Stackelberg Game Theoretic Approach Research Articles

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.

Adaptive robust control for fuzzy underactuated mechanical systems: A Stackelberg game-theoretic optimization approach

This article proposes a Stackelberg game-theoretic optimization approach for adaptive robust controller design of fuzzy underactuated mechanical systems (UMSs). As a commonly encountered challenge, several factors render it difficult to further improve the control performance of these UMSs, such as the coupling effects and nonlinearities resulting from the underactuated structure. Meanwhile, various sources of unexpected time-varying uncertainties can further add to the difficulty in the controller design procedure pipeline. To overcome the above-mentioned issues and further enhance the system performance, a dual-parameter optimization framework is presented here for adaptive robust controller design, leveraging fuzzy set theory and Stackelberg game. In this development, the time-varying uncertainty is characterized via suitable membership functions; and thus the appropriate fuzzy UMS is established. Then, an adaptive robust controller with a leakage-type adaptation law is presented to tackle the uncertainty appropriately. To further improve the system performance considering the trade-off among the transient performance; the steady-state performance; and the control cost; a Stackelberg game-based dual-parameter optimization method is proposed to determine the Stackelberg strategy. It is rigorously proved in the developments here that the proposed controller design and parameters optimization method guarantees the desired deterministic system performance, i.e., uniform boundedness (UB) and uniform ultimate boundedness (UUB). Moreover, a series of numerical simulations based on a flywheel inverted pendulum (FIP) are performed, which illustrate the effectiveness and superiority of the proposed method.

Pricing and bundling strategies for complementary products in a closed-loop green supply chain under manufacturers’ different behaviors

This study attempts to incorporate product complementarity and bundling strategy with green innovation and remanufacturing in a two-stage supply chain. For doing so, it considers a green closed-loop supply chain that combines two manufacturers and a typical retailer to deal with complementary products. Based on the manufacturer-led Stackelberg game-theoretic approach, it first develops two models considering the bundling strategies of the retailer. Each of these two models again establishes three sub-models under consideration of whether the manufacturers make their decisions jointly or simultaneously or sequentially. The optimal responses and the profitability under various models are compared both analytically and numerically to get some insights. The results exhibit that (a) regardless of different bundling strategies, the sequential decision-making scenario is beneficial for the leading manufacturer while the joint decision-making scenario is profitable for another manufacturer, the retailer, and the entire supply chain, (b) no bundling strategy is preferable in a green-sensitive market, even though it gives less profit to channel individuals, (c) in the Stackelberg scenario, the decision of which of two manufacturers will profit more depends on product complementarity and the residual values obtained from end-of-used products acquisition and their handling, and (d) the level of product complementarity and bundle price discount play important role in determining the appropriate bundling strategy.

Collaboration and coordination strategies for a multi-level AI-enabled healthcare supply chain under disaster

ABSTRACT Artificial Intelligence (AI)-based applications have been rising across the healthcare supply chain. Successful AI implementation requires proper collaboration among healthcare supply chain members. However, high investment associated with AI innovation often impedes collaboration. In this context, disruption caused by the disasters like pandemics and epidemics can add more complexity. This issue has not received substantial scholarly attention. Here, we design a multi-level AI-enabled healthcare supply chain by incorporating a three-level supply chain structure with a healthcare product manufacturer, a distributor, and a procurement agency, where the manufacturer and distributor invest in AI innovation. Here, we adopt wholesale price (W) and cost-sharing (C) contracts-based mechanisms considering four scenarios WW, WC, CW, and CC, to devise the three-level AI-enabled healthcare supply chain members’ collaboration and coordination strategies with and without disruption. Adopting a Stackelberg game-theoretic approach, we determine the supply chain members’ optimal AI innovation efforts, prices, and profits for all scenarios. We demonstrate the dominance of one scenario over other for the supply chain members’ decisions and profits and propose a scenario ranking framework. We also investigate the impact of the disruption cost-sharing between the manufacturer and retailer, the disruption probabilities, and AI innovation success on the supply chain decisions

How Does Green Store Brand Introduction Influence the Effects of Government Subsidy on Supply Chain Performance?

With the rising awareness of environmental protection and concern for sustainable development, green products have been highly favored by consumers, enterprises, and the government. As a matter of fact, not only do manufacturers produce green products, but retailers would also like to introduce their green store brands. However, the costly green investment hinders the improvement of the products’ green degree. Therefore, the government may provide financial support to motivate enterprises to increase their products’ green degree. This study investigates how the presence of green store brands and government subsidies affect green supply chain performance. Four models are discussed using the Stackelberg game theoretic approach, and then, the optimal solutions in different cases are compared. The results show that (1) regardless of the government subsidy, the green store brand introduction always reduces the manufacturer’s profit and improves the retailer’s profit and environmental benefit; (2) In most cases, the implementation of a government subsidy can effectively improve the products’ green degree and benefit the supply chain members. However, it is surprising to find that the government subsidy may be detrimental to the manufacturer once the green store brand is introduced; (3) Interestingly, the introduction of green store brand may have an expansion effect, a shrinkage effect or even an inverse effect on the effects of government subsidies on supply chain performance, and these effects become more significant with the increasing green preference of consumers, product substitute, and subsidy rate. The new findings also provide some implications for supply chain members and the government in green supply chain management (GSCM) and green innovation.

Collaboration Strategies for Private COVID-19 Vaccine Supply Chain Under Demand Uncertainty: An Indian Perspective

In 2020, the COVD-19 pandemic emerged as the most severe crisis of the century. Several vaccine manufacturing firms have taken the necessary initiatives to combat this problem. However, profitability issues can bring down these firms’ vaccine manufacturing efforts, thus leading to lower vaccination coverage. Motivated by this issue, we depict a private COVID-19 vaccine supply chain with a supply chain framework comprising of one vaccine manufacturer and multiple private hospitals under demand uncertainty. We incorporate a Stackelberg game-theoretic approach to demonstrate the collaboration between the vaccine manufacturer and the private hospital using wholesale price, two-part tariff and revenue sharing contracts. We determine the optimal number of vaccines and coordination criteria for each contract. Using a real-life approximation of Indian data, we conduct several numerical studies and facilitate the visual depiction of all the theoretical insights obtained from the model. We also discuss the managerial implications of this study. As per our analysis, when private hospitals procure a higher number of vaccines from the vaccine manufacturer, the two-part tariff contract-based collaboration mechanism yields a win-win situation for both the private hospitals and the vaccine manufacturer and is better than the wholesale price contract.

The Prospect of Reconfigurable Intelligent Surfaces in Integrated Access and Backhaul Networks

The Integrated Access and Backhaul (IAB) technology provides a new view of the backhauling problem, especially when targeting end-to-end service provisioning. The IAB paradigm - being well aligned with the vision of Unmanned Aerial Vehicles (UAVs) - when combined with the benefits of the Reconfigurable Intelligent Surface (RIS) technology, offers to the future wireless networks the attributes of reconfigurability and energy efficiency. In this paper, we demonstrate the prospect of RIS in an UAV-assisted IAB network targeting energy-efficient operation, while accounting for the transmissions established at both the wireless access and backhaul network parts. We introduce a dynamic resource management framework that targets end-to-end energy efficiency optimization, while considering as controllable parameters the RIS elements’ phase shifts, the system bandwidth split between access and backhaul, and the transmission powers of both the UAV and the users. The corresponding joint optimization problem is formulated and treated via a distributed single-leader multiple-followers Stackelberg game-theoretic approach. The adaptation of the proposed framework is, also, demonstrated for the treatment of the IAB network’s end-to-end data rate optimization. The framework’s performance evaluation highlights the benefits achieved at both the users’ and UAV’s energy efficiency, by the joint exploitation of UAVs, IAB, and RIS technologies.

Renewable energy supply chain management with flexibility and automation in a production system

Due to technological development, there has been a rapid increase in energy demand, but the amount of available energy is not infinite. There is a daily increase in the price per unit of energy. At present, renewable energy is the option as a substitute for traditional energy. Based on this premise, this study introduces an energy supply chain management, where renewable energy can be converted from waste. The significant benefit of this system is that the utilization of waste can mitigate environmental pollution and provide a primary renewable energy source. This way, almost all traditional energy utilized places may have the benefit of using the renewable energy with less cost as waste is the raw material. This study introduces the collection of all waste from a city and ways in which the city can generate renewable energy. The waste supplier and energy manufacturer are the two players involved in this energy supply chain. The supplier collects all waste and transfers it to the manufacturer. Based on equal an unequal power of both players, there are two cases: one case for unequal power with their own profit and the other equal power with their joint profit. The Kuhn–Tucker methodology is utilized because of inequality constraint and that the Stackelberg game theoretic approach maximizes the profit of the energy supply chain because the potentiality of the energy supply chain players may not be identical. The comparative study also provides the supply chain players with equal and unequal power. Numerical experiments prove the effectiveness of this energy supply chain. The numerical investigation finds that the profit associated with the coordination policy case is greater than that from the unequal power case. Though the equal and unequal power of supply chain players are considered, 43.05% more profit is obtained for the cooperation policy. Flexibility of production rate is found strongly dependent on the development cost for both game policy and coordination policy. The sensitivity analysis is conducted for the key parameters of the model. Fifty percentage with positive and negative direction of key parameters are verified to check the effectiveness on the profit. It gives energy selling price and scrap cost of manufacturer are the best and least parameters among all parameters.

Fresh Food Dual-Channel Supply Chain Considering Consumers’ Low-Carbon and Freshness Preferences

Due to growing concerns for environmental problems and food quality, consumers pay more attention to the carbon emission and freshness of fresh food. The booming e-commerce also accelerates the development of the dual-channel supply chain. In the dual-channel supply chain of fresh food, the carbon emission and freshness of fresh food are becoming important factors affecting consumers’ purchase demand. This paper focuses on the optimal decision of carbon emission reduction and pricing, which is investigated by a Stackelberg game-theoretic approach in three dual-channel supply chain sales models (retailer dual channel, producer dual channel, and mixed dual channel). A two-stage fresh food supply chain system composed of a producer and a retailer is explored. The sensitivity analysis and the comparison of three dual-channel models are carried out. The results show the following: (1) the sales price, carbon emission reduction, market demand, producer’s profit, retailer’s profit, and supply chain’s profit of fresh food under the three dual-channel supply chains show the same change on different levels of consumers’ low-carbon preference coefficient and freshness level, respectively; (2) the optimal decision of carbon emission reduction and pricing, demand, and profit of the three dual-channel models need to be determined according to the value of consumers’ purchasing preferences for the retailer’s offline channel. The paper gives some enlightenment to the decision-making members in the fresh dual-channel supply chain.

Trade and bank credit in a non-cooperative chain with a price-sensitive demand

ABSTRACT The purpose of this article is to examine the impact of the working capital in the borrowing decision of a retailer. The proposed analysis is based on a model with a retailer, a supplier and a bank in a non-cooperative game with price-sensitive demand. The retailer, the supplier and the bank (if concerned) determine, respectively, the ordering quantity, the wholesale price and the interest rate. A Stackelberg game-theoretic approach is employed where the retailer is a follower and either the supplier or the bank is the leader. Some structural properties are first derived from the mathematical models. Then, some numerical simulations show that: (i) a trade credit guarantees the same profits for the retailer and the supplier as in the case where the retailer has sufficient cash holdings, (ii) there exist some situations where the retailer has a better profit with a borrow than with sufficient cash holdings, and (iii) borrowing decision depends on both retailer's and supplier's discount rate and the retailer's cash holdings.

Human-Like Decision Making for Autonomous Driving: A Noncooperative Game Theoretic Approach

Considering that human-driven vehicles and autonomous vehicles (AVs) will coexist on roads in the future for a long time, how to merge AVs into human drivers' traffic ecology and minimize the effect of AVs and their misfit with human drivers, are issues worthy of consideration. Moreover, different passengers have different needs for AVs, thus, how to provide personalized choices for different passengers is another issue for AVs. Therefore, a human-like decision making framework is designed for AVs in this paper. Different driving styles and social interaction characteristics are formulated for AVs regarding driving safety, ride comfort and travel efficiency, which are considered in the modeling process of decision making. Then, Nash equilibrium and Stackelberg game theory are applied to the noncooperative decision making. In addition, potential field method and model predictive control (MPC) are combined to deal with the motion prediction and planning for AVs, which provides predicted motion information for the decision-making module. Finally, two typical testing scenarios of lane change, i.e., merging and overtaking, are carried out to evaluate the feasibility and effectiveness of the proposed decision-making framework considering different human-like behaviors. Testing results indicate that both the two game theoretic approaches can provide reasonable human-like decision making for AVs. Compared with the Nash equilibrium approach, under the normal driving style, the cost value of decision making using the Stackelberg game theoretic approach is reduced by over 20%.

Stackelberg Game Model of Railway Freight Pricing Based on Option Theory

In recent years, although rail transport has contributed significantly to the productivity of the Chinese economy, it has also been faced with the fierce competition and challenge from other modes of transportation, and therefore, freight-pricing issue has received more attention by researchers. In this paper, the rail freight option (RFO) based on option theory is proposed to study the optimal pricing decision of the railway transportation enterprise and contract customers’ optimal purchase decisions. To obtain an effective RFO contract, the railway freight contract transaction process is first analyzed. Then, the theoretical framework for the RFO contract trading is put forward in the railway freight market. Next, a two-stage Stackelberg game theoretic approach is presented based on the principle of utility maximization to achieve the optimal decision of RFO contract. Subsequently, the reverse reasoning method in dynamic programming is used to solve the optimal combination decision of the contract customer. Finally, the optimal pricing decision of RFO is discussed using Kuhn–Tucker conditions and Lagrangian function. The result shows that the railway transportation enterprise should pay more attention to the option strike price w1 in terms of maximizing system utility and achieving Pareto optimal.

An energy internet DERMS platform using a multi-level Stackelberg game

Realizing environmentally sustainable and socially resilient cities requires clean energy sources and controllable loads as part of the electricity distribution grid. We address the balance of supply and demand as a nexus between financial autonomy, service provision, and stakeholder participation. We consider an energy internet architecture of prosumers, aggregators and DSOs as transactive energy participants. To implement the distributed energy resource management system (DERMS), we develop a transparent decision support system to identify the fair allocation of financial resources. Using a reverse Stackelberg game theoretic approach, we map the multi-level architecture to sub-games interconnected through utility functions that describe realistic price response at each level. The existence and uniqueness of the Nash equilibrium (NE) is proven, and closed form solutions are given for the NE strategies (stakeholder energy contributions). Game dependence on very general parameters is illustrated through a noniterative algorithm. Numerical results shown in scenario assessments demonstrate game outcomes for DERMS operation in both stable and unstable NE situations, revealing stakeholder dependencies on the allocation of financial resources. Robustness and scalability, as necessary requirements for any transactive energy economic mechanism, are also demonstrated. Our approach is compatible with the IEEE2030.5 smart energy profile application protocol needed for DERMS implementation.

Mobile Social Services with Network Externality: From Separate Pricing to Bundled Pricing

Today, many wireless device providers choose to sell devices bundled with complementary mobile social services, which exhibit strong positive network externality. Taking a reverse engineering approach, this paper aims to quantify the benefits of selling devices and complementary services under the following three strategies: separate pricing, bundled pricing, and hybrid pricing (both the separate and bundled options are offered). A comprehensive comparison of the above three strategies is carried out for two popular service models, namely physical connectivity sharing and virtual content sharing, respectively. These two sharing service models are two popular examples under the emerging trend of sharing economy. We first study the physical service model where the provider (e.g., FON) offers users customized WiFi devices for indoor Internet access, and allows service subscribers to physically access all device owners’ WiFi when traveling. Observing that all device-owners contribute to the connectivity sharing, we show, via a Stackelberg game theoretic approach, that bundled pricing outperforms separate pricing as long as the total cost of device and service is reasonably low to stimulate network externality. Further, hybrid pricing strictly dominates bundled pricing thanks to the pricing flexibility to keep high marginal profit of device-selling. Next, we investigate the virtual sharing service model where the provider (e.g., Apple) sells devices and device-supported applications. Different from the connectivity service model, in this model service subscribers directly contribute to the virtual content sharing, and the network externality can be fairly strong. We prove that hybrid pricing degenerates to bundled pricing if the network externality degree is larger than the average device valuation, which is in stark contrast with the connectivity service model in which hybrid pricing always outperforms bundled pricing.

A Stackelberg game theoretic multi-objective synthesis of four-bar mechanisms

In this article, a Stackelberg game theoretic approach is used for multi-objective optimal synthesis of four-bar mechanisms for path generation. Two objective functions, namely, tracking error (TE)...

Pricing and coordination strategies of a dual-channel supply chain considering green quality and sales effort

Due to the rapid growth of the internet and smartphone users, the shopping behavior of customers is changing towards online purchasing. Hence, a manufacturer would like to include an online (direct) channel along with offline (indirect) channel. This study investigates the pricing strategies and coordination mechanism between the members in a dual-channel supply chain (DCSC). A manufacturer offers a new substitutable green (eco-friendly) product through a direct channel and a non-green (traditional) product through an offline retail channel. The demand is expressed as a linear function of selling (online/offline) prices, green quality level, and sales effort level. In this study, three models (centralized, decentralized, and collaboration) have been examined in the DCSC. A Stackelberg game-theoretic approach is applied to analyze the decentralized model, and the channel coordination is achieved through the surplus profit-sharing mechanism to obtain a win-win situation for each member of the supply chain. The optimal results are compared, and a sensitivity analysis is carried out to study the effect of some key parameters. It is revealed that the green quality level is high in the collaboration model, which is beneficial from the environmental perspective.

Mitigating eavesdropping by using fuzzy based MDPOP-Q learning approach and multilevel Stackelberg game theoretic approach in wireless CRN

The secrecy rate of physical layer security in the presence of eavesdropper of a Cognitive Radio Network (CRN) via multilevel Stackelberg Game is enhanced. Primary propagator rents its own licensed spectrum to the secondary propagator for remuneration. The secondary dispatcher is considered as trusted relays to send the messages in decipher and promote fashion. The secondary propagator uses its partial power to transmit the jamming signal along with the information signal and also charges will be claimed by the jammer for their service. A Stackelberg game is formulated for this topic; the leader and followers are jammer and dispatcher. An advanced encryption scheme is proposed to increase the effective security level while accessing the primary spectrum under eavesdropper scenario. The proposed methodology results in the secrecy rate maximization and the power consumption is minimized. Besides the power strategy, the eavesdropping is a major concern, where the outcomes of the transmission make the best effort strategy in CRN and this optimization is highlighted with a mathematical approach of fuzzy based Markov Decision Process outcome prediction (MDPOP)-Q learning algorithm to eradicate the eavesdropping occurrence in CRN with an optimal solution.

Designing supply contracts for the sustainable supply chain using game theory

The importance of sustainable operations in supply chains has been widely recognised in practice and the extant literature. In this paper, we study coordination issues of a sustainable supply chain that arise due to simultaneous consideration of greening and corporate social responsibility (CSR) initiatives undertaken by supply chain agents. We specifically consider the scenario where the supplier is responsible for greening and the buyer is accountable for social responsibility. We analyse our model using two-stage Stackelberg game-theoretic approach where the supplier acts as a Stackelberg leader. In this context, we analyse the decentralised supply chain setting using five different contract types, namely wholesale price, linear two-part tariff (LTT), greening-cost sharing, revenue sharing, and revenue and greening-cost sharing contracts (RGCS). We demonstrate how optimal greening level, CSR level, retail price and profits of supply chain agents are influenced by different contract types. Our analytical results show that greening and social efforts undertaken by supply chain agents are beneficial for the overall supply chain as long as consumer awareness towards greening and CSR exists. Our results show that channel coordinating mechanisms between supplier and buyer is conducive to improve greening and CSR level. LTT perfectly coordinates the supply chain. Through a numerical example with several key parameters we present the effectiveness of different contracts. The results reveal that as a profit maximising agent the supplier prefers LTT contract and the buyer prefers RGCS contract. This paper extends the understanding of supply chain coordination in the context of sustainability.

Modeling and Analyzing One Vendor-Multiple Retailers VMI SC Using Stackelberg Game Theory

Game theory is a powerful tool for analyzing the Supply chain (SC) with different conflicting elements. Among them, the Stackelberg game is the one in which a player as leader has more power than the other ones as followers. Since in many SC systems one element has, in essence, more power than the others; the Stackelberg game has found many applications in SC studies. In this paper, we apply the Stackelberg game-theoretic approach and the corresponding equilibrium point to formulate and analyze a two echelon VMI SC. Comprehensive computational results on an experimental case are conducted to numerically analyze the performance of VMI system against three groups of critical parameters. Moreover, a critical comparison demonstrates the poorer performance of decentralized VMI system than centralized one. This naturally necessitates designing proper contracts between VMI partners in order to more effectively implement the realistic decentralized system.

Multi-objective optimization of mechanism design using a bi-level game theoretic formulation

This article considers the design of a high-speed mechanism as a multi-objective optimization problem wherein the kinematic and dynamic criteria are optimized simultaneously. The kinematic criteria include minimization of the structural error and a minimization of deviation of the transmission angle from its ideal value. The dynamic criterion used is minimization of the peak torque required to drive the input link over a cycle. A Stackelberg (leader–follower) game theoretic approach is proposed to solve the multi-objective problem. Three variants, wherein both the kinematic and the dynamic criteria are treated as the leader, are considered. The design variables are the mechanism dimensions. A computational procedure using sensitivity information is proposed for approximating rational reaction sets needed for capturing exchange of information between the leader and the follower problems. A numerical example dealing with the design of a path generating four-bar mechanism is presented. It is shown that significant improvement in both kinematic and dynamic performance measures is simultaneously achieved using the proposed approach.