Stackelberg Model Research Articles

Green Credit Financing Equilibrium under Government Subsidy and Supply Uncertainty

In this paper, we study the green credit financing equilibrium in a green supply chain (GSC) with government subsidy and supply uncertainty. The GSC system is composed of one manufacturer, two retailers, one bank, and the government. The manufacturer is subject to both supply uncertainty and limited capital. The manufacturer invests in the R&D of green products and borrows loans from the bank. The government subsidizes banks to encourage banks to provide loans to manufacturers with lower interest rates, which is termed “green credit financing”. The two retailers decide their order quantities with horizontal competition or horizontal cooperation. We first developed a Stackelberg model to investigate the green credit financing equilibriums (i.e., the interest rate of the bank, the manufacturer’s product green degree and wholesale price, and the retailers’ order quantity) under horizontal competition and horizontal cooperation, respectively. Subsequently, we analyzed how the subsidy interest rate, supply uncertainty, and supply correlation affect financing decisions regarding equilibrium green credit. We found that a high subsidy interest rate leads to a low interest rate of bank and the manufacturer can set a high level of green product and high wholesale price, while the retailers can set a high order quantity. Finally, we compared the green credit financing equilibriums under horizontal competition with those under horizontal cooperation using numerical and analytical methods. We found that, in general, the optimal decisions and profits of bank and SC members, consumer surplus, and social welfare under horizontal competition are higher than those under horizontal cooperation. The findings in this research could provide valuable insights for the management of capital-constrained GSCs with government subsidies and supply uncertainty in a competing market.

Social responsibility and cost-learning in dyadic supply chain coordination

Over time, many leading organizations have started to include Corporate Social Responsibility as an instrument to enhance their brand image, and gain competitive advantage. In this paper, we develop a game-theoretic Stackelberg model for a two-periodic socially responsible supply chain with cost-learning capabilities. We study both the revenue sharing and wholesale price contracts under various permutations to achieve supply chain coordination. In the process, we use analytical, numerical, and graphical methods to understand how the contract parameters affect the channel partner’s performance under two-periodic setting. The results show that although the wholesale price contract fails to solve double marginalization, interestingly, the combination of the wholesale price and revenue sharing contracts can coordinate a two-period socially responsible supply chain, but fails to resolve the channel conflict. However, the revenue sharing contract does resolve the channel conflicts under two-periodic setting.

A game-theory analysis of electric vehicle adoption in Beijing under license plate control policy

To reduce traffic congestion and protect the environment, license plate control (LPC) policy has been implemented in Beijing since 2011. In 2019, 100,000 vehicle license plates were distributed, including 60,000 for electric vehicles (EVs) and 40,000 for gasoline vehicle (GVs). However, whether the current license plate allocation is optimal from a social welfare maximization perspective remains unclear. This paper proposes a two-level Stackelberg game, which portrays the interaction between vehicle applicants and the government to quantify the optimal number of EV license plates under the LPC policy in Beijing. The equilibrium number of EV license plates derived from the Stackelberg model is 58,800, which could increase the social welfare by 0.38%. Sensitivity analysis is conducted to illustrate the impact of important influential factors — total license plate quota, vehicle rental fee, and energy price — on EV adoption. The LPC policy under COVID-19 is also studied through a scenario analysis. If the government additionally increases the total quota by 20,000, 24% could be allocated to GV and 76% to EV. One third reduction of the current vehicle rental fee could increase EV license plates by 10.5%. In terms of energy prices, when gasoline price is low, reducing electricity prices could contribute to EV adoption significantly, while that effect tapers off as gasoline prices increase.

A multi-objective optimization model considering users' satisfaction and multi-type demand response in dynamic electricity price

Dynamic electricity price mechanism is an important regulation method adopted by power companies in various countries to solve the contradiction between source and charge. According to the principle of consumer psychology, a non-cooperative Stackelberg model is constructed based on game theory to study the demand response characteristics of multi-type users. The model classifies users to realize the comprehensive consideration of users with different preferences. Meanwhile, it quantifies the impact of grid load fluctuation on the benefits of the power company and users' satisfaction with electricity consumption. Finally, the model is applied to a practical example, the Nash equilibrium solution of the model is obtained by NSGA-Ⅱ algorithm, and the sensitivity analysis of correlation coefficient is carried out. The results show that the model has a good effect on utility optimization of power supply and demand. • Users were classified through induction and classification. • Users' satisfaction included electricity consumption mode and cost. • Different users had different satisfaction weights in electricity consumption. • A Nash-Stackelberg model based on consumer psychology and game theory. • Aims were to optimize the peak-valley difference, grid benefits and users' satisfaction.

The Green-Innovation-Inducing Effect of a Unit Progressive Carbon Tax

The major global economies are facing increasing pressure to reduce their carbon emissions. Introducing environmental policy instruments to stimulate green innovation is key to mitigating global warming. We propose a carbon tax design with a typical green innovation orientation that links carbon taxes with the low-carbon technology (LCT) of enterprises and imposes a progressive tax on heterogeneous enterprises with LCT stock to encourage green innovation. This study used a dynamic evolution game model based on the Stackelberg model of heterogeneous enterprises with LCT stock to analyze the green-innovation-inducing effect of unit progressive carbon taxes. A unit progressive carbon tax could encourage enterprises to participate in green innovation, regardless of their initial green innovation willingness. The progressive tax rate was more effective than a fixed rate for stimulating green innovation by all enterprises. There was a marginal diminishing effect of increases in the tax rate. An increase in the innovation cost coefficient of enterprises reduced the green-innovation-inducing effect of the unit progressive carbon tax. Increasing the tax rate was effective only under normal circumstances. A decline in the carbon reduction in enterprises also reduced the green-innovation-inducing effect of the unit progressive carbon tax. Furthermore, increasing the tax rate when the carbon reduction amount was extremely low caused enterprises to abandon green innovation.

Quality Improvement Incentive Strategy in Agricultural Products Supply Chain Under Social Preference

This paper sets Stackelberg model of bilateral quality efforts decision dominated by supermarket in the agricultural products supply chain by considering fairness concern and altruistic reciprocity. We use backward induction method to compute and prove that A3P’ fairness concern can play the role of profit distribution mechanism in agricultural products supply chain, and has no effect on the bilateral quality efforts decision, total profit of supply chain and objective efficiency, but can improve both the subjective and objective fairness degree. Meanwhile, supermarket’s altruistic reciprocity can improve the total quality efforts and total profit of supply chain, optimize the objective efficiency and subjective fairness of supply chain.

Technology Sharing and Competitiveness in a Stackelberg Model

The existing literature has made great achievements in technology sharing (licensing patents) contracts, which has defects in the selection of oligopoly models, the setting of innovation subjects, the consideration of product heterogeneity, and production costs. This paper aims to reveal the competitiveness strategies of leaders and followers for innovation, technology sharing, and sharing fees in a Stackelberg market. The three-stage sequential game method is used to achieve the objective. The results are as follows. First, whether an enterprise uses innovation or shares technology is related to the fixed cost of innovation, the return on innovation, and product differentiation. It will hinder innovation activities if the fixed cost of innovation is too high, the return on innovation is too low, or the products are too homogeneous. A relatively low return on innovation makes it possible for the two enterprises to engage in sharing. However, with a relatively high return on innovation, only a high level of product differentiation can ensure technology sharing. Second, the optimal sharing fee is dynamic, showing an upward and then downward trend as the return on innovation grows. Product differentiation has an uncertain impact on the cost. Third, either the leader or the follower is likely to be the optimal bearer of social responsibility depending on the returns on innovation and product differentiation. This study has theoretical significance for optimizing technology-sharing decisions, improving competitiveness for enterprises, and formulating effective industrial policy for the government. And it provides some practical guidance for competition and cooperation between enterprises with technological innovation behavior.

Game analysis of environmental cost allocation in green supply chain under fairness preference

Cost allocation is a way to promote enterprises to actively implement green supply chain management, and the behavior preference of decision makers will affect the process. This paper considers the situation that manufacturer has fairness preference and retailer is fair neutral, and constructs a secondary supply chain composed of a single manufacturer and a single retailer. We explore two models of cost allocation—based on the Stackelberg model, the impact of retailers’ nonparticipation/participation in cost allocation on supply chain is discussed, while through the Nash bargaining model, the range and optimal solution of the environmental cost allocation ratio are determined. And we show how product wholesale prices, retail prices, green innovation investment, and the optimal ratio of environmental cost allocation are influenced by fairness preference. The results show that retailers’ participation in environmental cost allocation will increase the level of product greenness and make the entire supply chain Pareto optimal. The strong fairness preference of manufacturer will weaken the positive effect of retailers participating in cost allocation on the supply chain. Therefore, the government and enterprises should adopt incentive measures to actively promote the collaboration between channel partners in order to share the environmental cost, and manufacturers should pay less attention to fairness.

A two-stage stochastic Stackelberg model for microgrid operation with chance constraints for renewable energy generation uncertainty

In order to reduce greenhouse gas emissions, countries worldwide are transforming their energy systems with higher shares of renewable energy and smart technologies for demand response. Microgrids play an essential role in the transformation of electric grids to smart grids. However, renewable sources present new challenges, particularly those of high variability, which creates uncertainties in the supply side that can affect the security of electricity access at affordable prices. This paper proposes a novel Stackelberg stochastic model to account for different sources of uncertainty. The Stackelberg model considers microgrids as leaders (upper-level problem) with uncertainty regarding the availability of wind and solar sources and electricity prices. Availability of renewable sources is modeled via chance constraints, which allows assessing the risk of microgrids over-committing supply levels. Uncertainty in electricity prices is modeled via a set of demand scenarios with a given probability distribution. The lower-level problem of the Stackelberg problem considers an electricity dispatch problem for each demand scenario. The proposed model allows measuring the strategic actions of microgrids when facing different types of uncertainties and how the smart grid should adapt to guarantee that demand levels are supplied. The results show the effectiveness of the proposed method. We find that microgrids risk levels above 30% do not correlate with further benefits, such as reduced electricity prices. We also identified that in average, depending on the social cost of carbon and demand level, microgrids can cover their own demand and supply 15% of the electricity demand in the grid.

Dynamic Stackelberg duopoly with sticky prices and a myopic follower

In this paper, we study a model of a market with asymmetric information and sticky prices—the dynamic Stackelberg model with a myopic follower and infinite time horizon of Fujiwara ("Economics Bulletin" 12(12), 1–9 (2006)). We perform a comprehensive analysis of the equilibria instead of concentrating on the steady state only. We study both the equilibria for open loop and feedback information structure, which turn out to coincide, and we compare the results with the results for Cournot-Nash equilibria.

Carbon emission reduction of coal-fired power supply chain enterprises under the revenue sharing contract: Perspective of coordination game

Implementing the overall goal of carbon emission reduction and allocating it to specific enterprises under the premise of coordination of interests is not only an important step and link of the development of carbon trading market but also a necessary guarantee for implementing China's overall goal of carbon emission reduction. In this paper, total quantity control of and trading conditions for carbon quota for coal-fired power supply chain enterprises were introduced based on the framework of the Stackelberg model and with the carbon quota constraints being taken into account, a coordination game model of carbon emission reduction of coal-fired power supply chain enterprises was constructed, and a revenue sharing coordination mechanism among supply chain enterprises were designed. In this coordination mechanism, the revenue sharing contract coordination game mechanism in coal-fired power supply chain was designed first on the basis of analyzing the coal production quantity and coal ordering quantity of the coal and electric power enterprises in their decentralized and centralized decision-making and their respective carbon emission reduction and profit situations without contract. And then, the implementation conditions for this revenue sharing contract coordination game was further analyzed, in other words, under the condition that the decision-making level of the coal and electric power enterprises should be equivalent to the centralized decision-making level without contract, it was guaranteed that the profits and carbon emission reduction levels of the coal and electric power enterprises under the revenue sharing contract were greater than under decentralized decision-making without contract, and the global coordination of coal-fired power supply chain was realized. The data calculation examples and parameter sensitivity analysis further verified the results of the theoretical analysis.

Lead-time quotation and hedging coordination in make-to-order supply chain

In the Make-To-Order (MTO) supply chain, for enticing the retailer to choose a shorter delivery lead-time, which improves the manufacturer's wholesale prices, the manufacturer adopts the Production Time Hedging (PTH) strategy as an incentive. Since the profit of the retailer depends not only on the Quoted Delivery Lead-Time (QDLT) but also on the Realized Delivery Lead-Time (RDLT), effectively hedging production time uncertainty reduces tardy delivery. We build an analytical model to investigate how PTH affects the retailer's QDLT decision and the supply chain performance. We consider models for four scenarios, namely (I) the centralized model, (II) the Nash model, (III) the manufacturer-led Stackelberg model, and (IV) the retailer-led Stackelberg model. We derive close-form results on the optimal hedging and QDLT decisions. In models II and III, PTH reduces the QDLT under all the conditions. However, in model IV, PTH can only coordinate the retailer when the hedging cost is low, or the holding cost/tardiness penalty is high. Besides, we find that model III is the dominant scenario for both players. Extending model IV to consider the case where the retailer sources from multiple manufacturers, we show that multiple sourcing is the dominant strategy when a manufacturer's hedging cost is high, or its holding cost/lead-time sensitivity factor is small. From the numerical study, we are interesting to find that the retailer's profit increases with the manufacturer's holding cost/lead-time sensitivity factor.

Demand response strategy of game between power supply and power consumption under multi-type user mode

Dynamic pricing strategy will play an increasingly important role in solving the contradiction between power supply and demand under the current electricity market environment. The performance of different users varies from the same pricing strategy, which further to exacerbate the difficulty of the optimal power dispatching. Therefore, a non-cooperative Stackelberg model based game theory is developed in this paper, which considers both the impact on load fluctuations in power grid and users’ dissatisfaction with electricity consumption. Firstly, users are divided into different types by induction and classification in this model to realize the comprehensive consideration of different types of electricity users. Secondly, two utility functions are set up in this model. The utility function of power supply side is set to represent the benefit obtained in the process of power supply by the power company. The utility function of the power demand side is set to express the dissatisfaction degree of electricity users. The developed model is solved by using the NSGA-Ⅱ algorithm in this paper. Finally, the developed model is applied to the actual case and the sensitivity analysis of relevant parameters is carried out to verify its effectiveness.

Optimal pricing for ferry services with a new entrant: a game-theoretic perspective

This paper investigates the pricing model between an incumbent ferry firm and a new-entrant sea bus firm. First, we study the influences of sea buses entering the ferry market. Next, based on the differences in power structures, we analyze the impact of weather on both companies’ operations in Bertrand and two Stackelberg models, and we consider a case in which both firms belong to the same parent firm. Finally, we study the strategies adopted by the ferry firm to protect its market share against the invasion of sea buses. We find that the sea bus firm’s entrance into the ferry market will increase the number of passengers taking ferries. Both companies’ profits are greater in the two Stackelberg models than in the Bertrand model. The two companies’ profits in the Stackelberg models partially rely on the weather. Finally, vicious price competition will lead to losses on both sides.

A Manipulation Game Based on Machiavellian Strategies

This paper suggests a manipulation game based on Machiavellianism, which is characterized by three concepts: views, tactics, and immorality. We consider a framework where manipulating players can partially control manipulated players’ information and affect both manipulated players’ information and their allocations. The parties involved are constrained both by adverse selection and moral hazard (immorality) restricted to a class of ergodic Bayesian–Markov problems. We investigate a mechanism that maximize the probability that the manipulated players accept the proposal of the manipulators. We show that a mechanism exists and can be found by solving a nonlinear programming problem for a set of constraints. The mechanism is obtained by introducing an auxiliary variable in the nonlinear programming problem and we develop the relations needed to derive the variables of interest. For the manipulation process, players learn their behavior through a sequence of interactions in a repeated game. The manipulators possess and benefit from some commitment power, which describes the distinctive nature of a manipulation game (views). Then, we represent the game using a Stackelberg model. We also compute the Stackelberg equilibrium (tactics) for our game of incomplete information. This novel perspective is of interest for the Bayesian manipulation and persuasion literature. A simulation and analysis over an example for manipulating emotions in negotiation verify the applicability of proposed model.

Profits Optimization Reasearch of Dual-Channel Supply Chain Oriented to Manufacturers Online Customization and Traditional Retail

Under the background of "Internet +", increasing manufacturers sell standard products through retail channels and sell customized products in electronic channel. The competition about dual-channel supply, relationship between production cost and delivery time and the influences of online market acceptance, product customization attribute value, price and delivery time on online customization and traditional retail markets are considered, based on the decision variables of the price of custom and standard products and the guaranteed delivery time, the Stackelberg models are constructed respectively for the manufacturer-led and retail-led supply chain under decentralized system and the overall profits maximization of the supply chain is modeled under centralized system, the existence and uniqueness of the optimal solutions is proved by the optimization theory. The optimal decisions, market demands and enterprises profits under different systems are compared through numerical examples, the relation between the sensitivity coefficients and the optimal enterprises profits are obtained through the parameters sensitivity analysis. The idea of model construction and relevant conclusions are of reference and significance for manufacturing enterprise management practices.

A Decision-making method for the Application of Pavement Repair Materials Based on Stackelberg Model

Highway repair cost mainly depends on the toll income, which in turn is associated with the traffic volume. Scientifically making decision for the application of repair materials is within the reasonable planning of managers regarding road maintenance scale and funds. For exploring effective strategy specific to the highway maintenance plan, the paper focuses on integrating the utility factor of traveler into the highway repair decision. Relevant problems are introduced, together with the establishment of the Stackelberg model. Considering the sensitivity analysis, the heuristic algorithm is employed specific to the traffic volume N. The paper solves the decision-making model with regard to the two expressways’ maintenance plan, as well as derives corresponding strategies. At last, the paper concludes, based on analyses, the general process regarding the maintenance decisions of multiple highways with the traffic volume N, assisting highway operators in making effective decisions.

Optimization of supply chain finance based on Stackelberg model

In recent years, the relationship between the concepts of operations management and finance management has been an attractive area of research among researchers. One of the emerging areas at the beginning of the 21st century in the literature of operations and supply chain management is the topic of supply chain finance (SCF). SCF is a new concept that provides efficient financing of the supply chain, where all parties can balance the working capital and improve cash flow at a reduced cost by utilizing the buyer's or other parties' credit rating. Hence, in this study, an approach to optimize financing based on the Stackelberg model in a three-level supply chain, considering the circumstances in which the supplier is financially constrained for fulfillment the buyer's order and funded by the bank as another member of the supply chain based on the purchase order financing (POF) is discussed. For this purpose, a nonlinear mathematical programming model has been developed to maximize the payoff function of the partners.

A Delivery Time-based Competition Strategy for Community O2O e-tailer: A Study

The community O2O e-tailer can offer the trade of life services within a five-kilometer radius of the community by building online and offline interactive e-tailer platforms between residents and businesses. However, the development of community O2O e-tailer has not been going as planned, failing many expectations. Hence, this paper investigates the two main influencers, namely price and delivery time, by taking the new e-tailers entering the online retail market as the research object. Through a Stackelberg model of community O2O e-tailer and B2C retailer, the competition strategies for the community O2O e-tailers are analyzed. The results revealed that the community O2O e-tailer could not gain any advantage under the homogenized competition. For the sustainable development of e-tailers, a thorough analysis of the community needs, and hence a differentiated competition strategy is required. The post-pandemic period offers a seamless opportunity to do that, which will allow the O2O e-tailer to transform and develop.

Carbon Emission Reduction Decision and Revenue-Sharing Contract with Consumers’ Low-Carbon Preference and CER Cost under Carbon Tax

Since the tax of carbon emission is popular and consumers are exhibiting low-carbon preference, the green manufactures have to spend more extra cost on investing carbon emission reduction (CER) technology to decrease the carbon emission. To encourage the manufacture’s CER investment efforts, this paper explores the impact of carbon tax, CER cost, and consumers’ low-carbon preference on low-carbon decision-making and designs a revenue-sharing contract (RS) by constructing Stackelberg models. Based on the theoretical and numerical analysis, this paper finds that the supply chain would benefit from the increment of consumer’s environmental awareness but be depressed by the increase of the CER investment cost factor. Additionally, there exists a unique optimal carbon tax to make CER degree the maximum. Furthermore, RS can effectively promote manufacturers to reduce carbon emissions and also improve the supply chain efficiency.