Leader-follower Game Model Research Articles

Research on time-of-use compensation pricing strategies for load aggregators based on user demand response

As the electric power market reform deepens, the strategic role of load aggregators in demand-side response becomes increasingly important. The inherent variability of distributed renewable energy generation and user demand response often leads to a mismatch between the purchased electricity and the market bid volume, resulting in punitive costs for companies. To address this issue, this study treats demand-side controllable loads as dispatchable resources and proposes a tiered pricing strategy to adjust power distribution. By establishing a Stackelberg leader-follower game model, the study promotes a mutually beneficial relationship between load aggregators and controllable load users. Through case studies, this paper examines the operational profits of load aggregators and the power adjustment behaviors of controllable load users under tiered and fixed compensation pricing schemes. The results indicate that tiered compensation pricing significantly reduces punitive costs and enhances user participation in demand response.

Sales mode selection strategic analysis for risk-averse manufacturers under revenue sharing contracts

This paper considers a sales mode selection problem under revenue sharing contracts between resale and agency modes for risk-averse manufacturers with traditional retail channel, direct selling channel, and e-commerce platform channel. By considering the factors including price competition intensity, market share, revenue sharing ratio, commission rate, and degree of risk aversion, we construct leader-follower game models with manufacturers as leaders and traditional retailers and e-commerce platforms as followers. To obtain optimal solutions, we discuss conditions to ensure the upper and lower models to be convex and then give the optimal strategies for all members in the network. Through numerical experiments, we analyze the involved parameters’ impact on sales mode selection strategy and the changing trends of each member's optimal pricing and profit under different sales modes. The numerical results reveal the following revelations: The manufacturer should choose the agency mode when the commission rate is low and the direct selling channel has a large market share. If both the commission rate and degree of risk aversion are high, direct selling channels have a low market share, and price competition intensity is weak, the manufacturer should choose the resale mode. The degree of risk aversion has an effect on each member’s optimal decision. Regardless of which sales mode the manufacturer chooses, the optimal price of each member decreases as the degree of risk aversion increases. Under certain conditions, the manufacturer’s choice of agency mode can create win-win situations with supply chain members.

Coordination between the energy-consumption permit trading scheme and carbon emissions trading: Evidence from China

Market-oriented instruments are expected to minimize energy costs and carbon abatement, but interactions among them may create challenges. The Chinese government issued a pilot energy-consumption permit trading scheme (ECPTS) in Fujian Province, where the carbon emissions trading scheme (ETS) is in operation, thus providing an opportunity to analyze the interactions between two related market instruments. Based on the game-fixed cost allocation model and leader-follower game model, this paper designed an allocation scheme of energy-consumption permits (ECPs) based on coordination, efficiency and equity, and compared the differences in the caps, allocation structure and regional economic inequity among cities. The results of the Fujian case study show that when considering the optimal cross efficiency, the allocation of ECPs and carbon allowances are dominated by coastal cities with booming economies, which may entrench economic inequality between cities in Fujian. By introducing the equity principle, the allocation structure of ECPs among cities will change significantly, especially in underdeveloped cities. With the coordination mechanism of the ECPTS and ETS, the inequity in the distribution of economic development rights among cities can be moderated, which indicates that the designed approach has advantages in resource allocation. In addition, it is more conducive to energy saving and emission reduction if the provincial government prioritizes the allocation efficiency of ECPs instead of carbon allowances.

Coordination mechanism of wooden furniture supply chains with consideration of carbon footprint

This study emphasizes a three-level wooden furniture supply chain, which involves one supplier, one manufacturer, and one retailer. Focusing on maximizing the profit of the supply chain while adhering to low-carbon principles, the Three-level Leader-follower Game (TLG) model, Stackelberg Game Model I (SGI model), Stackelberg Game Model II (SGlI model), and Cooperative Decision-making (CD) model were established by using game theory. The carbon emission reduction cost and benefit sharing contract was introduced into the model with the maximum profit, and the ranges of sharing coefficients for a solid wood bed supply chain and the optimal decision-making process for each supply chain member were discussed. Results showed that the profit for the solid wood bed supply chain reached maximum under the CD model, followed by the SGII model, and then the SGI model, and the TLG model showed the lowest profit. A higher preference for low-carbon products can lead to lower demand for products and higher retail prices. Through introducing the cost and benefit-sharing contract into the CD model, the profit of the supply chain can be guaranteed with different sharing coefficients, and the profit of each member was improved compared to the TLG model.

Optimal quality incentive scheme design in contracting out public bus services

Designing appropriate quality incentives in contracting out public bus services is essential to ensure that cost savings are not pursued at the expense of deteriorating quality. This study investigates a practical incentive design problem that links additional rewards and penalties to quality indicators of bus services. A leader–follower game model is proposed in which the transit authority (leader) determines the quality baseline of each bus service as well as the marginal reward for outperformance and penalty for underperformance. Subject to a given amount of budget, the transit authority has to guarantee a minimum profit margin for each transit operator so that they have enough incentives to improve the service quality. As a response, the profit-maximizing transit operators (followers) determine the level of service quality by weighing the marginal revenue and cost involved. A tailored solution approach is devised by exploiting the model properties. Motivated by Singapore’s recent trial, a case study is presented to demonstrate how the transit authority can determine the performance baseline as well as the reward-penalty levels for a large bus network and evaluate the amount of public funds needed to achieve a targeted quality outcome. Our analysis also cautions that quality deterioration may surprisingly occur in a few bus services after introducing the incentive scheme. This may be attributed to an unreasonably strict quality baseline and/or an inefficient operator running that service. It is thus suggested that the authority should figure out the real contributing factors and fine-tune the incentive scheme accordingly.

Comparison of Transboundary Water Resources Allocation Models Based on Game Theory and Multi-Objective Optimization

Transboundary water resources allocation is an effective measure to resolve water-related conflicts. Aiming at the problem of water conflicts, we constructed water resources allocation models based on game theory and multi-objective optimization, and revealed the differences between the two models. We compare the Pareto front solved by the AR-MOEA method and the NSGA-II method, and analyzed the difference between the Nash–Harsanyi Leader–Follower game model and the multi-objective optimization model. The Huaihe River basin was selected as a case study. The results show that: (1) The AR-MOEA method is better than the NSGA-II method in terms of the diversity metric (Δ); (2) the solution of the asymmetric Nash–Harsanyi Leader–Follower game model is a non-dominated solution, and the asymmetric game model can obtain the same water resources allocation scheme of the multi-objective optimal allocation model under a specific preference structure; (3) after the multi-objective optimization model obtains the Pareto front, it still needs to construct the preference information of the Pareto front for a second time to make the optimal solution of a multi-objective decision, while the game model can directly obtain the water resources allocation scheme at one time by participating in the negotiation. The results expand the solution method of water resources allocation models and provide support for rational water resources allocation.

Stackelberg game approach to a bi-objective robust design optimization

Robust design has received a great deal of attention from quality researchers in recent years, and a number of optimization methodologies based on the dual response format have been proposed. The majority of existing bi-objective optimization models concentrate on the trade-offs between the process mean and variability functions without investigating the interactions between control factors and quality characteristics. The primary objective of this research is to integrate the Stackelberg leadership model into the robust design procedure and propose a Stackelberg game-based robust design (SGRD) method to determine appropriate control factor settings by minimizing the values of desired optimization targets based on an analysis of possible combinations of input and output quality parameters. Herein, first, a bi-objective robust design optimization problem is formulated as a dual response model using response surface methodology (RSM). Second, the proposed SGRD model is developed via decomposition into two leader-follower game models. Finally, the mean square error (MSE) criterion is applied to evaluate models, and select non-dominated solutions in various situations. Numerical examples are used to demonstrate that the proposed method provides significant solutions in cases containing unidentified priorities between the dual responses and undiscovered correlations among several inputs and outcomes. In addition, according to the case study analysis, the proposed method is more efficient than the conventional dual response approach when dealing with bi-objective robust design optimization problems.

Contract vs. recruitment: Integrating an informal waste merchant to a formal collector for collection of municipal solid waste

Due to environmental and social issues caused by unauthorized processing of recyclables, waste merchants, key informal collectors with the door-step collection in China have been integrated into formal collectors. However, how to achieve effective integration is still underexamined. This study puts forward two strategies for integrating a waste merchant from a formal collector’s perspective, namely, contract strategy (CS) and recruitment strategy (RS). A leader-follower game model is developed to explore and compare the suggested integration strategies considering the minimum profit constraint of a waste merchant. On this basis, the feasible boundary for the selection of a reasonable strategy by the formal collector is identified. The results show that the formal collector remains reluctant to integrate the waste merchant through RS or CS if the created value by the recyclables is low. The likelihood of selecting RS increases with the higher reclaimed value. Reduced hassle costs for residents can expand the boundary of selection for RS. Besides, it is observed that CS has a greater chance when the ratio of the collection cost coefficient under RS to CS increases. In particular situations, the formal collector may gain a higher profit using RS, although it may not definitely result in higher collection quantity compared to the situations where CS is applied. Overall, this study provides insights for formal collectors for the selection of an effective integration strategy.

A game theoretical low impact development optimization model for urban storm water management

Abstract This study presents a novel framework to optimize Low Impact Development (LID) practices for urban storm water management. First, the Storm Water Management Model (SWMM) model was executed for different possible scenarios of input parameters and various LIDs to simulate runoff volume, Biochemical Oxygen Demand (BOD) and Total Suspended Solids (TSS) loads. Next, a neural network (MLP-ANN) was trained and validated, as a surrogate model, against the set of inputs and output variables from the SWMM model simulations. The inherent uncertainties in the rainfall-runoff modeling were accounted for using a Nonlinear Interval Number Programming (NINP) model, and stakeholders' interactions are considered using a leader-follower game model. Velenjak urban watershed in Tehran, Iran, with four key stakeholders was considered as the study area. Tehran Municipality is the financial service provider that makes the first decision the leader-follower structure, and is considered as the leader with the priority of minimizing LIDs’ construction and maintenance costs. Tehran Department of Environmental Protection, Tehran Regional Water company, and Tehran Province Water and Wastewater company are the main followers in the decision making structure in the study area. This game theoretical framework yields several Pareto optimal solutions given the conflicting utilities of various players, and a Multi Criteria Decision Making procedure – i.e. PROMETHEE model – selects the most preferred compromised option. Fourteen weighting scenarios were considered in the PROMETHEE model to determine the compromise solution among the 52 solutions on the trade-off curve. The novelty of this study lies in using a nonlinear interval conflict resolution multi-objective optimization model for urban storm water management based on a leader-follower game. The proposed methodology warrants BOD and TSS loads, as well as storm water volume, are all reduced, with the highest reductions of 93, 86 and 90 percent, respectively. Results testify to the efficacy of the proposed model for urban storm water management.

Water Resources Allocation in Transboundary River Basins Based on a Game Model Considering Inflow Forecasting Errors

Dynamic transboundary water resources allocation based on inflow prediction results is an important task for water resources management in river basins. This paper takes the watershed management agency as the leader and the associated area as the follower, and proposes a two-level asymmetric Nash-Harsanyi Leader-Follower game model considering inflow forecasting errors. In the proposed model, the Monte Carlo method is used to analyze the uncertainty of various stakeholder allocation results and the response regularity to the total water resource uncertainty. The quantitative relationship between the allocation results of stakeholders and the mean and standard deviation of total water resource uncertainty is subsequently established. The Huaihe River basin in China is selected as a case study. The results show the following: (1) the water allocated to the watershed management agency and three provinces has a normal distribution when the inflow forecasting error obeys the normal distribution; (2) the sum of the mean of the water allocated to stakeholders equals the mean of the forecast water resource and the sum of the standard deviations of the water allocated to stakeholders equals the standard deviation of the forecast water resource; (3) the mean and standard deviation of the allocation results have a good linear relationship with the mean and standard deviation of forecast water resource; (4) the distribution parameters of the stakeholder allocation results can be directly derived from the distribution parameters of the forecast information, thus aiding the stakeholders in making decisions and improving the practical value of the method.

An Analysis of Service Bundles of Mobile Network Operators with Free Services Included

To attract more users, mobile network operators may offer both chargeable/metered and free services as parts of their product bundles. However, an extra cost of providing the free services and their substitution effect on metered services in the bundles may reduce their profitability. Therefore, the mobile network operators must decide on including free services in their offered bundles based on the profitability. In this paper, we develop an analytical framework composed of leader-follower game models to obtain the Stackelberg equilibrium strategy of the mobile network operators and analyze several important properties of the equilibrium. The proposed framework takes into account the congestion effect resulting from incorporating free services in the bundles. The game models are general and capable of analyzing different setting of bundles. Extensive performance evaluations show that the inclusion of free services can improve the profit of the mobile network operators when (i) the users’ interest for the free services is above a certain value, (ii) the free services add small cost to the bundle, and (iii) the users’ demand of free services is less dependent on that of metered services in the bundle.

Water Resources Allocation in Transboundary River Based on Asymmetric Nash–Harsanyi Leader–Follower Game Model

Transboundary river water resources allocation is important in water resources management. Conflicts often arise when different water users compete for a limited water supply. This study proposes a two-level asymmetric Nash–Harsanyi Leader–Follower game model to resolve conflicts of interest in transboundary river water resources allocation problems. In the proposed model, we use bankruptcy theory to derive disagreement points and determine the bargaining weights considering the principles of equity and efficiency. For comparison, a model that does not consider disagreement points and bargaining weights are also used to demonstrate the importance of disagreement points and bargaining weights. The proposed model is applied to a real case of the Huaihe River basin in China, which is facing water shortages. In the case study, the watershed management agency serves as the leader, three provinces (Henan, Anhui and Jiangsu) serve as followers, and successive linear programming is used to solve the model for followers. The results show that the proposed disagreement points can guarantee basic water demand, and the bargaining weights can better balance the economic development levels among followers.

Investigating the future supply distribution of industrial grade wood pellets in the global bioenergy market

ABSTRACTMany factors may globally affect the trade pattern for industrial-grade wood pellets, with one such factor being the decision strategies by potential buyers and suppliers to optimize feedstock price and volume. This study investigated the industrial-grade wood pellet market assuming potential buyers and suppliers optimize their decision independently. A non-cooperative, bi-level, Stackelberg, leader-follower game model was developed to predict potential resource distribution in global competitive feedstock markets for industrial-grade wood pellets. Based on historic trade patterns and expected future production and demand structures, a set of potential buyers and suppliers of industrial-grade wood pellets were identified for 2022, 2030, and 2040. Projected trade volume and patterns among buyers and suppliers were identified in different scenarios. Potential buyers for US-sourced industrial grade-wood pellet were identified. Results shows that the expected demand growth from the European Union, South Korea, and Japan until the year 2030 limits the resources available to the USA. Competitive prices offered by international buyers cause the US industry to primarily sell overseas. International trade could contribute to 83.4% of the total volume in 2022 and 90.2% of the total trade value in 2022. High-demand markets with a respective high willingness-to-pay dominate international trade.

Efficiency evaluation of an interactive system by data envelopment analysis approach

Many different network data envelopment analysis (DEA) models have been built to investigate the internal structure of a system which used to be considered as a “black box” in traditional DEA models. However, few of these previous works have taken into account the interactive relationship between system components, that is, one component’s output (input) may be the input (output) of another component. The interactive network becomes more and more common in a system because of complex competition circumstances, it is therefore necessary to develop a new method to measure the efficiency of these systems. In this paper, a centralized model and two leader-follower game models were built to measure the efficiency of a parallel system with two components that have an interactive relationship in a centralized mode and non-centralized mode, respectively. Besides, since the centralized model is non-linear, a heuristic method is proposed for solving it. Finally, our approach is applied to analyze Chinese “985 Project” universities’ performance.

Bi‐level Programing Merger Evaluation and Application to Banking Operations

The potential for operational efficiency improvement is a key consideration for firms contemplating the consolidation of both internal and external business units. This paper develops a leader–follower game model to assess such potential gains from the merger of different organizations with constrained resources. A profit‐sharing strategy and algorithm are proposed to solve the model while maintaining incentive compatibility within each unit's decision‐making process. This paper further demonstrates that in a framework, within the data envelopment analysis paradigm, a supply chain with an upstream leader and downstream followers is efficient if and only if both the leader and the followers are individually efficient. A case study of a banking operations merger shows how incentive compatible merger of operations can produce overall efficiency improvement.

Closed-loop supply chain coordination strategy for the remanufacture of patented products under competitive demand

In this study, we consider a closed-loop supply chain (CLSC) system comprising an original manufacturer, third-party remanufacturer, and retailer. In this system, the remanufacturer can only recycle and remanufacture the patented products with patent licensing from the original manufacturer, where newly manufactured and remanufactured products are sold together in the same market at different prices, and the demand for the two types of product is sensitive to their retail prices. First, we establish a leader–follower game model and a joint decision-making model, and we compare the performance of the components of the CLSC, i.e., the collection price, selling prices, and profits. Second, we investigate the contract coordination issues among the three parties in the decentralized case, where we develop a coordinated pricing mechanism that incorporates a revenue-and-sharing contract and two-part tariffs, which can perfectly coordinate the CLSC. Thus, a reasonable range can be identified for the sharing coefficient as well as the agency fees for qualifications. Finally, based some numerical examples, we analyze the impact of the salvage value, substitute ratio, coordination parameters, and other factors on the optimal supply chain performance.

Game-theoretic control of PHEV charging with power flow analysis

Due to an ever-increasing market penetration of plug-in hybrid electric vehicles (PHEVs), the charging demand is expected to become a main determinant of the load in future distribution systems. In this paper, we investigate the problem of controlling in-home charging of PHEVs to accomplish peak load shifting while maximizing the revenue of the distribution service provider (DSP) and PHEV owners. A leader-follower game model is proposed to characterize the preference and revenue expectation of PHEV owners and DSP, respectively. The follower (PHEV owner) decides when to start charging based on the pricing schedule provided by the leader (DSP). The DSP can incentivize the charging of PHEV owners to avoid system peak load. The costs associated with power distribution, line loss, and voltage regulation are incorporated in the game model via power flow analysis. Based on a linear approximation of the power flow equations, the solution of sub-game perfect Nash equilibrium (SPNE) is obtained. A case study is performed based on the IEEE 13-bus test feeder and realistic PHEV charging statistics, and the results demonstrate that our proposed PHEV charging control scheme can significantly improve the power quality in distribution systems by reducing the peak load and voltage fluctuations.

The Differential Game Analysis on the Construction Problem of the Public Libraries

Using the differential game theory, we studied the investment problem on public libraries, and established the Leader-follower differential game model, which is between the governments and the private enterprises (social organization). By building the Hamiltonian solving the Stackelberg balanced optimal solutions in the main two game players when they choose their strategies. By adjusting the strategy of government and social utility’s coefficient of dynamic to increase the comprehensive social utility of libraries.

Research on Supply Chain Profit Coordination Mechanism Based on JIT Lot-Splitting

A supply chain profit coordination mechanism based on JIT lot-splitting, which involves a two stage supply chain consisted of a supplier and a buyer, is discussed. Based on the bargaining power of supplier, the profit coordination with and without incentives are respectively explored. For the total cost minimizations of buyer and supplier separately, two stage stackelberg leader-follower game models, in which buyer is the leader and supplier is the follower, are established. Supplier applies JIT delivery to reduce buyer’s cost and the total cost of the supply chain via dividing buyer’s order per batch into some batches to deliver. Finally, a numerical example and a simulation analysis are given and the impact of the variation of relative parameters on the total cost saving of buyer, supplier and system is discussed. In addition, the efficiency of game decision on the basis of JIT lot-splitting is proved.

A Game Theoretical Model for Location of Terror Response Facilities under Capacitated Resources

This paper is concerned with the effect of capacity constraints on the locations of terror response facilities. We assume that the state has limited resources, and multiple facilities may be involved in the response until the demand is satisfied consequently. We formulate a leader-follower game model between the state and the terrorist and prove the existence and uniqueness of the Nash equilibrium. An integer linear programming is proposed to obtain the equilibrium results when the facility number is fixed. The problem is demonstrated by a case study of the 19 districts of Shanghai, China.