Stackelberg Model Research Articles

Green degree decision and pricing strategy of dual-channel supply chains

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.

The Competition Between Taxi Services and On-Demand Ride-Sharing Services: A Service Quality Perspective

On-demand ride-sharing services change our travel behavior, which threatens the survival of taxi services. Motivated by this, this paper examines the impact of on-demand ride-sharing services on taxi services and how to achieve the coexistence of two services from a service quality perspective. This paper analyzes the coexistence condition of two services considering the network effect. First, the profit target for taxi drivers is nonnegative. A Stackelberg model is built in which the taxi service is the leader and the on-demand ride-sharing service is the follower. Then, the reference dependency theory is introduced to modify the profit target of taxi drivers. And the new coexistence condition is compared with the benchmark status. The results find that the coexistence of the two services depends on the type of riders and the quality difference in both cases. When two services and riders are highly heterogenous, two services are more likely to coexist. Services with different qualities could better satisfy the diverse preferences of riders. Considering taxi profit without competition as the profit reference point, the requirement of service quality difference and the diversity of rider composition is increased. In terms of the network effect, the negative network effect is more beneficial to the coexistence of two services.

Decision Analysis of Game Behavior for the Fresh Food Industry: Potential Entrants, Incumbents and Consumers

This paper conducts a decision analysis of game behavior for the fresh food industry, including potential entrants, incumbents and consumers. Potential entrants are the key research object in the analysis of game behavior. The Stackelberg model, considering the uncertainty of market, consumer preference, freshness and greenness of fresh products, is used to analyze the best entry strategies for potential entrants. This paper then establishes an evolutionary game model to further analyze the most optimal entry mode of potential entrants. The combination of two game models can help potential entrants determine the optimal price, output, product freshness, greenness and sales channels.

Stackelberg game analysis of the energy performance contracting considering altruistic preferences

The Stackelberg game analysis of an Energy Performance Contracting(EPC) is established to correctly analyze the impact of altruistic preference behaviors on the decision-makers, energy service companies(ESCOs) and energy-consuming units(EUs). Its motivation comes from the fact that, to achieve a win-win situation, EUs usually engage in altruistic behaviors, but the implementation results of the EPC are always contrary to their expectations. Using nonlinear optimization theory, analyzed the decisions of the Stackelberg models under different altruistic preference attributes, and then compared the impacts of altruistic preferences on decisions and profits. Results reveal: (1)compared to a situation lacking altruistic preference, when the leader, the EU, has an altruistic preference, the EU only needs to transfer a small part of its own interests to significantly increase the ESCO's profit and ultimately improve the overall EPC profit; (2) the altruistic preference of the ESCO functions akin to a "poison," engrossing the company in the satisfaction derived from the increased revenue of the energy-consuming entity and gradually eroding its own profits; and (3)the altruistic preference behavior of both parties is a kind of “benefit transfer behavior,” which is conducive to stable operation and long-term development of EPC industry. The research results can provide a theoretical reference to enhance the development of energy-saving service industry.

Effect of Governmental Subsidies on Green Energy Supply Chains: A Perspective of Meteorological Disasters

The energy sector, serving as a pivotal propellant within the macroeconomic framework, finds its production, distribution, and consumption aspects considerably influenced by climatic variations. In this study, a two-tier Stackelberg model for the green energy supply chain is developed, which is employed to analyze the profit disparities between suppliers and retailers both in the absence and presence of meteorological disasters. Furthermore, the research delves into the optimal supply chain strategies under three distinct scenarios in the context of meteorological disasters. A comparative analysis is conducted to examine the decision-making variances and the shifts in the interests of each supply chain participant under these scenarios. The findings reveal two critical insights: First, meteorological disasters detrimentally affect the environmental friendliness of energy products, as well as the profits of both retailers and suppliers. Second, the selection of the optimal strategy varies depending on the evaluation criterion used. When product greenness is the metric, subsidies aimed at promoting sales costs emerge as the superior strategy. Conversely, for retailers and suppliers, subsidies that target the environmental friendliness of energy products prove to be the most effective. Based on the conclusions, the paper also makes recommendations for governments and companies.

Comparison of Cournot Duopoly Model and Stackelberg Model

Comparison of Cournot Duopoly Model and Stackelberg Model

The optimal reinsurance strategy with price-competition between two reinsurers

We study optimal reinsurance for an insurer and two reinsurers in the market through stochastic game theory. The relationship between the insurer and reinsurers is described by a Stackelberg model, where reinsurers, as market leaders, set prices for reinsurance treaties, and the insurer, as a price taker, determines reinsurance demand. Furthermore, we employ a Nash game to model the price competition between the two reinsurers who adopt different premium principles: the variance premium principle and the expected value premium principle. Both the insurer and reinsurers aim to maximize their respective mean-variance cost functions, leading to a time inconsistency control problem. This issue is resolved using a corresponding extended Hamilton-Jacobi-Bellman equation in the game-theoretic framework. We find that the insurer will adopt propositional and excess-of-loss reinsurance strategies with two reinsurers, respectively. Moreover, under an exponential claim size distribution, there exists a unique equilibrium reinsurance premium strategy. Our numerical analysis illuminates the effects of claim size, risk aversion, and the interest rates of the insurer and reinsurers on the equilibrium reinsurance and premium strategies, enhancing the understanding of competition in the reinsurance market.

Photovoltaic sizing assessment for microgrid communities under load shifting constraints and endogenous electricity prices: A Stackelberg approach

Renewable energy resources are crucial for decarbonizing the energy sector. Distributed energy resources, such as renewable generation by microgrids, aid the transition to net-zero systems. As microgrids proliferate, renewable generation often exceeds self-supply capacities, necessitating either the sale of excess electricity or the implementation of demand-response strategies. The optimal approach for microgrids (selling or shifting demand) hinges on electricity prices. This article examines the interplay between microgrids, demand response, photovoltaic investments, and pricing mechanisms. A novel Stackelberg model is proposed to minimize microgrid investment and operational costs. The upper-level problem determines energy community investments and demand response levels based on electricity prices, while the lower-level problem addresses market dispatch and endogenous pricing for microgrids. Case studies with varying battery storage levels, demand response limits, and pricing mechanisms are conducted. The research results illustrate the responsiveness of market transactions to supply conditions and pricing. Key findings show that microgrid flexibility in demand response reduces grid dependency, prompting significant investments in solar energy and battery storage, driven by economic incentives, especially under spot market conditions. Investments in solar energy more than double when microgrids trade energy at spot prices compared to flat prices.

Decentralization policies and sustainable rural development: A path to eradicating poverty (SDG 1) and hunger (SDG 2)

AbstractRural infrastructure development is crucial for achieving sustainable development. It enhances quality of life, improves connectivity, promotes economic growth, and supports food security. Whereas rural infrastructure development is influenced by fiscal decentralization, which enables local administrations to prioritize investments and allocate resources based on local needs and priorities. Given this background, this empirical study investigates the impact of devolution reform policy on rural infrastructure development in Pakistan, employing the Stackelberg model. The findings exhibit a positive relationship between subnational government spending through decentralization and the accessibility to transport and communication services, rural development, and development of irrigation infrastructure. The theoretical model proposes that decentralized information permits efficient decision‐making, with local authorities better equipped to deliver public services aligned with local preferences. Increased public utilization of services is expected as a result of decentralization. The combination of empirical analysis and theoretical foundations suggests that the 2001 decentralization policy enhances the accountability of subnational governments. By providing them with more informed and essential benefits for resource allocation according to voter priorities, this policy ultimately increases the efficiency of public expenditures in achieving sustainable development.

Research on Division of Labor Decision and System Stability of Swarm Robots Based on Mutual Information.

In rational decision-making processes, the information interaction among individual robots is a critical factor influencing system stability. We establish a game-theoretic model based on mutual information to address division of labor decision-making and stability issues arising from differential information interaction among swarm robots. Firstly, a mutual information model is employed to measure the information interaction among robots and analyze its influence on the behavior of individual robots. Secondly, employing the Cournot model and the Stackelberg model, we model the diverse decision-making behaviors of swarm robots influenced by discrepancies in mutual information. The intricate decision dynamics exhibited by the system under the disparity mutual information values during the game process, along with the stability of Nash equilibrium points, are analyzed. Finally, dynamic complexity simulations of the game models are simulated under the disparity mutual information values: (1) When ν1 of the game model varies within a certain range, the Nash equilibrium point loses stability and enters a chaotic state. (2) As I(X;Y) increases, the decision-making pattern of robots transitions gradually from the Cournot game to the Stackelberg game. Concurrently, the sensitivity of swarm robotics systems to changes in decision parameter decreases, reducing the likelihood of the system entering a chaotic state.

How does the power structure affect the acquisition price and inventory decisions in the reverse supply chain

With growing concerns about environmental sustainability, reverse supply chains play a crucial role in recycling, remanufacturing, and reducing waste. Investigating the power structure’s impact on decisions related to acquisition prices and inventory management can provide insights into the integration of sustainable practices. This study analyzes a reverse supply chain with a supplier and a remanufacturer, in which the supplier provides the remanufacturer with sorted used cores. We investigate the acquisition pricing and inventory decisions under different power structures (supplierled Stackelberg model, remanufacturer-led Stackelberg model) through game theory analysis. We first establish the centralized model to explore optimal acquisition decisions and profit of the total system. Then we evaluate the acquisition quantity, wholesale prices, the profit of supplier and remanufacturer in the supplier-led model and in the remanufacturer-led model. Finally, the impact of power structure on the performance of supplier and remanufacturer are explored by numerical analysis, as well as the supply chain system. Our significant findings show that (i) the total profit of the supplier-led and remanufacturer-led reverse supply chain are less than the centralized model due to the double marginalization; (ii) the remanufacturer-led reverse supply chain is superior to the supplier-led model reverse supply chain; (iii) the selected grades in the supplier-led model is proved the same as that in the remanufacturer-led model, which could not been affected by the wholesale price; (iv) the greater the inventory risk (the uncertainty in demand), the greater the profit share for the remanufacturer (supplier) in the supplier-led (remanufacturer-led) model.

The impact of platform audits on the manipulation of online reviews

To reduce sellers’ manipulation of online reviews, platforms conduct audits and impose penalties on abusive practices. In this article, we study the effectiveness of self-regulation in preventing fake reviews and increasing consumer and social welfare. To this purpose, we use a Stackelberg model with the platform as the leader. Our major contribution is to explain the auditing game between the platform and the seller. These are our major findings. First, we found a self-regulation’s Achilles’ heel. Despite its noble intent, the self-regulation system often falters. Why? The platform faces a powerful incentive to accommodate fake reviews, especially when consumers heavily rely on the seller’s information and regulatory repercussions remain mild. For this reason, consumer activism and external supervision are the key factors leading the platform to audit the seller. Second, we discovered the paradox of fake reviews, establishing the conditions under which, counter-intuitively, fake reviews create social value. Finally, by considering an endogenous retail price, we found evidence of a complex relationship between pricing, auditing, and review manipulation policies, all dependent on consumer sophistication and product quality, which can only be analyzed numerically, as there is no closed-form solution.

Contract adoption of motivating green technological innovation in a supply chain

AbstractGreen technological innovation has been widely recognized around the world; however, consumer environmental awareness may result in uncertain market demand growth and lead to manufacturers’ risk‐averse attitude towards green technological innovation. This paper focuses on the contract adoption problem of a risk‐averse manufacturer who is responsible for green technological innovation, through a resell contract (RC) or agency contract (AC) with a retail platform. Stackelberg models are built, and the conditional value at risk method is used to measure the manufacturer's risk‐averse behavior. The differences between two contracts are compared. We find that when the commission rate is less than some threshold, the green technological level under AC is greater than that under RC regardless of the fixed cost coefficient, otherwise the green technological level under RC is higher. Further, there is the dual excellent region for AC and RC where the manufacturer can not only obtain a higher level of green technology but also achieve better utility. Finally, consumer surplus and social welfare under two contracts are performed through numerical experiments.

Contracting Supply Chains Considering Retailers’ Marketing Efforts

Strategic cooperation has garnered significant attention in business. In this study, we explored the operating mechanisms of supply chains utilizing three Stackelberg models, in the following ascending order of cooperation level: price only, marketing cost sharing, and cross-shareholding. Further, we investigated the impact of cooperation on prices, marketing efforts, and profits, and analyzed the strategic cooperation preferences of different supply chain members. The results show that the influence of the level of cooperation on the wholesale and selling price is nonlinear. Interestingly, increased levels of cooperation do not always result in better outcomes. The marketing cost-sharing strategy aggravates the marketing burden on retailers. In contrast, the cross-shareholding strategy not only increases the total marketing effort level, but also efficiently reduces the burden of marketing on retailers. Moreover, all cooperation strategies solely benefit manufacturers rather than retailers, and not all of them improve the supply chain’s performance. Finally, the cross-shareholding cooperation strategy only maximizes the consumer surplus and social welfare under certain conditions. Overall, our study describes the operational mechanisms of diverse cooperative strategies and provides managerial guidance for those seeking to enhance marketing efforts and economic and social performance using a cooperation strategy.

Effects of manufacturer fairness concerns and carbon emission reduction investment on pricing decisions under countervailing power

Government policies have focused on carbon emissions from the green supply chain (GSC). To discuss how price decision-making in GSC is affected by the manufacturer's fairness concerns, retailer's countervailing power, and carbon emissions reduction, the Stackelberg model assumes that consumers are environmentally sensitive. To explore this problem considering the type of manufacturer's behavior preferences, we built four models that pertain to the following two situations: the retailer has countervailing power, and the retailer has no countervailing power. The results show that (1) the manufacturer's disadvantageous fairness concerns reduce the overall supply chain profits and utility; influenced by countervailing power, the members witness a win-win situation; (2) moderate advantageous fairness concerns benefit GSC members; furthermore, under advantageous fairness concerns, the manufacturer can “give profits” to the retailer; (3) affected by the retailer's countervailing power, no bargaining agreement is made in the GSC under advantageous fairness concerns. Finally, the interplay between member decisions and consumer sensitivity is explored. This study can help manufacturers achieve emission reduction targets in response to consumer environmental awareness and government regulation.

Manufacturer vs. Retailer: A Comparative Analysis of Different Government Subsidy Strategies in a Dual-Channel Supply Chain Considering Green Quality and Channel Preferences

As escalating environmental pollution results from economic development, the green supply chain is vital in enhancing ecological quality. In light of the rapid growth of online shopping, the dual-channel supply chain has gained significant popularity. Governments have implemented policies to achieve carbon peaks and neutrality worldwide. Considering green quality and channel preferences, this study constructs a Stackelberg model led by the manufacturer within a dual-channel supply chain to compare the effects under two government subsidy strategies. A Stackelberg game-theoretic approach is applied to analyze the model. The findings indicate the following: (1) Increases in the subsidy coefficient can increase product greenness and the overall profit in both subsidy strategies, which makes sense; (2) When direct sales channels become dominant, subsidizing the manufacturer proves superior to subsidizing the retailer in terms of promoting green quality and overall profit, which extends existing studies of government subsidy decisions. Furthermore, subsidizing the retailer may negatively affect the total supply chain profit; (3) Consistent with previous literature, intense competition between manufacturers and retailers is expected to enhance the overall profit of the supply chain; (4) Interestingly, customer preference for online channels does not influence product green quality under manufacturer subsidization strategies but exhibits a negative impact under retailer subsidization strategies. Finally, this research provides managerial implications for decision-makers and potential issues for future research.

Transmission planning in an imperfectly competitive power sector with environmental externalities

Policymakers face the challenge of integrating intermittent output from variable renewable energy (VRE). Even in a well-functioning power sector with flexible generation, producers’ incentives may not align with society’s welfare-maximisation objective. At the same time, political pressure can obstruct policymakers from pricing damage from CO2 emissions according to its social costs. In facilitating decarbonisation, transmission planning will have to adapt to such economic and environmental distortions. Using a Stackelberg model of the Nordic power sector, we find that a first-best transmission-expansion plan involves better resource sharing between zones, which actually reduces the need for some VRE adoption. Next, we allow for departures from perfect competition and identify an extended transmission-expansion plan under market power by nuclear plants. By contrast, temporal arbitrage by hydro reservoirs does not necessitate transmission expansion beyond that of perfect competition because it incentivises sufficient VRE adoption using existing lines. Meanwhile, incomplete CO2 pricing under perfect competition requires a transmission plan that matches hydro-rich zones with sites for VRE adoption. However, since incomplete CO2 pricing leaves fossil-fuelled generation economically viable, it reduces the leverage of strategic producers, thereby catalysing less (more) extensive transmission expansion under market power by nuclear (hydro) plants.

Research on pricing strategy of dual-channel supply chain based on blockchain technology under carbon trading

In the context of the dual-carbon goal, it is of great significance to study the application of blockchain technology in the dual-channel supply chain under the carbon trading mechanism for the carbon emission reduction of enterprises and the overall profit maximization of the supply chain.In this paper, two decision models of the supply chain under secondary carbon trading are constructed to analyze the two cases of whether to adopt blockchain technology. Stackelberg model is used to study the impact of blockchain technology on the pricing decision of the dual-channel supply chain under carbon trading, and the two models are compared and analyzed.According to the research results, after the application of blockchain technology, wholesale prices, direct sales prices, retail prices, and profits of retailers and manufacturers have increased compared with the non-use of blockchain technology, which is conducive to promoting the development of carbon emission reduction for manufacturers.

Optimal pricing strategy in the closed-loop supply chain using game theory under government subsidy scenario: A case study

Automotive battery production always receives government supports which directly affect the recycling of used products collected from secondary markets. Accordingly, an optimal product pricing strategy and efficient policy suggestions must be provided for this industry. This study used Stackelberg models to analyze three categories of pricing strategies related to the recycling process of car batteries when government subsidy is paid. These models are applied to make optimal decisions in two centralized and decentralized modes to investigate the links between and influences of different parameters of the problem on one another. Finally, a numerical example based on a real case study in Iran is applied to the models. The results indicate that making centralized decisions leads to a higher level of profitability than decentralized decision-making in the under-study industry. Accordingly, maintaining coordination and integration among the supply chain components in the decision-making process increases the profitability of the entire network.

Digitalization and carbon emission reduction technology R&D in a Stackelberg model

ABSTRACT This paper constructs a four-stage sequential game model considering digitalization and carbon emission reduction decisions, examines the effects of digitalization on firms’ emission reduction and carbon emission reduction technology R&D, and analyzes the optimal digitalization level. The results show that emissions reduction is correlated with the digitalization level, the cost-reduction effects, and the carbon tax rate; technology R&D benefits from digitalization support; there exists an optimal digitalization level that is nonlinearly affected by the carbon tax rate, and the digitalization level that satisfies the maximization of social welfare is higher, so the government should provide digitalization incentives.