Showing papers on "Stackelberg competition published in 2016"
TL;DR: Simulation analysis showed that the Stackelberg game-based DR algorithm is effective for achieving the optimal load control of devices in response to RTP changes with a trivial computation burden.
Abstract: This paper proposes a real-time price (RTP)-based demand-response (DR) algorithm for achieving optimal load control of devices in a facility by forming a virtual electricity-trading process, where the energy management center of the facility is the virtual retailer (leader) offering virtual retail prices, from which devices (followers) are supposed to purchase energy. A one-leader, ${N}$ -follower Stackelberg game is formulated to capture the interactions between them, and optimization problems are formed for each player to help in selecting the optimal strategy. The existence of a unique Stackelberg equilibrium that provides optimal energy demands for each device was demonstrated. The simulation analysis showed that the Stackelberg game-based DR algorithm is effective for achieving the optimal load control of devices in response to RTP changes with a trivial computation burden.
282 citations
TL;DR: The results show that with dominant power shifting from the manufacturer to the retailer, the retailer's profit always increases and the manufacturer may also benefit when the demand expansion effectiveness of collection effort is large enough.
255 citations
TL;DR: This paper mainly focuses on the energy management of microgrids (MGs) consisting of combined heat and power (CHP) and photovoltaic (PV) prosumers, and an optimization model based on Stackelberg game is designed.
Abstract: This paper mainly focuses on the energy management of microgrids (MGs) consisting of combined heat and power (CHP) and photovoltaic (PV) prosumers. A multiparty energy management framework is proposed for joint operation of CHP and PV prosumers with the internal price-based demand response. In particular, an optimization model based on Stackelberg game is designed, where the microgrid operator (MGO) acts as the leader and PV prosumers are the followers. The properties of the game are studied and it is proved that the game possesses a unique Stackelberg equilibrium. The heuristic algorithm based on differential evolution is proposed that can be adopted by the MGO, and nonlinear constrained programing can be adopted by each prosumer to reach the Stackelberg equilibrium. Finally, via a practical example, the effectiveness of the model is verified in terms of determining MGO's prices and optimizing net load characteristic, etc.
225 citations
TL;DR: It is shown that the proposed auction possesses the incentive compatibility and the individual rationality properties, which are leveraged via the unique Stackelberg equilibrium solution of the game.
Abstract: This paper studies the solution of joint energy storage (ES) ownership sharing between multiple shared facility controllers (SFCs) and those dwelling in a residential community. The main objective is to enable the residential units (RUs) to decide on the fraction of their ES capacity that they want to share with the SFCs of the community in order to assist them in storing electricity, e.g., for fulfilling the demand of various shared facilities. To this end, a modified auction-based mechanism is designed that captures the interaction between the SFCs and the RUs so as to determine the auction price and the allocation of ES shared by the RUs that governs the proposed joint ES ownership. The fraction of the capacity of the storage that each RU decides to put into the market to share with the SFCs and the auction price are determined by a noncooperative Stackelberg game formulated between the RUs and the auctioneer. It is shown that the proposed auction possesses the incentive compatibility and the individual rationality properties, which are leveraged via the unique Stackelberg equilibrium solution of the game. Numerical experiments are provided to confirm the effectiveness of the proposed scheme.
209 citations
TL;DR: In this paper, the interactions between the utility company and users were formulated into a 1-leader, N-follower Stackelberg game, where optimization problems were formed for each player to help select the optimal strategy.
197 citations
TL;DR: It is shown that the distributed scheme is effective for the resource allocation and could protect the CUs with limited signaling overhead and the signaling overhead is compared between the centralized and decentralized schemes.
Abstract: This paper addresses the joint spectrum sharing and power allocation problem for device-to-device (D2D) communications underlaying a cellular network (CN). In the context of orthogonal frequency-division multiple-access systems, with the uplink resources shared with D2D links, both centralized and decentralized methods are proposed. Assuming global channel state information (CSI), the resource allocation problem is first formulated as a nonconvex optimization problem, which is solved using convex approximation techniques. We prove that the approximation method converges to a suboptimal solution and is often very close to the global optimal solution. On the other hand, by exploiting the decentralized network structure with only local CSI at each node, the Stackelberg game model is then adopted to devise a distributed resource allocation scheme. In this game-theoretic model, the base station (BS), which is modeled as the leader, coordinates the interference from the D2D transmission to the cellular users (CUs) by pricing the interference. Subsequently, the D2D pairs, as followers, compete for the spectrum in a noncooperative fashion. Sufficient conditions for the existence of the Nash equilibrium (NE) and the uniqueness of the solution are presented, and an iterative algorithm is proposed to solve the problem. In addition, the signaling overhead is compared between the centralized and decentralized schemes. Finally, numerical results are presented to verify the proposed schemes. It is shown that the distributed scheme is effective for the resource allocation and could protect the CUs with limited signaling overhead.
189 citations
TL;DR: A hierarchical system model that captures the decision making processes involved in a network of multiple providers and a large number of consumers in the smart grid, incorporating multiple processes from power generation to market activities and to power consumption is introduced.
Abstract: In this paper, we introduce a hierarchical system model that captures the decision making processes involved in a network of multiple providers and a large number of consumers in the smart grid, incorporating multiple processes from power generation to market activities and to power consumption. We establish a Stackelberg game between providers and end users, where the providers behave as leaders maximizing their profit and end users act as the followers maximizing their individual welfare. We obtain closed-form expressions for the Stackelberg equilibrium of the game and prove that a unique equilibrium solution exists. In the large population regime, we show that a higher number of providers help to improve profits for the providers. This is inline with the goal of facilitating multiple distributed power generation units, one of the main design considerations in the smart grid. We further prove that there exist a unique number of providers that maximize their profits, and develop an iterative and distributed algorithm to obtain it. Finally, we provide numerical examples to illustrate the solutions and to corroborate the results.
180 citations
TL;DR: In this paper, a dual-channel supply chain consisting of a risk-neutral supplier and a riskaverse retailer is considered, where the market demand is uncertain and the supplier opens an e-channel, thus directly participating in the market.
154 citations
TL;DR: A Stackelberg game is used to model interactions between a retailer and its customers; the retailer sets the day-ahead hourly price of electricity and consumers adjust real-time consumptions to maximize individual consumer surplus.
Abstract: The problem of dynamic pricing of electricity in a retail market is considered. A Stackelberg game is used to model interactions between a retailer and its customers; the retailer sets the day-ahead hourly price of electricity and consumers adjust real-time consumptions to maximize individual consumer surplus. For thermostatic demands, the optimal aggregated demand is shown to be an affine function of the day-ahead hourly price. A complete characterization of the tradeoffs between consumer surplus and retail profit is obtained. The Pareto front of achievable tradeoffs is shown to be concave, and each point on the Pareto front is achieved by an optimal day-ahead hourly price. Effects of integrating renewables and local storage are analyzed. It is shown that benefits of renewable integration all go to the retailer when the capacity of renewable is relatively small. As the capacity increases beyond a certain threshold, the benefit from renewable that goes to consumers increases.
143 citations
TL;DR: In this article, the authors consider a dual-channel supply chain where a manufacturer with a direct channel acts as the leader and a retailer is the follower, and they show that the entire supply chain cannot be coordinated with a constant wholesale price when the retailer provides value-added services and has fairness concerns.
130 citations
TL;DR: In this article, the authors considered a commercialized small-cell caching system consisting of a network service provider (NSP), several video retailers (VRs), and mobile users (MUs), and formulated a Stackelberg game to jointly maximize the average profit of both the NSP and the VRs.
Abstract: Evidence indicates that downloading on-demand videos accounts for a dramatic increase in data traffic over cellular networks. Caching popular videos in the storage of small-cell base stations (SBS), namely, small-cell caching, is an efficient technology for reducing the transmission latency while mitigating the redundant transmissions of popular videos over back-haul channels. In this paper, we consider a commercialized small-cell caching system consisting of a network service provider (NSP), several video retailers (VRs), and mobile users (MUs). The NSP leases its SBSs to the VRs for the purpose of making profits, and the VRs, after storing popular videos in the rented SBSs, can provide faster local video transmissions to the MUs, thereby gaining more profits. We conceive this system within the framework of Stackelberg game by treating the SBSs as specific types of resources. We first model the MUs and SBSs as two independent Poisson point processes, and develop, via stochastic geometry theory, the probability of the specific event that an MU obtains the video of its choice directly from the memory of an SBS. Then, based on the probability derived, we formulate a Stackelberg game to jointly maximize the average profit of both the NSP and the VRs. In addition, we investigate the Stackelberg equilibrium by solving a non-convex optimization problem. With the aid of this game theoretic framework, we shed light on the relationship between four important factors: the optimal pricing of leasing an SBS, the SBSs allocation among the VRs, the storage size of the SBSs, and the popularity distribution of the VRs. Monte Carlo simulations show that our stochastic geometry-based analytical results closely match the empirical ones. Numerical results are also provided for quantifying the proposed game-theoretic framework by showing its efficiency on pricing and resource allocation.
TL;DR: In this paper, the authors explored channel coordination and profit division issues of a manufacturer-distributer-duopolistic retailers supply chain for a product, where the manufacturer supplies lotsize of the product that contains a random portion of imperfect quality item.
22 May 2016
TL;DR: An incentive mechanism in which the base station (BS) rewards those UTs that share contents with others using D2D communication and an iterative gradient algorithm (IGA) is proposed to obtain the Stackelberg Equilibrium.
Abstract: Caching in wireless device-to-device (D2D) networks can be utilized to offload data traffic during peak times. However, the design of incentive mechanisms is challenging due to the heterogeneous preference and selfish nature of user terminals (UTs). In this paper, we propose an incentive mechanism in which the base station (BS) rewards those UTs that share contents with others using D2D communication. We study the cost minimization problem for the BS and the utility maximization problem for each UT. In particular, the BS determines the rewarding policy to minimize his total cost, while each UT aims to maximize his utility by choosing his caching policy. We formulate the conflict among UTs and the tension between the BS and the UTs as a Stackelberg game. We show the existence of the equilibrium and propose an iterative gradient algorithm (IGA) to obtain the Stackelberg Equilibrium. Extensive simulations are carried out to evaluate the performance of the proposed caching scheme and comparisons are drawn with several baseline caching schemes with no incentives. Numerical results show that the caching scheme under our incentive mechanism outperforms other schemes in terms of the BS serving cost and the utilities of the UTs.
TL;DR: This paper considers a commercialized small-cell caching system consisting of a network service provider, several video retailers (VRs), and mobile users, and formulates a Stackelberg game to jointly maximize the average profit of both the NSP and the VRs.
Abstract: Evidence indicates that downloading on-demand videos accounts for a dramatic increase in data traffic over cellular networks. Caching popular videos in the storage of small-cell base stations (SBS), namely, small-cell caching, is an efficient technology for reducing the transmission latency whilst mitigating the redundant transmissions of popular videos over back-haul channels. In this paper, we consider a commercialized small-cell caching system consisting of a network service provider (NSP), several video retailers (VR), and mobile users (MU). The NSP leases its SBSs to the VRs for the purpose of making profits, and the VRs, after storing popular videos in the rented SBSs, can provide faster local video transmissions to the MUs, thereby gaining more profits. We conceive this system within the framework of Stackelberg game by treating the SBSs as a specific type of resources. We first model the MUs and SBSs as two independent Poisson point processes, and develop, via stochastic geometry theory, the probability of the specific event that an MU obtains the video of its choice directly from the memory of an SBS. Then, based on the probability derived, we formulate a Stackelberg game to jointly maximize the average profit of both the NSP and the VRs. Also, we investigate the Stackelberg equilibrium by solving a non-convex optimization problem. With the aid of this game theoretic framework, we shed light on the relationship between four important factors: the optimal pricing of leasing an SBS, the SBSs allocation among the VRs, the storage size of the SBSs, and the popularity distribution of the VRs. Monte-Carlo simulations show that our stochastic geometry-based analytical results closely match the empirical ones. Numerical results are also provided for quantifying the proposed game-theoretic framework by showing its efficiency on pricing and resource allocation.
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TL;DR: In this article, it was shown that a marginal contraction of two firms in a triopoly has no effect on the profits of firms in the subset if cost and demand functions are linear; if instead cost is linear but the inverse demand function is strictly concave (strictly convex), a marginal contract will strictly decrease profits.
Abstract: Consider an industry composed of N firms in a symmetric equilibrium. Designate a subset of S (< N) firms and marginally reduce the strategic variables of the firms in the subset. If the remaining firms simultaneously make the best reply to this exogenous displacement, under what circumstances will profits of the firms in the designated subset increase? We show that, in the case of Cournot competition among producers of perfect substitutes, a marginal contraction is strictly beneficial (strictly harmful) if and only if the number of firms in the designated subset exceeds the "adjusted" number of firms outside it by strictly more (strictly less) than one. The adjustment factor is unity when cost and demand functions are linear but, more generally, depends on the convexity of the cost and demand curves. Thus, a marginal contraction of two firms in a triopoly has no effect on the profits of firms in the subset if cost and demand functions are linear; if instead cost is linear but the inverse demand function is strictly concave (strictly convex), a marginal contraction will strictly decrease (strictly increase) profits. The analysis is extended to the effects of nonmarginal exogenous changes in the outputs of the constrained firms. This extension has implications for the relationship of Stackelberg (sequential move) and Nash (simultaneous move) equilibria. Our analysis has broad application. To illustrate, we show that it unifies results in the literature on export subsidies, horizontal mergers, and strikes. The paper is organized as follows. In Section I, our comparative-static result is derived. In Section II, we present a wide range of applications. In the conclusion and the Appendix we generalize our analysis to other situations involving strategic substitutes.
TL;DR: Results show that by defending a very small set of measurements, the grid operator can achieve an equilibrium through which the optimal attacks have no effect on the system, and how, at equilibrium, multiple attackers can play a destructive role toward each other by choosing to carry out attacks that cancel each other out, leaving the system unaffected.
Abstract: Data injection attacks have emerged as a significant threat on the smart power grid. By launching data injection attacks, an adversary can manipulate the real-time locational marginal prices to obtain economic benefits. Despite the surge of existing literature on data injection, most such works assume the presence of a single attacker and assume no cost for attack or defense. In contrast, in this paper, a model for data injection attacks with multiple adversaries and a single smart grid defender is introduced. To study the interactions between the defender and the attackers, two game models are considered. In the first, a Stackelberg game is proposed in which the defender acts as a leader that can anticipate the actions of the adversaries, that act as followers, before deciding on which measurements to protect. The existence and properties of the Stackelberg equilibrium of this game are studied. To find the equilibrium, a distributed learning algorithm that operates under limited system information is proposed and shown to converge to the game solution. In the second proposed game model, it is considered that the defender cannot anticipate the actions of the adversaries. To this end, a hybrid satisfaction equilibrium—Nash equilibrium game is proposed. To find the equilibrium of this hybrid game, a search-based algorithm is introduced. Numerical results using the IEEE 30-bus system are used to illustrate and analyze the strategic interactions between the attackers and defender. The results show that by defending a very small set of measurements, the grid operator can achieve an equilibrium through which the optimal attacks have no effect on the system. Moreover, the results also show how, at equilibrium, multiple attackers can play a destructive role toward each other by choosing to carry out attacks that cancel each other out, leaving the system unaffected. In addition, the obtained equilibrium strategies under the Stackelberg and the hybrid models are compared while characterizing the amount of loss that the defender endures due to its inability to anticipate the attackers’ actions.
TL;DR: A game theoretic resource allocation scheme for media cloud to allocate resource to mobile social users though brokers and results show that each player in the game can obtain the optimal strategy where the Stackelberg equilibrium exists stably.
Abstract: Due to the rapid increases in both the population of mobile social users and the demand for quality of experience (QoE), providing mobile social users with satisfied multimedia services has become an important issue. Media cloud has been shown to be an efficient solution to resolve the above issue, by allowing mobile social users to connect to it through a group of distributed brokers. However, as the resource in media cloud is limited, how to allocate resource among media cloud, brokers, and mobile social users becomes a new challenge. Therefore, in this paper, we propose a game theoretic resource allocation scheme for media cloud to allocate resource to mobile social users though brokers. First, a framework of resource allocation among media cloud, brokers, and mobile social users is presented. Media cloud can dynamically determine the price of the resource and allocate its resource to brokers. A mobile social user can select his broker to connect to the media cloud by adjusting the strategy to achieve the maximum revenue, based on the social features in the community. Next, we formulate the interactions among media cloud, brokers, and mobile social users by a four-stage Stackelberg game. In addition, through the backward induction method, we propose an iterative algorithm to implement the proposed scheme and obtain the Stackelberg equilibrium. Finally, simulation results show that each player in the game can obtain the optimal strategy where the Stackelberg equilibrium exists stably.
TL;DR: This study models an at-home EV charging scenario as a Stackelberg game and proves that this game reaches an equilibrium point at which the EV charging requirements are satisfied, and retailer profits are maximized when customers use the proposed utility function.
Abstract: Consumer electricity consumption can be controlled through electricity prices, which is called demand response. Under demand response, retailers determine their electricity prices, and customers respond accordingly with their electricity consumption levels. In particular, the demands of customers who own electric vehicles (EVs) are elastic with respect to price. The interaction between retailers and customers can be seen as a game because both attempt to maximize their own payoffs. This study models an at-home EV charging scenario as a Stackelberg game and proves that this game reaches an equilibrium point at which the EV charging requirements are satisfied, and retailer profits are maximized when customers use our proposed utility function. The equilibrium of our game can vary according to the weighting factor for the utility function of each customer, resulting in various strategic choices. Our numerical results confirm that the equilibrium of the proposed game lies somewhere between the minimum-generation-cost solution and the result of the equal-charging scheme.
TL;DR: In this article, the authors studied the short and long-term behavior of agents in implementing the appropriate collecting strategy in a two-echelon closed-loop supply chain (CLSC) management.
Abstract: Closed-loop supply chain (CLSC) management is an environmental approach to supply chain management that aims to prevent hazardous material from entering the nature by means of creating a reverse flow. This paper studies the short- and long-term behaviour of agents in implementing the appropriate collecting strategy in a two-echelon CLSC. In short-term, based on the Stackelberg game, several novel pricing models for different collecting strategies are proposed and compared. Then, the optimal policies of the pricing decisions are determined for each model. The long-term behaviour of companies in implementing collecting process is examined by evolutionary game theory and the most stable strategy is selected. Furthermore, a numerical example is presented to compare the different collecting structures. Finally, a managerial insight is provided to indicate the effect of key parameters such as remanufacturing rate, marketing elasticity and government subsidies on selecting the appropriate strategy.
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TL;DR: In this article, the authors advocate a generalized N-firm Stackelberg model as a plausible testable alternative description of oligopoly and show that efficiency obtains in the limit as the scale of each firm is shrunk relative to demand.
Abstract: This paper advocates a generalized N-firm Stackelberg model as a plausible testable alternative description of oligopoly. A pure-strategy equilibrium must exist for this model. The main result is that efficiency obtains in the limit as the scale of each firm is shrunk relative to demand. This is demonstrated for the case of U-shaped average cost and also for that of natural monopoly. Copyright 1990 by American Economic Association.
TL;DR: This work studies the demand response of geo-distributed data centers using smart grid's pricing signals set by local electric utilities using a two-stage Stackelberg game, and shows that its pricing scheme significantly outperforms other baseline schemes in terms of flattening the power demand over time and space.
Abstract: We study the demand response (DR) of geo-distributed data centers (DCs) using smart grid’s pricing signals set by local electric utilities. The geo-distributed DCs are suitable candidates for the DR programs due to their huge energy consumption and flexibility to distribute their energy demand across time and location, whereas the price signal is well-known for DR programs to reduce the peak-to-average load ratio. There are two dependencies that make the pricing design difficult: 1) dependency among utilities; and 2) dependency between DCs and their local utilities. Our proposed pricing scheme is constructed based on a two-stage Stackelberg game in which each utility sets a real-time price to maximize its own profit in Stage I and based on these prices, the DCs’ service provider minimizes its cost via workload shifting and dynamic server allocation in Stage II. For the first dependency, we show that there exists a unique Nash equilibrium. For the second dependency, we propose an iterative and distributed algorithm that can converge to this equilibrium, where the “right prices” are set for the “right demands.” We also verify our proposal by trace-based simulations, and results show that our pricing scheme significantly outperforms other baseline schemes in terms of flattening the power demand over time and space.
TL;DR: The smart jammers pose a severe threat to wireless communications due to their abilities of learning the users' transmission strategies and a Stackelberg game can be formulated to model and analyze the hierarchical interactions between the user and the smart jammer.
Abstract: The smart jammers pose a severe threat to wireless communications due to their abilities of learning the users’ transmission strategies. A Stackelberg game can be formulated to model and analyze the hierarchical interactions between the user and the smart jammer. In this letter, an antijamming Bayesian Stackelberg game with incomplete information is proposed. In the proposed game, the user who acts as the leader has the privilege over the smart jammer and takes actions first, whereas the smart jammer acting as the follower moves subsequently. Moreover, the Stackelberg equilibrium (SE) is derived, and the existence and the uniqueness of SE are demonstrated. Simulation results are presented to validate the effectiveness of the proposed antijamming Bayesian Stackelberg game.
TL;DR: This paper theoretically prove the existence and uniqueness of robust Stackelberg equilibrium for the two approaches and develop distributed algorithms to converge to the global optimal solution that are robust against the demand uncertainty.
Abstract: This paper studies the problem of energy charging using a robust Stackelberg game approach in a power system composed of an aggregator and multiple electric vehicles (EVs) in the presence of demand uncertainty, where the aggregator and EVs are considered to be a leader and multiple followers, respectively. We propose two different robust approaches under demand uncertainty: a noncooperative optimization and a cooperative design. In the robust noncooperative approach, we formulate the energy charging problem as a competitive game among self-interested EVs, where each EV chooses its own demand strategy to maximize its own benefit selfishly. In the robust cooperative model, we present an optimal distributed energy scheduling algorithm that maximizes the sum benefit of the connected EVs. We theoretically prove the existence and uniqueness of robust Stackelberg equilibrium for the two approaches and develop distributed algorithms to converge to the global optimal solution that are robust against the demand uncertainty. Moreover, we extend the two robust models to a time-varying power system to handle the slowly varying environments. Simulation results show the effectiveness of the robust solutions in uncertain environments.
TL;DR: In this article, a leader-follower stochastic differential game with asymmetric information is studied, where the information available to the follower is based on some sub-? -algebra of that available to leader.
TL;DR: In this article, the authors considered a dual-channel problem with one manufacturer and one retailer, where the manufacturer, acting as the Stackelberg leader, sells a single type of product through a traditional channel to the retailer and/or through a direct channel to customers.
TL;DR: This paper considers a commercialized small-cell caching system consisting of a video retailer, multiple network service providers (NSPs), and mobile users, and formulates a Stackelberg game to maximize jointly the average profit of the VR and the NSPs.
Abstract: Evidence indicates that downloading on-demand videos accounts for a dramatic increase in data traffic over cellular networks. Caching popular videos in the storage of small-cell base stations (SBSs), namely, small-cell caching, is an efficient technology for mitigating redundant data transmissions over backhaul channels in heterogeneous networks (HetNets). In this paper, we consider a commercialized small-cell caching system consisting of a video retailer (VR), multiple network service providers (NSPs), and mobile users (MUs). The VR leases its popular videos to the NSPs to make profits, and the NSPs, after placing these videos to their SBSs, can efficiently reduce the repetitive video transmissions over their backhaul channels. We study such a system within the framework of the Stackelberg game. We first model the MUs and SBSs as two independent Poisson point processes (PPPs) and develop the probability of the event that an MU can obtain the demanded video directly from the memory of an SBS. Then, based on the derived probability, we formulate a Stackelberg game to maximize jointly the average profit of the VR and the NSPs. Moreover, we investigate the Stackelberg equilibrium (SE) via solving an optimization problem. Numerical results are provided for verifying the proposed framework by showing its effectiveness on pricing and resource allocation.
TL;DR: The cooperation game is strongly found to be infeasible depending on the certain channel's parameters and the manufacturer's price is entirely stable compared to classical linear model and increases as effectiveness ratio of national to local advertising increases.
TL;DR: The resilient control system is modelled as a multi-stage hierarchical game with a corresponding hierarchy of decisions made at cyber and physical layer, respectively, which demonstrates its effectiveness under denial-of-service attack launched by the intelligent attacker.
Abstract: This paper is concerned with the resilient control under denial-of-service attack launched by the intelligent attacker. The resilient control system is modelled as a multi-stage hierarchical game with a corresponding hierarchy of decisions made at cyber and physical layer, respectively. Specifically, the interaction in the cyber layer between different security agents is modelled as a static infinite Stackelberg game, while in the underlying physical layer the full-information H∞ minimax control with package drops is modelled as a different Stackelberg game. Both games are solved sequentially, which is consistent with the actual situations. Finally, the proposed method is applied to the load frequency control of the power system, which demonstrates its effectiveness.
TL;DR: In this article, a Stackelberg model with the supplier being a leader in the game is proposed to make the supply chain more stable and a win-win outcome can be realized.
TL;DR: In this paper, the authors consider two competing supply chains where both chains launch the same product under different brands to the market by applying different composite coordinating strategies, such as discount, return, refund, buyback, or other coordinating policies to abate the operation costs of the chains.
Abstract: In today’s global highly competitive markets, competition happens among supply chains instead of companies, as the members of supply chains. So, the partners of the chains seek to apply efficient coordinating strategies like discount, return, refund, buyback, or the other coordinating policies to abate the operation costs of the chains and subsequently increase market shares. Hence, because of the importance and application of these strategies in the current non-exclusive markets, in this study, we introduce different composite coordinating strategies to enhance the coordination of the supply chains. Here, we consider two competing supply chains where both chains launch the same product under different brands to the market by applying different composite coordinating strategies. Each supply chain comprises one manufacturer and a group of non-competing retailers where the manufacturer receives raw materials from an outside supplier and transforms them into a finished product; then, the products are sold to...