles validate the model's effectiveness, achieving a transaction success rate of 92.70% with an average of 6.86 bargaining rounds. These findings underscore the model's capacity to optimize transaction outcomes, promote pricing equity, and enhance bargaining efficiency. The proposed model has broad applications in sectors such as finance, healthcare, and e-commerce, where precise data pricing mechanisms are essential to maximize transactional value. [ABSTRACT FROM AUTHOR]

The growing importance of critical infrastructure systems (CIS) makes maintaining their normal operation against deliberate attacks such as terrorism a significant challenge. Combining game theory and complex network theory provides a framework for analyzing CIS robustness in adversarial scenarios. Most existing studies focus on single-layer networks, while CIS are better modeled as multilayer networks. Research on multilayer network games is limited, lacking methods for constructing incomplete information through link hiding and neglecting the impact of cascading failures. We propose a multilayer network Stackelberg game model with incomplete information considering cascading failures (MSGM-IICF). First, we describe the multilayer network model and define the multilayer node-weighted degree. Then, we present link hiding rules and a cascading failure model. Finally, we construct MSGM-IICF, providing methods for calculating payoff functions from the different perspectives of attackers and defenders. Experiments on synthetic and real-world networks demonstrate that link hiding improves network robustness without considering cascading failures. However, when cascading failures are considered, they become the primary factor determining network robustness. Dynamic capacity allocation enhances network robustness, while changes in dynamic costs make the network more vulnerable. The proposed method provides a new way of analyzing the robustness of diverse CIS, supporting resilient CIS design. [ABSTRACT FROM AUTHOR]

The importance of curbside management is quickly growing in a modernized urban setting. Dynamic allocation of curb space to different usages and dynamic pricing for those usages can help meet the growing demand for curb space more effectively and promote user turnover. To model curbside operations, we formulate a Stackelberg leader-follower game between a leader operating curbside spaces, who sets space allocation and pricing of each curbside usage, and multi-followers, one for each type of curbside usage, who accept the proposed prices or reject them in favor of outside options. The proposed model offers flexible adaptability to manage curb space usages characterized by high turnover rates, such as parking and ride-sourcing pickup and drop-off, alongside accommodating usages that require more permanent infrastructure allocation, such as micromobility stations. Furthermore, the proposed model is able to capture the sensitivity of users to both prices, which are determined solely by the operator, and the occupancy levels of the curb space, which are determined by the complex interactions between the curbside operator and the users. We model a Stackelberg leader-follower game as a bilevel nonlinear optimization problem and reconstruct the problem into a single-level convex program by applying the Karush-Kuhn-Tucker conditions, objective function transformation, and constraint linearization. Then, we develop a solution algorithm that leverages valid inequalities produced via Benders decomposition. We validate the practicability of the model and draw insights into curbside management using numerical experiments. History: This paper has been accepted for the Transportation Sci. Special Issue on the ISTTT25 Conference. Funding: This work was supported by the National Science Foundation, Division of Civil, Mechanical and Manufacturing Innovation [Grant 2046372]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0507. [ABSTRACT FROM AUTHOR]

With the rapid development and growing popularity of Internet of Things (IoT), edge-assisted crowdsensing has emerged as a new mode of data collection and data processing. In an edge-assisted crowdsensing system, a reasonable data task allocation and pricing mechanism is urgently required to promote the active participation of each part of the system. However, existing mechanisms either did not consider the impact of data quality on participant profits or ignored some parts of the whole system. We therefore propose a novel task allocation and pricing mechanism based on the Stackelberg game model, considering all four parties (data requesters, crowdsensing platform, edge servers and IoT sensors) in an edge-assisted crowdsensing system. Specifically, we decompose the problem into three game sub-problems, and design our mechanism using KKT conditional approaches, with the aim of maximising the benefits of each party in the crowdsensing system. We demonstrate mathematically that the Stackelberg equilibrium can be achieved in all three games, and validate its performance through simulation experiments. [ABSTRACT FROM AUTHOR]

We consider a supplier selling substituted products to an e‐retailer through wholesale selling mode or mixed use of wholesale and agency selling mode (hybrid contracts). This paper explains the curious failure of the agency model and investigates the contract selection problem. We build the stylized models that consider consumer formats preferences and distribution sequence. We find that an excessively high agency fee can lead to failure but this is on the condition of substituted products simultaneously distributed. However, we find no failure phenomenon in sequential distribution scenarios. Because it is optimal to mark down the price of the delayed product that prevents inefficiency with a lower price in the agency model than in the wholesale model. Furthermore, in the e‐books industry, when consumers prefer digital (traditional) formats, the equilibrium strategy is that the e‐retailer claims a low agency fee, and the supplier chooses simultaneous (sequential) distribution through hybrid contracts. Besides, the equilibrium is robust. [ABSTRACT FROM AUTHOR]

With the rapid growth of the electric vehicle industry, the recycling of power batteries has attracted significant attention. In light of current circumstances, the question of how the government can incentivize relevant stakeholders to actively engage in recycling and improve its efficiency has become increasingly pressing. In this context, this study analyses and develops four closed-loop supply chain recycling models to investigate how different government subsidy recipients under varying power structures influence recycling efficiency, profitability, and the overall supply chain structures. The following conclusions are derived from numerical simulations: (1) Government subsidies serve to elevate recycling prices, expand profit margins, and consequently boost the volume of recycled batteries, thus incentivizing corporate engagement in recycling initiatives. (2) When the processor assumes the role of the leader in the Stackelberg game framework, it can maximize the overall efficiency and profitability of the supply chain. (3) The sensitivity coefficient and the competition coefficient are closely interrelated, exerting opposing impacts on the recycling decision made by enterprises. (4) The supply chain leader plays a crucial role in ensuring orderly supply chain development, with government subsidies of the supply chain being transmitted to its members through the leader. Consequently, this study offers a theoretical foundation for the government to enhance policy-making and for enterprises to make informed decisions. It also holds significant practical relevance in addressing the challenges associated with power battery recycling. [ABSTRACT FROM AUTHOR]

Celebrities can significantly influence the public towards any desired outcome. In a bid to tackle an infectious disease, a leader (government) exploits such influence towards motivating a fraction of public to get vaccinated, sufficient enough to ensure eradication. The leader also aims to minimize the vaccinated fraction of public (that ensures eradication) and use minimal incentives to motivate the influencers; it also controls vaccine supply rates. Towards this, we consider a three-layered Stackelberg game, with the leader at the top. A set of influencers at the middle layer are involved in a stochastic vaccination game driven by incentives. The public at the bottom layer is involved in an evolutionary game with respect to vaccine responses. We prove the disease can always be eradicated once the public is sufficiently sensitive towards the vaccination choices of the influencers—with a minimal fraction of public vaccinated. This minimal fraction depends only on the disease characteristics and not on other aspects. Interestingly, there are many configurations to achieve eradication, each configuration is specified by a dynamic vaccine supply rate and a number—this number represents the count of the influencers that needs to be vaccinated to achieve the desired influence. Incentive schemes are optimal when this number equals all or just one; the former curbs free-riding among influencers, while the latter minimizes the dependency on influencers. [ABSTRACT FROM AUTHOR]

Purpose: This paper investigates the dual interactive effects of manufacturer encroachment on the supply chain and retailer provision of retail services. Design/methodology/approach: Consider a supply chain dominated by manufacturers, retailers, and e-commerce platforms, with the manufacturers selling the same product online and offline. Utilizing Stackelberg's game theory, examples of wholesale and retail prices and profits of participants in the supply chain under different channels are analyzed. An effective encroachment strategy for manufacturers facing different retail service investment strategies of traditional retailers is given. Findings: When traditional retailers do not invest in retail services, they will lose more profit due to competition with the manufacturer. At this time, the retailer does not want the manufacturer to encroach. The traditional retailer's investment in retail services will enhance its and the manufacturer's profits, incentivizing the manufacturer to pursue an aggressive expansion strategy. Originality/value: (1) Considers a situation where the selling efficiency of the manufacturer is lower than that of the traditional retailer. (2) The interaction between traditional retailers' retail service investment strategies and manufacturers' encroachment strategies is investigated where the manufacturer is the dominant player. The three modes of online direct sales, resale, and third-party platform agency are compared to provide a basis for decision-making on different types of manufacturers' encroachment. (3) Offline retail services not only directly increase sales in the offline market but also indirectly have a negative effect on the online market. [ABSTRACT FROM AUTHOR]

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

Commercial buildings have abundant flexible energy resources for demand response (DR). The electricity price for tenants in the commercial building is generally issued by a subcontracting power supplier (SPS), and the tenants cannot directly interact with the energy retailer. Therefore, the incentive for tenants to participate in DR is insufficient, and their potential is not fully explored. To address these issues, this paper proposes a dynamic pricing method based on the Stackelberg game, helping tenants actively participate in DR. Then, with the optimized energy consumption of the tenants, a virtual energy storage model of the commercial building is constructed by aggregating the adjustable capabilities of flexible energy resources such as air-conditioning (AC) and electric vehicles (EVs) in the public area. Finally, simulation tests are conducted based on a real commercial building to demonstrate the effectiveness of the game-theoretic pricing approach and validate the role of virtual energy storage of the building in DR. [ABSTRACT FROM AUTHOR]

Accepted by: Giorgio Consigli In this article, we consider a reinsurance contract design by taking into account the joint interests of multiple insurers and a reinsurer. The reinsurance contract consists of optimal reinsurance strategies and reinsurance prices. The former are chosen by the competitive–cooperative insurers and the latter are determined by a reinsurer. Both insurers and the reinsurer can invest in the common risk-free asset and one different risky asset. The optimal time-consistent reinsurance–investment strategies of the insurers and the optimal reinsurance prices and investment strategy of the reinsurer are derived analytically. Numerical experiments are carried out to illustrate the influences of model parameters on the optimal reinsurance contract and optimal investment strategies. We find that the establishment of the reinsurance contract is affected by the correlation between the claim sizes of insurers as well as that of claim numbers. The results reveal that competition and cooperation will lead to a decrease and increase of the reinsurance price, respectively, showing the importance of opting for cooperation among insurers. Both competition and cooperation are beneficial to insurers, especially for those with high risk aversion. [ABSTRACT FROM AUTHOR]

Researchers have become interested in security games in recent decades as a result of its successful application in real-world security issues. The security model is based on the Stackelberg Security Game (SSG), in which defenders (leaders) select a defensive strategy based on the optimal reaction of attackers (followers), who, at equilibrium, select the predicted assaulting strategy as a response. These applications, on the other hand, do not account for the time constraints posed by the game's players' journey time. Furthermore, players should be able to cope with dynamic settings in which their knowledge of the environment changes on a regular basis, allowing them to perform more effectively. This research proposes a security model based on a continuous-time Reinforcement Learning (RL) approach implemented using a temporal difference method that takes prior information into account to address these issues. We use a controlled, ergodic continuous-time Markov game to model the SSG. The game framework model assumes that all information is available. We calculate the number of transitions over a time interval divided by the entire value of the holding time to estimate the transition rates. The arithmetic mean of the observed cost of the individual players is used to estimate the cost for defenders and attackers. An iterated proximal/gradient approach is used to calculate the SSG equilibrium point. We offer a continuous-time random walk method for game implementation. In a numerical case relevant to rain-forest hazards, we analyze the performance of the suggested RL security solution and discuss the problems that should be considered in future. [ABSTRACT FROM AUTHOR]

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 essence of credit guarantee financing (CGF) is the risk sharing between the guarantor and financial institution. Inspired by the case of the CGF of Evergrowing Bank, this study aims to explore the risk compensation strategies and guarantee decisions for guarantors under CGF and provide decision support for the efficient operation of the supply chain CGF. Considering three kinds of risk compensation contracts, namely cost-sharing, revenue-sharing, and quantity-flexibility, the Stackelberg game method is used to construct the supplier CGF model under the retailer's financial constraints. The results show that additional contract parameters, interest rate, debtor's initial capital, and implicit bankruptcy cost are the main factors affecting the credit guarantee coefficient decision. Besides, we find optimal additional contract parameters that can optimize the profits of supply chain members and complete the contract parameter design. The quantity-flexibility contract is the most effective strategy for the supplier to compensate for guarantee risk. However, the retailer's choice of additional contract depends on the initial capital or implicit bankruptcy cost. The main innovation of this study is that it endogenizes the credit guarantee decision and explores the details of the risk compensation contract. Further, the impact of implicit bankruptcy cost on CGF decision is also mentioned for the first time in supply chain finance. Our findings lead to recommendations for the optimal credit guarantee scheme and contract design of compensation for guarantee risk in the supply chain. [ABSTRACT FROM AUTHOR]

This article introduces a class of Nash games among Stackelberg players (NASPs), namely, a class of simultaneous noncooperative games where the players solve sequential Stackelberg games. Specifically, each player solves a Stackelberg game where a leader optimizes a (parametrized) linear objective function subject to linear constraints, whereas its followers solve convex quadratic problems subject to the standard optimistic assumption. Although we prove that deciding if a NASP instance admits a Nash equilibrium is generally a Σ2p -hard decision problem, we devise two exact and computationally efficient algorithms to compute and select Nash equilibria or certify that no equilibrium exists. We use NASPs to model the hierarchical interactions of international energy markets where climate change aware regulators oversee the operations of profit-driven energy producers. By combining real-world data with our models, we find that Nash equilibria provide informative, and often counterintuitive, managerial insights for market regulators. This paper was accepted by Chung Piaw Teo, optimization. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.03418. [ABSTRACT FROM AUTHOR]

The integration of photovoltaic, energy storage, direct current, and flexible load (PEDF) technologies in building power systems is an important means to address the energy crisis and promote the development of green buildings. The friendly interaction between the PEDF systems and the power grid can promote the utilization of renewable energy and enhance the stability of the power grid. For this purpose, this work introduces a framework of multiple incentive mechanisms for a PEDF park, a building energy system that implements PEDF technologies. The incentive mechanisms proposed in this paper include both economic and noneconomic aspects, which is the most significant innovation of this paper. By modeling the relationship between a PEDF park and the power grid into a Stackelberg game, we demonstrate the effectiveness of these incentive measures in promoting the friendly interaction between the two entities. In this game model, the power grid determines on the prices of electricity trading and incentive subsidy, aiming to maximize its revenue while reducing the peak load of the PEDF park. On the other hand, the PEDF park make its dispatch plan according to the prices established by the grid, in order to reduce electricity consumption expense, improve electricity utility, and enhance the penetration rate of renewable energy. The results show that the proposed incentive mechanisms for the PEDF park can help to optimize energy consumption and promote sustainable energy practices. [ABSTRACT FROM AUTHOR]

Abstract To solve the optimization problem of tugboat scheduling for assisting ships in entering and exiting ports in uncertain environments, this study investigates the impact of the decisions of tugboat operators and port dispatchers on tugboat scheduling under the scenario of dynamic task arrival and fuzzy tugboat operation time. Considering the features of the shortest distance tugboat principle, the first available tugboat principle, and the principle of fairness in the task volume of each tugboat, the tugboat company aims to minimize the total daily fuel consumption of tugboat operations, maximize the total buffer time of dynamic tasks, and minimize the total completion time as the objective functions. Due to the limitations of port vessel berthing and departure, as well as the allocation standards for piloting or relocating tugboats, the present study proposes a Stackelberg game-based fuzzy model for port tugboat scheduling with the tugboat operator and port dispatcher acting as decision makers at the upper and lower levels, respectively. A seagull optimization algorithm based on priority encoding and genetic operators is designed as a solution approach. CPLEX, genetic algorithm, standard seagull optimization algorithm, and simulated annealing algorithm are used to compare and analyze the solution results for the 45 problem cases generated from the actual data obtained from the Guangzhou Port. The results verify the efficiency of the proposed seagull optimization algorithm based on priority encoding and genetic operators. Furthermore, additional experiments are conducted to evaluate the changes in fairness coefficient, uncertain parameter correlation coefficients, and objective function correlation coefficients to demonstrate the practicality of the fuzzy programming model. This analysis involves adjusting the confidence level incrementally from 0 to 100% with respect to the model’s uncertain parameters.

Abstract In order to solve the influence of the complex interaction relationships among subjects on the system solution accuracy and speed of the Multi-Microgrid system under the high penetration rate of new energy. Firstly, the paper establishes the bi-level optimal scheduling Stackelberg game model based on shared energy storage, considering the inter-subject interaction in MMG. Subsequently, based on the four improvement methods of Chaotic Map, Quantum Behavior, Gaussian Distribution, and Nonlinear Control Strategy, the Chaotic Gaussian Quantum Crayfish Optimization Algorithm is proposed to solve the optimization scheduling model. The improved algorithm exhibits superior initial solutions and enhanced search capability. In comparison to the original algorithm, the relative errors of the CGQCOA optimization outcomes are 98%, 20.96%, 98.74% and 16.55%, respectively, enhancing the model-solving accuracy and the speed of convergence to the optimal solution. Finally, the simulation demonstrates that the revenue of Microgrid 1, Microgrid 2, and Microgrid 3 have increased by 0.73%, 1.17%, and 1.04%, respectively. Concurrently, the penalty cost of pollutant emission has decreased by 5.9%, 11.5%, and 12.68%, respectively. Furthermore, the revenue of the shared storage have increased by 1.91%. These findings validate the efficacy of the methodology proposed in enhancing the revenue of the various subjects and reducing pollutant gas emission.

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.

Extended warranties are widely adopted and accepted in the marketplace by manufacturers and retailers as it helps to enhance the customers' post-sale satisfaction. In closed-loop supply chains, the extended warranty not only generates profit for the manufacturer, but also provides warranty returns of the new products for remanufacturing. In this paper, a two-period model is developed and optimal pricing strategies for the extended warranties are derived. We compare the optimal pricing and retailing strategies of the extended warranties for remanufactured and new products offered by the manufacturer with and without the retailer's own extended warranty while considering the competition between the manufacturer and the retailer for the extended warranty of new products. We find that the introduction of the retailer's extended warranty does not always hurt the manufacturer's profit. Numerical analyses also show that there exists an optimal extended warranty length for the manufacturer that maximises its profit. Moreover, we show that the retailer cannot extract more profit by increasing the length of its own extended warranty. [ABSTRACT FROM AUTHOR]

Abstract The proposed study introduces a novel anti-jamming approach for cognitive radio networks (CRNs) by integrating the Stackelberg game model with direct sequence spread spectrum (DSSS) techniques. This innovative combination enhances the security and performance of CRNs by optimizing resource allocation and fortifying network resilience against jamming attacks. The Stackelberg game model provides a strategic framework where the Defender and Adversary dynamically adjust their strategies to achieve Nash equilibrium, ensuring strategic stability. The application of DSSS further improves signal robustness, mitigating interference from jamming attempts. Simulation results demonstrate significant improvements in network security, resource utilization, and overall performance, validating the efficacy and advantages of the proposed scheme in maintaining reliable communication in the presence of adversarial threats.

In the context of dual carbon goals， this paper proposes a multi-energy pricing and dispatch optimization strategy for integrated electricity-heat energy systems in an industrial park， based on the Stackelberg game to address low-carbon scheduling issues. Firstly， the paper introduces the transaction model between the park operator and the users. Secondly， a Stackelberg game model is developed， with the park operator acting as the leader and the user loads within the park acting as followers. The park operator model incorporates a tiered carbon trading mechanism， while the user load model considers the users’ electricity and heat demand response. Finally， the beetle antennae search-improved particle swarm optimization （BAS-PSO） algorithm and the CPLEX solver are utilized to determine the park operator’s pricing strategy and the users’ energy consumption strategies. Simulation results demonstrate that the proposed optimization strategy effectively balances the interests of all parties， resulting in a reduction in the peak-to-valley difference of user loads and a decrease in carbon emissions.

A virtual power plant (VPP) is proposed to aggregate various resources to participate as a whole in both electricity and carbon trading markets. As the scale of VPPs continues to expand, they are transitioning from being price takers to price makers. To this end, this paper treats the VPP as a price maker and proposes a bi-level bidding strategy in the day-ahead electricity market, considering the impact of carbon trading. Firstly, an introduction and analysis of the day-ahead electricity market mechanism, considering carbon trading, are provided. Secondly, based on the Stackelberg game theory, a bi-level bidding model in the day-ahead electricity market is established with the VPP as the bidding entity. The upper-level model aims to maximize the anticipated profit of the VPP, while the lower-level model aims to minimize the system's clearing cost. Considering the uncertainty in wind farm output predictions within the VPP, operators are provided with two bidding strategies: risk-averse and opportunity seeker strategies based on the information gap decision theory (IGDT). Then, utilizing the strong duality theory, the Karush-Kuhn-Tucker (KKT) optimality conditions, and the big-M method, the bi-level model is simplified into a mixed-integer linear programming problem for resolution. Finally, an example is provided to illustrate the optimal bidding strategy and operation plan for the VPP, along with an analysis of how uncertainty in wind farm output predictions within the VPP affects the expected profit of the VPP. The example shows that VPPs can influence market prices through strategic bidding decisions. After considering carbon trading, the expected revenue of the VPP increased by 5.1% compared to the scenario without carbon trading.

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This article discusses the need for a multi-grade pricing strategy for emergency power supply services provided by mobile energy storage systems. The authors argue that the existing uniform pricing model fails to meet the differentiated demands of customers and undermines their enthusiasm for purchasing emergency supply services. They propose a hierarchical trading framework and a bi-level pricing optimization model based on a Stackelberg game to obtain tiered prices of emergency power supply and increase the revenue of mobile energy storage while reducing the cost for customers. The article provides insights and discussions on this pricing strategy, considering power supply capacity, duration, and response time as metrics for differentiating power supply levels. The document also suggests future research directions, such as integrating real-time scheduling of mobile energy storage into the pricing model. The research was supported by the Guangdong Basic and Applied Basic Research Foundation and the Scientific Research Startup Fund for Shenzhen High-Caliber Personnel. Additionally, there is a list of references cited in an article or research paper, which includes various sources related to the topic of energy storage systems, such as studies on optimal configuration and operation methods, pricing strategies, and the use of mobile energy storage in distribution networks. The document provides a range of perspectives and approaches to the subject, allowing library patrons to explore different aspects of energy storage for their research. [Extracted from the article]

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]

The proposed study introduces a novel anti-jamming approach for cognitive radio networks (CRNs) by integrating the Stackelberg game model with direct sequence spread spectrum (DSSS) techniques. This innovative combination enhances the security and performance of CRNs by optimizing resource allocation and fortifying network resilience against jamming attacks. The Stackelberg game model provides a strategic framework where the Defender and Adversary dynamically adjust their strategies to achieve Nash equilibrium, ensuring strategic stability. The application of DSSS further improves signal robustness, mitigating interference from jamming attempts. Simulation results demonstrate significant improvements in network security, resource utilization, and overall performance, validating the efficacy and advantages of the proposed scheme in maintaining reliable communication in the presence of adversarial threats. [ABSTRACT FROM AUTHOR]

An optimal credit term decision in supply chain finance often needs to be made in a dynamic way considering the varying market demand among other factors. We study the dynamic credit term optimization problem (DCTOP), where a supplier determines the credit term in conjunction with its production and inventory decision, while anticipating a buyer's order quantity in a leader-follower game setting. The DCTOP is first approached to using a continuous time optimal control model, with analytical results characterizing the structural properties of the optimal solution. To complement the structural properties, we then develop a discrete time bilevel programming model to provide computationally tractable and implementable numerical solutions. A comprehensive computational study shows significant advantage of our optimal solutions over the heuristic credit term rules in practice, and provides managerial insights regarding the impacts of key problem parameters on the optimal solutions and coordination scheme. [ABSTRACT FROM AUTHOR]

Electricity markets are intricate systems that facilitate efficient energy exchange within interconnected grids. With the rise of low-carbon transportation driven by environmental policies and tech advancements, energy trading has become crucial. This trend towards Electric Vehicles (EVs) is bolstered by the pivotal role played by EV charging operators in providing essential charging infrastructure and services for widespread EV adoption. This paper introduces a blockchain-assisted secure electricity trading framework between EV charging operators and the electricity market with renewable energy sources. We propose a single-leader, multi-follower Stackelberg game between the electricity market and EV charging operators. In the two-stage Stackelberg game, the electricity market acts as the leader, deciding the price of electric energy. The EV charging aggregator leverages blockchain technology to record and verify energy trading transactions securely. The EV charging operators, acting as followers, then decide their demand for electric energy based on the set price. To find the Stackelberg equilibrium, we employ a Deep Reinforcement Learning (DRL) algorithm that tackles non-stationary challenges through policy, action space, and reward function formulation. To optimize efficiency, we propose the integration of pruning techniques into DRL, referred to as Tiny DRL. Numerical results demonstrate that our proposed schemes outperform traditional approaches. [ABSTRACT FROM AUTHOR]

In the context of supply disruption, having a resilient supply chain is crucial for the survival and growth of enterprises. It is also essential for gaining a competitive advantage in a turbulent environment. Enterprises need to invest in supply chain resilience to better deal with future uncertainties. This paper constructs a Stackelberg game model with the manufacturer as the leader and the retailer as the follower. We explored how supply chain-related factors under supply interruption risk affect supply chain resilience investment, and studied how to choose supply chain coordination strategies to improve the effectiveness of manufacturer capacity recovery and mutual profits in the context of supply interruption. The study also analyzes the asymmetrical impact of changes in product order quantity, supply disruption probability, and the capacity recovery coefficient on retailer decision-making and the profits of supply chain members. The results indicate that manufacturer profits are negatively correlated with supply disruption probability, while retailer profits are positively correlated with supply disruption probability when product order quantities are low and negatively correlated when product order quantities are high. The supply chain resilience investment is positively correlated with the supply disruption probability. Furthermore, the effectiveness of the cost-sharing contract is closely related to product order quantity and supply disruption probability. When the product order quantity d < α L − c [ 1 − ξ a L + ξ a H ] + s α H ξ + w α L (1 − ξ) k or α H − c [ 1 − ξ a L + ξ a H ] + s α H ξ + w α L (1 − ξ) k < d < α H [ 1 − ξ a L + ξ a H ] (w − c) k , manufacturers can withstand the risk of supply interruption by investing in supply chain resilience alone. But when the product order quantity is α L − c [ 1 − ξ a L + ξ a H ] + s α H ξ + w α L (1 − ξ) k < d < α H − c [ 1 − ξ a L + ξ a H ] + s α H ξ + w α L (1 − ξ) k and α H [ 1 − ξ a L + ξ a H ] (w − c) k < d , the use of cost-sharing contracts is more effective. Additionally, when the sensitivity analysis is conducted, the capacity recovery coefficient positively correlates with supply chain profits in a decentralized mode. However, under the cost-sharing contract mode, it exhibits a U-shaped fluctuation pattern, indicating that the impact of improving capacity recovery efficiency on the profits of both parties is not symmetrical and linear. As ξ approaches 0.5, the profits of manufacturers and retailers decrease. Instead, it undergoes an initial decline followed by a subsequent increase, highlighting the nonlinear benefits of capacity recovery strategies under the cooperative approach. [ABSTRACT FROM AUTHOR]

With the increasing awareness for sustainable future and green energy, the demand for electric vehicles (EVs) is growing rapidly, thus placing immense pressure on the energy grid. To alleviate this, local trading between EVs should be encouraged. In this paper, we propose a blockchain and public key infrastructure (PKI)-based secure vehicle-to-vehicle (V2V) energy-trading protocol. A permissioned blockchain utilizing the proof of authority (PoA) consensus and smart contracts is used to securely store data. Encrypted communication is ensured through transport layer security (TLS), with PKI managing the necessary digital certificates and keys. A multi-leader, multi-follower Stackelberg game-based trade algorithm is formulated to determine the optimal energy demands, supplies, and prices. Finally, we propose a detailed communication protocol that ties all the components together, enabling smooth interaction between them. Key findings, such as system behavior and performance, scalability of the trade algorithm and the blockchain, smart contract execution costs, etc., are presented through numerical results by implementing and simulating the protocol in various scenarios. This work not only enhances local energy trading among EVs, encouraging efficient energy usage and reducing burden on the power grid, but also paves a way for future research in sustainable energy management. [ABSTRACT FROM AUTHOR]

This paper studies life reinsurance as a solution to default risk in equity-linked life insurance products with surplus participation. The problem is considered under both perfect and asymmetric information about the insurer's risk profile between the reinsurer and the insurer. In both cases, we analyze the existence of proportional reinsurance and the impact of the insurer's investment strategies on optimal reinsurance. We find that the more risky the insurer's investment portfolio is, the more risk the insurer tends to transfer to the reinsurer. Further, information asymmetry leads to additional information costs and consequently to a larger reinsurance premium and a lower reinsurance share. [ABSTRACT FROM AUTHOR]

This paper studies a partially observed stochastic Stackelberg game with two followers, where state satisfies a linear stochastic differential equation of mean-field type, and cost functionals are quadratic. Using decomposition technique and backward separation approach, we derive the followers' optimal strategy. The leader focuses on an optimal control problem driven by a fully coupled mean-field forward–backward stochastic differential equation with conditional expectation. By layer-by-layer decomposition technique, some inequalities and Riccati equations, we not only get the existence and uniqueness of solution to the corresponding Hamiltonian system but also give a feedback form of Stackelberg solution. Finally, we tackle a government debt problem by the above theoretical results. [ABSTRACT FROM AUTHOR]

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

Damming can promote flood control, water supply, power generation, and shipping but often changes the downstream hydrological regimes, producing adverse externality effects. Maximizing downstream social and ecological benefits will inevitably reduce upstream power generation. This study presents two novel bi-level hybrid game models, called the non-cooperative hybrid game model (NCHG) and the cooperative hybrid game model (CHG), to facilitate integrated water resource management in reservoir systems. The performance index of propensity to disrupt is applied to evaluate the stability of CHG, and an improved reliability index and Gini coefficient are adopted to evaluate the reliability and equity of both two models. The Three Gorges Reservoir and its adjacent cities were chosen as a case to inspect the two models' performance. A range of scheduling schemes was derived by proposed bi-level hybrid game models in wet, normal, and dry years. Results reveal that (i) the RI values of the watershed system obtained by the CHG are less than those in NCHG in three typical years (for example, 0.1201 VS 0.1930 in the wet year), showing higher systemic reliability. The Gini coefficients of the watershed system obtained by the CHG are all less than those obtained by the NCHG in all typical years (for example, 0.1016 VS 0.1020 in the wet year), which shows better performance of CHG on fairness for the allocation results; (ii) in the case of a multi-function reservoir system, the CHG generates favorable allocation schemes with higher systemic characteristic values by 32.43, 34.39, and 33.54 in wet, normal, and dry years, respectively, than those in NCHG (32.03, 33.16, and 31.42 in wet, normal, and dry years, respectively); (iii) compared with NCHG, the economic benefits obtained by CHG decreased by 0.98%, 1.04%, and 5.42% in wet, normal, and dry years, respectively; the social negative benefits decreased by 3.49%, 9.84%, and 28.69%; and the ecological negative benefits decreased by 1.77%, 5.65%, and 5.59%, respectively. It indicates that a minor sacrifice of the reservoir benefit could significantly improve the welfare at the system level by the CHG. The developed CHG can provide optimal water scheduling schemes in balancing inter-regional water conflicts and can be widely used to produce an equilibrium management strategy for a multi-function reservoir system. [ABSTRACT FROM AUTHOR]

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We consider a multi-device wireless-powered communication network, where an intelligent reflecting surface (IRS) is deployed to assist the wireless energy transfer (WET) from the power station (PS) to the information transmitter (IT) and the wireless information transfer (WIT) from the IT to the devices. The IRS, IT, and PS belong to different service providers, where the PS receives revenue from the IT for WET and pays fees to its energy source and the IRS, and the IT receives revenue from the devices for WIT and pays fees to the PS and the IRS. We model the interactions between the IT and the PS through a Stackelberg game and aim to achieve a win-win situation between them in terms of utility. Specifically, we solve a follower problem that maximizes the utility of the PS by jointly optimizing the IRS reflection coefficients and the transmit power of the PS, and a leader problem that maximizes the utility of the IT by jointly optimizing the energy price, the transmit power allocation of the IT, and the time allocation as well as the IRS reflection coefficients in the WET and WIT phases. The results show that, by deploying IRS, it is possible to effectively enhance the signal strength and thus increase the revenue of the system, and by using Time Division Multiple Access (TDMA), the performance of the system is greatly improved by coordinating the timing of the reception of the signal by each device. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel approach to study the production of consumption goods within a price floor carbon emission trading scheme. A stochastic Stackelberg game is set up between the environment authority (Player 1), and the manufacturer/producer (Player 2). In such a hybrid emission trading scheme, the authority sets an emissions target and producers will choose to participate in carbon trading on this basis, subject to a stochastic demand with information delayed. When the stochastic demand is determined by the market sale price and the scale of carbon emission reduction, we apply the maximum principle to obtain both the optimal production and market price. We show when the demand is determined by both the market sales price and carbon emission reduction, manufacturers are persuaded to set the market sales price first (ex ante incentive) and then proceed to a carbon trading scheme, thus providing a backward-looking advantage to manufacturers. Consequently, the manufacturer and the environmental authority can find a subgame-perfect Nash equilibrium via backward induction. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Chongqing University of Technology (Natural Science) is the property of Chongqing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Environmental policies such as carbon tax implementation significantly impact the technology choice and cost structure of the upstream manufacturer, affecting the downstream retailer's the procurement decision and risk management in a sustainable supply chain. This study constructs a single-manufacturer-single-retailer supply chain model constrained by carbon tax policies to analyze the influence of retailer's anticipated regret on the supply chain operation and environmental performance. Utilizing game theory, the research finds that the retailer's anticipated regret behavior suppresses manufacturer's willingness to invest in the green initiative, resulting in a non-monotonic effect on profits. When the retailer's regret level is low and her demand for eco-friendly products is also low, the manufacturer tends to reduce the green investment and increase the wholesale price to maximize the marginal return. Although such the anticipated regret behavior by the retailer may stimulate the manufacturer's profit growth, it reduces retailer's profit. Conversely, as the retailer's regret level increases, the manufacturer increases the green investment and reduces the wholesale price to induce higher procurement by the retailer, leading to a decline in the manufacturer's profit but an upward trend in the retailer's profit. This discovery suggests that the upstream supply chain manager, should closely the monitor retailer's potential anticipated regret and adjust the corresponding strategy accordingly. Furthermore, the study finds that the lower level of retailer's anticipated regret positively impact environmental behavior, offering the policymaker a new perspective on promoting the green supply chain practice. [ABSTRACT FROM AUTHOR]