Competitiveversuscooperative performances of a Stackelberg game between two suppliers

2016 ◽  
Vol 50 (4-5) ◽  
pp. 767-780 ◽  
Author(s):  
Ibtissem Ernez-Gahbiche ◽  
Khaled Hadjyoussef ◽  
Abdelwaheb Dogui ◽  
Zied Jemai
Keyword(s):  
Stackelberg Game

Cloud Provider's Response to Multiple Models of Attack Behaviors

2019 ◽  
Vol 13 (4) ◽  
pp. 325-333
Author(s):  
Xu Liu ◽  
Xiaoqiang Di ◽  
Jinqing Li ◽  
Huamin Yang ◽  
Ligang Cong ◽  
...  
Keyword(s):  
Stackelberg Game ◽  
Multiple Models ◽  
Theoretic Model ◽  
Cloud Provider ◽  
Game Model ◽  
Attack Behavior ◽  
Behavior Model ◽  
Protection Strategy ◽  
Behavior Models ◽  
Optimal Protection

Background: User behavior models have been widely used to simulate attack behaviors in the security domain. We revised all patents related to response to attack behavior models. How to decide the protected target against multiple models of attack behaviors is studied. Methods: We utilize one perfect rational and three bounded rational behavior models to simulate attack behaviors in cloud computing, and then investigate cloud provider’s response based on Stackelberg game. The cloud provider plays the role of defender and it is assumed to be intelligent enough to predict the attack behavior model. Based on the prediction accuracy, two schemes are built in two situations. Results: If the defender can predict the attack behavior model accurately, a single-objective game model is built to find the optimal protection strategy; otherwise, a multi-objective game model is built to find the optimal protection strategy. Conclusion: The numerical results prove that the game theoretic model performs better in the corresponding situation.

Game-Based Resource Allocation Mechanism in B5G HetNets with Incomplete Information

2020 ◽  
Vol 10 (5) ◽  
pp. 1557
Author(s):  
Weijia Feng ◽  
Xiaohui Li
Keyword(s):  
Resource Allocation ◽  
Incomplete Information ◽  
Stackelberg Game ◽  
Superior Performance ◽  
Channel Gain ◽  
Mobile Users ◽  
Pricing Strategies ◽  
Game Equilibrium ◽  
Allocation Process ◽  
Realistic Situation

Ultra-dense and highly heterogeneous network (HetNet) deployments make the allocation of limited wireless resources among ubiquitous Internet of Things (IoT) devices an unprecedented challenge in 5G and beyond (B5G) networks. The interactions among mobile users and HetNets remain to be analyzed, where mobile users choose optimal networks to access and the HetNets adopt proper methods for allocating their own network resource. Existing works always need complete information among mobile users and HetNets. However, it is not practical in a realistic situation where important individual information is protected and will not be public to others. This paper proposes a distributed pricing and resource allocation scheme based on a Stackelberg game with incomplete information. The proposed model proves to be more practical by solving the problem that important information of either mobile users or HetNets is difficult to acquire during the resource allocation process. Considering the unknowability of channel gain information, the follower game among users is modeled as an incomplete information game, and channel gain is regarded as the type of each player. Given the pricing strategies of networks, users will adjust their bandwidth requesting strategies to maximize their expected utility. While based on the sub-equilibrium obtained in the follower game, networks will correspondingly update their pricing strategies to be optimal. The existence and uniqueness of Bayesian Nash equilibrium is proved. A probabilistic prediction method realizes the feasibility of the incomplete information game, and a reverse deduction method is utilized to obtain the game equilibrium. Simulation results show the superior performance of the proposed method.

scholarly journals Stackelberg pricing games with congestion effects

2021 ◽  
Author(s):  
Tobias Harks ◽  
Anja Schedel
Keyword(s):  
Cost Function ◽  
Stackelberg Game ◽  
Pure Strategy ◽  
Closed Form Expression ◽  
Social Optimum ◽  
Service Capacity ◽  
Worst Case ◽  
Congestion Cost ◽  
Pricing Games ◽  
Congestion Effects

AbstractWe study a Stackelberg game with multiple leaders and a continuum of followers that are coupled via congestion effects. The followers’ problem constitutes a nonatomic congestion game, where a population of infinitesimal players is given and each player chooses a resource. Each resource has a linear cost function which depends on the congestion of this resource. The leaders of the Stackelberg game each control a resource and determine a price per unit as well as a service capacity for the resource influencing the slope of the linear congestion cost function. As our main result, we establish existence of pure-strategy Nash–Stackelberg equilibria for this multi-leader Stackelberg game. The existence result requires a completely new proof approach compared to previous approaches, since the leaders’ objective functions are discontinuous in our game. As a consequence, best responses of leaders do not always exist, and thus standard fixed-point arguments á la Kakutani (Duke Math J 8(3):457–458, 1941) are not directly applicable. We show that the game is C-secure (a concept introduced by Reny (Econometrica 67(5):1029–1056, 1999) and refined by McLennan et al. (Econometrica 79(5):1643–1664, 2011), which leads to the existence of an equilibrium. We furthermore show that the equilibrium is essentially unique, and analyze its efficiency compared to a social optimum. We prove that the worst-case quality is unbounded. For identical leaders, we derive a closed-form expression for the efficiency of the equilibrium.

scholarly journals Research on Closed-Loop Supply Chain Decision-Making in Different Cooperation Modes with Government’s Reward-Penalty Mechanism

2021 ◽  
Vol 13 (11) ◽  
pp. 6425
Author(s):  
Quanxi Li ◽  
Haowei Zhang ◽  
Kailing Liu
Keyword(s):  
Supply Chain ◽  
Closed Loop ◽  
Stackelberg Game ◽  
Recycling Rate ◽  
Transfer Payment ◽  
Closed Loop Supply Chain ◽  
Asymmetry Of Information ◽  
Optimal Decisions ◽  
The Government ◽  
The Impact

In closed-loop supply chains (CLSC), manufacturers, retailers, and recyclers perform their duties. Due to the asymmetry of information among enterprises, it is difficult for them to maximize efficiency and profits. To maximize the efficiency and profit of the CLSC, this study establishes five cooperation models of CLSC under the government‘s reward–penalty mechanism. We make decisions on wholesale prices, retail prices, transfer payment prices, and recovery rates relying on the Stackelberg game method and compare the optimal decisions. This paper analyzes the impact of the government reward-penalty mechanism on optimal decisions and how members in CLSC choose partners. We find that the government’s reward-penalty mechanism can effectively increase the recycling rate of used products and the total profit of the closed-loop supply chain. According to the calculation results of the models, under the government’s reward-penalty mechanism, the cooperation can improve the CLSC’s used products recycling capacity and profitability. In a supply chain, the more members participate in the cooperation, the higher profit the CLSC obtain. However, the cooperation mode of all members may lead to monopoly, which is not approved by government and customers.

scholarly journals Decisions and Coordination in E-Commerce Supply Chain under Logistics Outsourcing and Altruistic Preferences

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 253
Author(s):  
Yuyan Wang ◽  
Zhaoqing Yu ◽  
Liang Shen ◽  
Runjie Fan ◽  
Rongyun Tang
Keyword(s):  
Supply Chain ◽  
Supply Chains ◽  
Stackelberg Game ◽  
Consumer Preferences ◽  
Third Party ◽  
Altruistic Behavior ◽  
Fixed Cost ◽  
Equilibrium Solutions ◽  
Factors Affecting ◽  
Dual Channel

Considering the peculiarities of logistics in the electronic commerce (e-commerce) supply chain (ESC) and e-commerce platform’s altruistic preferences, a model including an e-commerce platform, third-party logistics service provider, and manufacturer is constructed. Based on this, three decision models are proposed and equilibrium solutions are obtained by the Stackelberg game. Then, an “altruistic preference joint fixed-cost” contract is proposed to maximize system efficiency. Finally, numerical analysis is used to validate the findings of the paper. The article not only analyzes and compares the optimal decisions under different ESC models, but also explores the intrinsic factors affecting the decisions. This paper finds that the conclusions of dual-channel supply chains or traditional supply chains do not necessarily apply to ESC, and that the effect of altruistic behavior under ESC is influenced by consumer preferences. Moreover, there is a multiparty win–win state for ESC, and this state can be achieved through the “altruistic preference joint fixed-cost” contract. Therefore, the findings of this paper contribute to the development of an e-commerce market and the cooperation of ESC members.

scholarly journals Single-Manufacturer Multi-Retailer Supply Chain Models with Discrete Stochastic Demand

2021 ◽  
Vol 13 (15) ◽  
pp. 8271
Author(s):  
Yaqing Xu ◽  
Jiang Zhang ◽  
Zihao Chen ◽  
Yihua Wei
Keyword(s):  
Dynamic Programming ◽  
Supply Chain ◽  
Computational Complexity ◽  
Stackelberg Game ◽  
Programming Model ◽  
Dynamic Programming Method ◽  
Game Model ◽  
Chain Model ◽  
Stochastic Demands ◽  
Demand Models

Although there are highly discrete stochastic demands in practical supply chain problems, they are seldom considered in the research on supply chain systems, especially the single-manufacturer multi-retailer supply chain systems. There are no significant differences between continuous and discrete demand supply chain models, but the solutions for discrete random demand models are more challenging and difficult. This paper studies a supply chain system of a single manufacturer and multiple retailers with discrete stochastic demands. Each retailer faces a random discrete demand, and the manufacturer utilizes different wholesale prices to influence each retailer’s ordering decision. Both Make-To-Order and Make-To-Stock scenarios are considered. For each scenario, the corresponding Stackelberg game model is constructed respectively. By proving a series of theorems, we transfer the solution of the game model into non-linear integer programming model, which can be easily solved by a dynamic programming method. However, with the increase in the number of retailers and the production capacity of manufacturers, the computational complexity of dynamic programming drastically increases due to the Dimension Barrier. Therefore, the Fast Fourier Transform (FFT) approach is introduced, which significantly reduces the computational complexity of solving the supply chain model.

scholarly journals Pricing Policies in a Retailer Stackelberg O2O Green Supply Chain

2020 ◽  
Vol 12 (8) ◽  
pp. 3236
Author(s):  
Gan Wan ◽  
Gang Kou ◽  
Tie Li ◽  
Feng Xiao ◽  
Yang Chen
Keyword(s):  
Supply Chain ◽  
Stackelberg Game ◽  
Good Combination ◽  
Green Supply Chain ◽  
Game Model ◽  
Mathematical Function ◽  
Pricing Strategies ◽  
Direct Channel ◽  
Retail Channel ◽  
Offline Channels

Due to the popularization of the concept of “new retailing”, we study a new commercial model named O2O (online-to-offline), which is a good combination model of a direct channel and a traditional retail channel. We analyze an O2O supply chain in which manufacturers are responsible for making green products and selling them through both online and offline channels. The retailer is responsible for all online and offline channels’ orders, and the manufacturer gives the retailer a fixed fee. We construct a mathematical function model and analyze the greenness and pricing strategies of centralized and decentralized settings through the retailer Stackelberg game model. Due to the effects of the double marginalization of supply chain members, we adopt a simple contract to coordinate the green supply chain. The paper’s contributions are that we obtain pricing and greening strategies by taking the cooperation of offline channels and online channels into consideration under the O2O green supply chain environment.

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