manufacturer-Stackelberg Game Research Articles

Game theoretical analysis in two-echelon sustainable supply chains to manage and coordinate strategic decisions

Business firms and consumers are increasingly and rapidly realizing the benefits of adopting environmental responsibility. The business firms stress including it in their supply chain strategy and/or operations. This paper explores the environmental consciousness and quality attentiveness of consumers in a supply chain. Demand for the product depends on its price, eco-friendly level, and quality of the product. Three decentralized models are developed under three different game theoretical settings. A comparative study of the three game-theoretical models reveals several characteristics. It determines conditions under which channel members can decide the policy for the best possible benefit. The present work explores the effect of customer environmental awareness on the optimal decision. Production of eco-friendly items is also the prime consideration of our paper. It reveals that the manufacturer gets the most profit in the manufacturer Stackelberg game model, but the retailer gets the maximum profit from the retailer Stackelberg game model. Although channel members prefer their leading position to make the game theoretical decision-making process, the most decentralized channel profit is obtained from the Nash game model. Thus, consumers will also benefit, and the best channel profit can be obtained if the channel members agree to make decentralized decisions using the Nash game model. The centralized channel profit outperforms all three decentralized channel profits. The paper applies the concepts of sub-game perfect equilibrium and alternating offer bargaining to coordinate the channel and distribute surplus profit. Finally, analytical results are verified using numerical examples.

Examining B2B channel decision-making within differential quality-level zone: a supply chain design using a non-cooperative strategic game theoretic approach (“Stackelberg Supply Chain for B2B”)

Purpose The consumers want to purchase the target products in the right place, whereas the manufacturers want to allocate their possible products to optimal distribution channels. The manufacturer must know how to handle itself in this business. The study aims to examine the B2B channel decision-making with different product qualities in a non-cooperative supply chain. Design/methodology/approach The authors develop a B2B Manufacturer-Stackelberg game as an analytical framework, combining asymmetric preference of purchase channels choice by the consumers, a continuous quality setting of the manufacturer and differential channel structure to study the manufacturer’s product strategy and channel optimisation. By horizontal comparisons across four channel structures, product variety can be classified into the differential quality-level zone through exogenous quality intervention, and the preference of manufacturers in each quality-level zone within the structures can be ranked. Findings Theoretically and practically, the hybrid-channel structure should be completely neglected when the direct channel dominates the retail channel. In contrast, dual-channel structures dominate single channels irrespective of the channel power, and channel preferences between high-quality and low-quality zones are stable, whereas the preference in medium-quality zone is unstable. In addition, the supply chain system cannot achieve global Pareto improvement without any additional coordination mechanism between the manufacturer and the retailer. Originality/value The extended results by numerical examples suggest that the bigger the area of the medium-quality zone, the more significant the product variety of the manufacturer.

Operation strategy for new energy vehicle enterprises based on dual credit policy

<p style='text-indent:20px;'>This article constructs a two-stage supply chain consisting of a manufacturer (producing both fuel vehicles (FV) and new energy vehicles) and a retailer (selling both fuel vehicles and new energy vehicles) based on dual credit policy, considers three different power structure models, including the vertical Nash game model, the manufacturer Stackelberg game model, the retailer Stackelberg game model, and explores the operational strategy issues of new energy vehicle (NEV) enterprises under the dual credit policy. By comparing the optimal equilibrium solutions under different channel power structures, our findings indicate that (1) When the demand function is linear, the vertical Nash game model can achieve the highest system profit of the automotive supply chain, and in the manufacturer Stackelberg game model, the profit of the automaker is higher than that of the retailer, while in the retailer Stackelberg game model, the profit of the automaker is lower than that of the retailer. (2) The demand and pricing for FV and NEV in different models are determined by the range of FV and NEV production costs, credit trading prices, and the proportion of NEV credits. (3) Both the increase in the credit trading prices and the proportion of NEV credits will promote increased profits for the manufacturer and retailer. (4) The increase of the price sensitivity coefficient will reduce the demand as well as the profit of auto supply chain members.</p>

Decision Analysis of Manufacturer-Led Closed-Loop Supply Chain Considering Corporate Social Responsibility.

With the rapid development of the economy, a growing number of consumers and enterprises are paying attention to corporate social responsibility (CSR). Meanwhile, there exist a variety of conflicts in closed-loop supply chain management. To analyse and deal with the decision problems of the manufacturer-led closed-loop supply chain with CSR, by using the manufacturer Stackelberg game, we construct some basic models considering CSR, and exploit them to analyse the optimal decisions of supply chains with and without CSR under centralized and decentralized decision making and explore the influence of CSR on supply chain, and then we establish a coordination mechanism through two-part tariff.

Effects of channel power structures on pricing and service provision decisions in a supply chain: A perspective of demand disruptions

This paper investigates the service investment and pricing decisions under different power structures when there exist demand disruptions. We consider a supply chain consisting of a single manufacturer and a single retailer, and establish a game theory model under three typical channel power structures: Manufacturer Stackelberg game, Retailer Stackelberg game, and Nash game. We find that when the demand is disrupted, whether it is a centralized system or decentralized system with different power structures, the service level and production quantity are robust when the demand disruption is sufficiently small, and the wholesale price is also robust under certain circumstance. The comparison results of equilibrium pricing and service level under different power structures are affected by the supply chain power and service cost coefficient no matter who provides the demand-enhancing services. Moreover, it can be found that the power structure most suitable for the manufacturer or the retailer is not invariable and the results are related to the change of some parameters.

Optimizing payment schemes in a decentralized supply chain: A Stackelberg game with quality investment and bank credit

In reality, supply chain members need to determine the best suitable payment scheme when transacting with their business partners. We investigate the optimization of payment schemes with quality investment and bank credit in a decentralized supply chain consisting of one manufacturer and one retailer, both of which are capital-constrained and in need of short-term financing from the bank for their operations. First, we provide a function to describe the market demand by analyzing the impacts of price and quality on the demand. Then, we develop the profit functions of advance payment scheme (APS), normal payment scheme (NPS), and delay payment scheme (DPS) for the capital-constrained manufacturer and retailer. Furthermore, we construct the joint pricing and quality level decision models under APS, NPS, and DPS to determine the optimal profits of the supply chain, manufacturer, and retailer, respectively. On this basis, we conduct theoretical and numerical analyses on the selection of the optimal payment scheme. Our research results in manufacturer Stackelberg game indicate that, the optimal payment scheme from the perspective of supply chain, manufacturer or retailer is not uniquely determined, but generally tends to be DPS. For different perspectives, the optimal payment schemes may be different, and can be affected by the parameters. Especially, for increasing bank rate for the loan of the retailer, the supply chain, manufacturer and retailer generally tend to select DPS. In addition, for increasing bank rate for the loan of the manufacturer, the supply chain and retailer tend to select DPS, but the manufacturer tends to select APS.

Pricing and Channel Coordination in Online-to-Offline Supply Chain Considering Corporate Environmental Responsibility and Lateral Inventory Transshipment

In this study, we investigate pricing policy and coordination conditions in an online-to-offline supply chain considering corporate environmental responsibility and lateral inventory transshipment. First, we provide demand functions to capture effects of price, corporate environmental responsibility level, and preference degree of the consumer to online channel. Then, we build profit functions and develop three joint pricing and corporate environmental responsibility-level decision models for centralized decision (Scenario CD), retailer Stackelberg game (Scenario RS), and manufacturer Stackelberg game (Scenario MS). Furthermore, we determine the optimal decision policies by solving developed models, and conduct sensitivity analysis of significant factors. Finally, we use a revenue-sharing contract to realize supply chain coordination and find coordination conditions for Scenario RS and MS, and further show the impacts of revenue-sharing rate and investment cost sensitivity on the conditions using numerical studies. We find that optimal joint decision policies can be affected by significant factors to a varying degree. In certain conditions, the revenue-sharing contract can coordinate online-to-offline supply chains considering corporate environmental responsibility and lateral inventory transshipment. Our study proposes a new decision problem, constructs new joint decision models, determines new optimal joint policies, conducts new coordination analysis, and thus contributes to the research on supply chain operations considering corporate environmental responsibility and lateral inventory transshipment.

Pricing and ordering strategies in a two-echelon supply chain under price discount policy: a Stackelberg game approach

Supply chain management coordinates different strategies for the production system. The manufacturer requires some incentive schemes to motivate the retailer to change his policy, optimal for the whole system. This paper suggests a discount mechanism by which companies can coordinate their ordering and pricing strategies throughout a supply chain model with a single manufacturer and single retailer. Also, the demand curve is iso-elastic price sensitive. Channel members have decided their selling price and order quantity jointly and independently to maximize the supply chain profit. A coordination mechanism is proposed based on quantity discounts to correlate pricing and ordering strategies simultaneously. The decentralized case is analyzed under the manufacturer-Stackelberg game approach. The result of numerical investigation shows that the suggested discount mechanism has improved the supply chain profit as well as each channel member's profit in comparison with the centralized and decentralized decisions without discount.

Possibilistic cooperative advertising and pricing games for a two-echelon supply chain

This paper addresses coordination of pricing and cooperative advertising policies in a two-echelon supply chain under fuzziness of demand function’s parameters and manufacturing costs. Three different decentralized scenarios are introduced with regard to the players’ market power: (1) manufacturer-Stackelberg game where the manufacturer has the dominant power in the channel, (2) retailer-Stackelberg game where the manufacturer follows the strategies taken by a dominant retailer, and (3) Nash game where the manufacture and the retailer with the same market power make the decisions simultaneously. The equilibrium wholesale and retail prices, national and local advertising expenditures, and participation rate are determined using the concepts of possibilistic game theory, and the results are compared with the centralized channel scenario. A numerical example is presented to illustrate the effectiveness of the proposed modeling approach, and sensitivity analyses are carried out to measure the impact of the demand function’s parameters as well as the levels of uncertainty.

Implications of Product Substitutability in a Distribution Channel

This paper examines the effect of product substitutability on the equilibrium profits in a distribution channel, where two symmetric manufacturers sell substitutable products to consumers through a non-exclusive retailer. Conventional wisdom suggests that the retailer will be better off while the manufacturers will be worse off, the more substitutable are the manufacturers’ products, owing to the competition effect of substitutability. By contrast, we identify the hitherto neglected demand effect of substitutability that could alter this result. As products become more substitutable, upstream competition is intensified but the demand may expand. In a Manufacturer-Stackelberg game facing a class of aggregate demand functions with a constant product substitutability, we show that the interests of the retailer and manufacturers can be aligned in terms of product substitutability. Surprisingly, the conventional result can be even completely reversed such that the manufacturers benefit from a certain level of substitutability. In the extensions, we examine alternative utility-based Hotelling model and different bargaining power balance, respectively, further validating the important role of demand effect. For example, as the retailer gains more bargaining power under linear demands, the (negative) demand effect can overshadow the (positive) competition effect such that a higher degree of substitutability could actually hurt the retailer. Our findings have substantive implications for persuasive advertising and category management.

Pricing and inventory decisions in a manufacturer-Stackelberg supply chain with deteriorating items

PurposeIntegrated decision of pricing and inventory control for a deteriorating product is known as a good practice in revenue management discipline. The purpose of this paper is to formulate the problem of joint pricing and inventory decision in a manufacturer–retailer supply chain with deteriorating items and backlogging. Furthermore, the other purpose is to develop an efficient algorithm to obtain the equilibrium solution.Design/methodology/approachIn this study, a manufacturer–retailer supply chain of a deteriorating product is considered. The retailer aims to maximize his profit, for which he jointly determines the retail price and replenishment cycle. In addition, the manufacturer should decide on the wholesale price to maximize her profit. Considering the problem as a manufacturer-Stackelberg game, the equilibrium solution is formulated and analyzed for both the manufacturer and the retailer. Moreover, two different procedures are developed to obtain the equilibrium solution. The first procedure is an exact procedure for the Taylor-approximated model and the second is a simulated annealing (SA)-embedded algorithm for the actual model.FindingsIt is found that Taylor-approximated procedure is more accurate than SA-embedded procedure. However, the latter is more time-efficient. Moreover, it is observed that the obtained solution is highly sensitive to demand parameters, while it is not the case for the cost parameters.Originality/valueThe paper models a real industrial problem, and its results could be used in analyzing any manufacturer–retailer supply chain with deteriorating items. Among others, the fruit and vegetable supply chains are more likely to have a similar setting, and this study’s results are applicable for such chains in food industry.

Which contract is more effective in improving product greenness under different power structures: Revenue sharing or cost sharing?

In practice, a large number of enterprises tend to cooperate to improve product greenness by various contract mechanisms, such as revenue sharing and cost sharing contracts. The objective of this study is to examine which contract is more effective in motivating enterprises to boost product greenness and benefits them under different power structures. Specifically, we consider a differential game framework where a manufacturer produces a particular green product and sells it to end consumers through a retailer. The manufacturer decides the innovation investment to increase product greenness, and wholesale price, while the retailer sets the retail margin; the manufacturer and the retailer implement a revenue sharing or cost sharing contract under the manufacturer or retailer Stackelberg game, where the sharing proportion is also determined by the retailer. Intuitively, the cost sharing contract would result in higher product greenness since it is widely used to improve the manufacturer’s innovation investment directly. However, our analysis shows that this intuition holds only under the retailer Stackelberg game. When the manufacturer acts as the leader of the Stackelberg game, the revenue sharing contract brings higher product greenness, which makes the manufacturer and the retailer better off. This is because the retailer sets a sufficiently high revenue sharing proportion, which gives the manufacturer additional capital to invest in product innovation. Whereas, the revenue sharing contract hurts the two players under the retailer Stackelberg game. Moreover, we show that a revenue sharing and cooperative investment contract can improve the product greenness and the two players’ profits, relative to one kind of contract under the manufacturer Stackelberg game.

Implications for pure profit, environmental impact and social welfare in a socially responsible supply chain

PurposeMembers in a supply chain account for corporate social responsibility (CSR) in different ways. This paper considers a socially responsible supply chain in which the manufacturer innovates in a sustainable product while the retailer exhibits CSR concerns. This paper aims to investigate how socially responsible behavior, namely, sustainable innovations or CSR concerns, affects the pure profit, environmental impact and social welfare, in such a socially responsible supply chain.Design/methodology/approachThis paper first constructs an integrated case as a benchmark and then develops a Manufacturer-Stackelberg game in a decentralized scenario. The pure profit, environmental impact and social welfare are confirmed and analyzed in centralized and decentralized cases. Moreover, two unique coordinating contracts, i.e. wholesale price discount contract and revenue-sharing contract, are used in this socially responsible supply chain.FindingsAnalytical analysis shows that, under certain conditions, the optimal CSR strategies hold for maximizing pure channel profit, minimizing environmental impact and maximizing social welfare. Whether the performance in a centralized case outnumbers that in a decentralized case depends on the CSR concerns level and environment-friendly degree of the product. In addition, it is found that a wholesale price discount contract is better for the retailer whereas a revenue-sharing contract is better for the manufacturer in pure profit to improve coordinating efficiency.Practical implicationsThese results can offer managerial implications to the socially responsible supply chain in terms of pricing decisions, CSR strategies and sustainability innovations. Specifically, under certain conditions, placing more CSR concerns level increases pure channel profit and the social welfare. A balance between the pure profit and the social welfare is hereby achieved for the two socially responsible individuals by designing a proper contract.Originality/valueTo the best of the authors’ knowledge, this paper is among the first studies so far to combine the CSR concerns strategy and sustainability innovation into a socially responsible supply chain.

Decision-making of online channels under three power structures

In recent years, e-commerce has developed rapidly. Many manufacturers are beginning to integrate with the Internet and regard online platforms, such as online marketplaces and self-owned online malls, as important sale channels for their products. Considering the difference of shopping experience between the two online channels, this paper models price and service competition between the two channels. This paper discusses the decisions of supply chain participants with three power structures, that is, the manufacturer Stackelberg game, the online marketplace firm Stackelberg game, and the Nash game. The results show that the channel service level and the consumer sensitivity to channel service positively affect the channel price and demand. We characterize a threshold for the wholesale price. When the wholesale price is below the threshold, the channel prices are lowest in the Nash game, and when the wholesale price is greater than the threshold, the channel prices are lowest when the manufacture acts as the leader. Differentiated services can improve the supply chain participants’ profits and the system’s profit compared with the same service. More interestingly, this paper finds that the online marketplace firm should pay attention to improving its service level, while the manufacturer should pay attention to other work differently, such as focusing on generating promotional value and shaping corporate brand image by the self-owned online mall channel.

Game-Theoretic Analysis to Examine How Government Subsidy Policies Affect a Closed-Loop Supply Chain Decision

The pros and cons of government subsidy policies in a closed-loop supply chain (CLSC) setting on optimal pricing, investment decisions in improving product quality, and used product collection under social welfare (SW) optimization goal have not been examined comprehensively. This study compares the outcomes of three government policies under manufacturer-Stackelberg (MS) and retailer-Stackelberg (RS), namely (i) direct subsidy to the consumer, (ii) subsidy to the manufacturer to stimulate used product collection, and (iii) subsidy to the manufacturer to improve product quality. Results demonstrate that the greening level, used product collection, and SW are always higher under the RS game, but the rate of a subsidy granted by the government is always higher under the MS game. Profits for the CLSC members and SW are always higher if the government provides a subsidy directly to the consumer, but productivity of investment in the perspective of the manufacturer or government are less. In a second policy, the government organizations grant a subsidy to the manufacturer to stimulate used product collection, but it does not necessarily yield the desired outcome compared to others. In a third policy, the manufacturer receives a subsidy on a research and development (R&D) investment, but it yields a sub-optimal greening level. This study reveals that the outcomes of subsidy policies can bring benefit to consumers and add a degree of complication for CLSC members; government organizations need to inspect carefully among attributes, mainly product type, power of CLSC members, and investment efficiency for the manufacturer, before implementing any subsidy policies so that it can lead to an environmentally and economically viable outcome.

A hybrid circular economy - Game theoretical approach in a dual-channel green supply chain considering sale’s effort, delivery time, and hybrid remanufacturing

The circular economy (CE) and the marketing activities are the key subjects to attract the market share in today’s complex supply chain. Here, dual selling channels, the online delivery time, and the distributor sales effort are considered as marketing activities to attract the customers. Moreover, in order to meets the economic and environmental principles of the CE, three responsibilities to ease the carbon emission, as approaches for the return on investment, are devised, including investment in the green production, the cap and trade regulation, and the hybrid remanufacturing via both the manufacturer and the distributor under the technology license. This such complex supply chain needs to determine the equilibrium amounts of the distinguishing elements, including the pricing strategy, remanufacturing approaches, delivery time, and sales effort to abate the conflicts between the members, and consequently, to enhance the economic and CE objectives of the supply chain (SC). In order to obtain the equilibrium decision makings, three game theoretical approaches, including the manufacturer-Stackelberg game (SM), the distributor-Stackelberg game (SR) and the Nash game (N) are employed. The interaction between the game sequences and the remanufacturing process is the key purpose of this paper to not only maximize the profit of SC but also to enrich the CE and marketing goals of this research. The outcomes presented that the SM game, where the manufacturer remanufactures most of the defected products which are collected via the distributor, is the best game strategy to improve the profits of both the distributor and the manufacturer, and also to enhance the other distinguishing elements. In addition, in the SR game, when most of the returns remanufacture via the distributor under the manufacturer license, it not only maximizes the profits of members but also lead to the improvement of the distinguishing elements. In the Nash game, however, there is a conflict between the members about the remanufacturing process, which reduces the SC profit in this game as compared to other ones.

Analyzing a socially responsible closed-loop distribution channel with recycling facility

This paper deals with a closed-loop distribution channel consisting of a socially responsible manufacturer, multiple retailers and a third party collector. In reality, collection of used products (plastic, glass, metal) by a third party collector is more common than the collection through retailers. This is because retailers generally faces difficulties such as lack of space and manpower. Aligned with many closed loop supply chains, this paper assumes that the third party operates the reverse channel by collecting the used products. The third party collects used products, segregates recyclable items and sends them to the manufacturer for further use. The manufacturer not only shows social responsibility to the stakeholders and shareholders, but also collects the used products from the third party and recycles them to new products. Considering profit maximizing motives of the channel members, the paper examines the effect of manufacturer’s degree of social responsibility on the collection activity of the third party. Under manufacturer Stackelberg game setting, it is found that product recycling is directly proportional to the manufacturer’s corporate social responsibility (CSR) concerns and there must be a threshold of recycling for the optimal benefit that can be acquired through CSR practice. The proposed model is illustrated by a numerical example and a sensitivity analysis reveals nature of the parameters.

Comparative analysis of government incentives and game structures on single and two-period green supply chain

The Government organizations provide incentives to the manufacturers for adopting green technologies in different ways. The objective of this study is to generate a decision support framework in perspectives of the selection and successful implementation towards environment-friendly products by comparing profits of each member, greening level, consumer surplus and environmental improvement under two different incentive policies. Twelve analytical models are formulated and analyzed by considering the impact of two game structures, single and two-period procurement decisions on the sustainability goals of supply chain members. The objectives of government's social welfare are optimized here. A comprehensive analysis reveals that the manufacturer receives higher profits and the greening level is always at higher end in two-period procurement decision under manufacturer-Stackelberg game. The greening level and profit of the retailer are maximum in single-period procurement decision under retailer-Stackelberg game. As a result, optimal preference is highly sensitive to game structure and procurement decision. When the manufacturer sets a premeditated threshold for greening level, supply chain members receive higher profits under incentive policy on per-unit product because of lower sales price, higher consumer surplus and environmental improvement compared to government incentive policy on total investment in R&D. The greening level is maximum under incentive policy on total investment in R&D that results in higher environmental improvement. Supply chain members can compromise with their sustainable goals to receive higher profits in presence of incentives.

Exploring the intervention of intermediary in a green supply chain

In many countries, the contribution of unorganized or micro-retailers to the overall economy and sustainability is a topic of increasing importance. Although these retailers are commonly dependent on the intermediaries for trading, there is scarce literature addressing the influence of intermediaries in green supply chain practice. This study explores the repercussions of a dominant intermediary in a three-echelon green supply chain under price and greening level sensitive demand in both single and two-period setting. The results demonstrates that the manufacturer is able to sell maximum amount of products and the retailer receives higher profits if an intermediary dominates the market. A dominant intermediary can urge the manufacturer to promote products with a lower greening level. In such scenario, the unit R&D investment in producing green products is less, but each participant may receive higher profits. A sequential profit-sharing mechanism is proposed from the perspective of the manufacturer that can be employed under leadership of the wholesaler. Under this mechanism, the retailer can maintain strategic inventory, each member can receive higher profits, and most importantly, the manufacturer can promote products at highest greening level to achieve sustainability goals. If consumer takes into account the GL-price ratio, then two-period procurement planning always outperforms single period optimal decision under manufacturer-Stackelberg game. The insights can assist manufacturers to create a foundation for sustainable business practices.

An adjustable bi-level wholesale price contract for coordinating a supply chain under scenario-based stochastic demand

Recently, significant research attention has been paid to supply chain (SC) coordination. However, previous studies assume that the market demand is deterministic or has a certain probability distribution. Taking a new approach, this paper analytically addresses the coordination of an SC under a scenario-based demand and proposes an adjustable bi-level wholesale price contract. To analyse the coordination problem under a scenario-based demand, we focus on corporate social responsibility (CSR) investment as an important decision in the SC context and consider a three-tier SC (one manufacturer, one distributor, and one retailer) where the retailer faces a scenario-based stochastic CSR-sensitive demand. Considering a manufacturer-Stackelberg game model, the manufacturer as a leader determines the amount of investment in the CSR issues and the retailer as a follower decides on the order quantity by considering possible demand scenarios. First, we propose the decentralized and centralized decision-making models using a scenario-based approach. Afterward, to resolve the channel conflict in each possible demand scenario, an adjustable bi-level wholesale contract is proposed to entice all SC actors to take part in the coordination scheme. Moreover, a profit-sharing plan is developed based on the Nash-bargaining model to fairly share the extra profits among SC actors. Finally, in order to analyse the efficacy of proposed models, a numerical example and a set of sensitivity analyses are carried out. The results indicate that the proposed contract not only coordinates the three-level SC under a scenario-based stochastic demand, but also improves the CSR level in comparison with the decentralized structure.