Articoli di riviste: "Single-Leader-Multi-Follower game"

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Harks, Tobias, Mona Henle, Max Klimm, Jannik Matuschke e Anja Schedel. "Multi-Leader Congestion Games with an Adversary". Proceedings of the AAAI Conference on Artificial Intelligence 36, n. 5 (28 giugno 2022): 5068–75. http://dx.doi.org/10.1609/aaai.v36i5.20439.

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We study a multi-leader single-follower congestion game where multiple users (leaders) choose one resource out of a set of resources and, after observing the realized loads, an adversary (single-follower) attacks the resources with maximum loads causing additional costs for the leaders. For the resulting strategic game among the leaders, we show that pure Nash equilibria fail to exist and therefore, we consider approximate equilibria instead. As our first main result, we show that the existence of a K-approximate equilibrium can always be guaranteed, where K (approximately equal to 1.1974) is the unique solution of a cubic polynomial equation. To this end, we give a polynomial time combinatorial algorithm which computes a K-approximate equilibrium. The factor K is tight, meaning that there is an instance that does not admit an A-approximate equilibrium for any A < K. Thus A = K is the smallest possible value of A such that the existence of an A-approximate equilibrium can be guaranteed for any instance of the considered game. Secondly, we focus on approximate equilibria of a given fixed instance. We show how to compute efficiently a best approximate equilibrium, that is, with smallest possible A among all A-approximate equilibria of the given instance.

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Liu, Lu-Ping, e Wen-Sheng Jia. "An Intelligent Algorithm for Solving the Efficient Nash Equilibrium of a Single-Leader Multi-Follower Game". Mathematics 9, n. 5 (24 febbraio 2021): 454. http://dx.doi.org/10.3390/math9050454.

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This aim of this paper is to provide the immune particle swarm optimization (IPSO) algorithm for solving the single-leader–multi-follower game (SLMFG). Through cooperating with the particle swarm optimization (PSO) algorithm and an immune memory mechanism, the IPSO algorithm is designed. Furthermore, we define the efficient Nash equilibrium from the perspective of mathematical economics, which maximizes social welfare and further refines the number of Nash equilibria. In the end, numerical experiments show that the IPSO algorithm has fast convergence speed and high effectiveness.

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Kumar, Akhilesh, Anjana Gupta e Aparna Mehra. "A bilevel game model for ascertaining competitive target prices for a buyer in negotiation with multiple suppliers". RAIRO - Operations Research 56, n. 1 (gennaio 2022): 293–330. http://dx.doi.org/10.1051/ro/2021185.

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In this paper, a decision-support is developed for a strategic problem of identifying target prices for the single buyer to negotiate with multiple suppliers to achieve common goal of maintaining sustained business environment. For this purpose, oligopolistic-competitive equilibrium prices of suppliers are suggested to be considered as target prices. The problem of identifying these prices is modeled as a multi-leader-single-follower bilevel programming problem involving linear constraints and bilinear objective functions. Herein, the multiple suppliers are considered leaders competing in a Nash game to maximize individual profits, and the buyer is a follower responding with demand-order allocations to minimize the total procurement-cost. Profit of each supplier is formulated on assessing respective operational cost to fulfill demand-orders by integrating aggregate-production-distribution-planning mechanism into the problem. A genetic-algorithm-based technique is designed in general for solving large-scale instances of the variant of bilevel programming problems with multiple leaders and single follower, and the same is applied to solve the modeled problem. The developed decision support is appropriately demonstrated on the data of a leading FMCG manufacturing firm, which manufactures goods through multiple sourcing.

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Shi, Chenguang, Wei Qiu, Fei Wang, Sana Salous e Jianjiang Zhou. "Stackelberg Game-Theoretic Low Probability of Intercept Performance Optimization for Multistatic Radar System". Electronics 8, n. 4 (2 aprile 2019): 397. http://dx.doi.org/10.3390/electronics8040397.

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In this paper, the problem of Stackelberg game-theoretic low probability of intercept (LPI) performance optimization in multistatic radar system is investigated. The goal of the proposed LPI optimization strategy is to minimize the transmitted power of each radar while satisfying a predetermined signal-to-interference-plus-noise ratio (SINR) requirement for target detection. Firstly, a single-leader multi-follower Stackelberg game is adopted to formulate the LPI optimization problem of multistatic radar system. In the considered game model, the hostile intercept receiver plays a role of leader, who decides the prices of power resource first through the maximization of its own utility function. The multiple radars are followers to compete with each other in a non-cooperative game according to the imposed prices from the intercept receiver subsequently. Then, the Nash equilibrium (NE) for the considered game model is derived, and the existence and uniqueness of the NE are analytically proved. Furthermore, a pricing-based distributed iterative power control algorithm is proposed. Finally, some simulation examples are provided to demonstrate that the proposed scheme has remarkable potential to enhance the LPI performance of the multistatic radar system.

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Bao, Xiao-Ying, e Lei Zhang. "Green Procurement Relationships Development under Carbon Emissions Regulations: A Bi-Level Programming Approach". International Journal of Environmental Research and Public Health 15, n. 10 (6 ottobre 2018): 2183. http://dx.doi.org/10.3390/ijerph15102183.

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A multi-period Stackelberg game is adopted to study a green procurement relationship between manufacturers and suppliers in a supply chain. The manufacturers are considered as leaders, while the suppliers are modelled as followers in this Stackelberg game. Accordingly, a mixed binary linear bi-level programming model is developed to elaborate the game in consideration of carbon tax scheme. The upper level (the leader) aims at selecting a proper number of suitable suppliers to provide heterogeneous raw materials at the lowest operational cost. The objective of the lower level (the follower) is to find optimal purchasing quantities of raw materials. In addition, two lemmas are introduced to transform the mixed linear bi-level programming model into a single level linear programming model. The numerical example illustrates that: (1) the manufacturer prefers to adopt the multiple sourcing strategy due to the flexibility; (2) keeping stable supplies and large order volumes could effectively reduce carbon emissions for the suppliers and make the supply chain greener.

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Zuo, Juan, WenBo Wang e XiangMin Hou. "A two-tier game model based scheduling strategy for Virtual Power Plants". Journal of Physics: Conference Series 2378, n. 1 (1 dicembre 2022): 012096. http://dx.doi.org/10.1088/1742-6596/2378/1/012096.

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Abstract Recently, there has been a lot of attention on how to enhance the management capabilities of distributed electricity production and demand aggregation by Virtual Power Plants (VPPs), which poses the challenge of leveraging their ability to participate in electricity markets to maximize operating profits. This paper analyzes the scheduling problem in fully distributed controlled VPP and proposes a two-level game model. In this model, the Stackelberg game is used to describe the interaction between Distributed Energy Resources (DER) and Energy Management System (EMS). On the other hand, the competition between DERs is formulated by the Cournot game. EMS sets its electric rate as single-leader, and DERs generate the optimal generation capacity accordingly as multi-follower. Then, we analyze and obtain the relationship between the demand and the resource supply to achieve market equilibrium on maximizing the utility of EMS and DERs. Simulation results show the analysis’s correctness and the proposed strategies’ performance improvement.

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Ganguly, Baishakhi, Biswajit Sarkar, Mitali Sarkar, Sarla Pareek e Muhammad Omair. "Influence of controllable lead time, premium price, and unequal shipments under environmental effects in a supply chain management". RAIRO - Operations Research 53, n. 4 (13 settembre 2019): 1427–51. http://dx.doi.org/10.1051/ro/2018041.

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Recently, carbon emission becomes a major issue during transportation of products from one player to another player. Due to the increasing number of single-setup-multi-delivery (SSMD) policies by several industries, fixed and variable transportation cost and carbon emission cost are considered. The aim of the model is to reduce the total cost of supply chain for controlling the lead time and to diminish setup cost by a discrete investment. A premium cost is introduced and Stackelberg game policy is employed to obtain the analytical solution. Some numerical examples are given to validate the model. Sensitivity analysis and managerial insights are given to show the applicability of the model. Finally, the outcomes show that the model minimizes the optimum cost at the optimal values of the decision variables. It is found that the total cost is minimized when the multi-buyer is leader and vendor is follower.

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Scopelliti, Domenico. "On a Class of Multistage Stochastic Hierarchical Problems". Mathematics 10, n. 21 (31 ottobre 2022): 4044. http://dx.doi.org/10.3390/math10214044.

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In this paper, following the multistage stochastic approach proposed by Rockafellar and Wets, we analyze a class of multistage stochastic hierarchical problems: the Multistage Stochastic Optimization Problem with Quasi-Variational Inequality Constraints. Such a problem is defined in a suitable functional setting relative to a finite set of possible scenarios and certain information fields. The key of this multistage stochastic hierarchical problem turns out to be the nonanticipativity: some constraints have to be included in the formulation to take into account the partial information progressively revealed. In this way, we are able to study real-world problems in which the hierarchical decision processes are characterized by sequential decisions in response to an increasing level of information. As an application of this class of multistage stochastic hierarchical problems, we focus on the study of a suitable Single-Leader-Multi-Follower game.

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Han, Qi, Guangming Tan, Xiang Fu, Yadong Mei e Zhenyu Yang. "Water Resource Optimal Allocation Based on Multi-Agent Game Theory of HanJiang River Basin". Water 10, n. 9 (4 settembre 2018): 1184. http://dx.doi.org/10.3390/w10091184.

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Water scarcity is an important issue in many countries, and it is therefore necessary to improve the efficiency and equality of water resource allocation for decision makers. Based on game theory (GT), a bi-level optimization model is developed from the perspective of a leader-follower relationship among agents (stakeholders) of a river basin in this study, which consists of a single-agent GT-based optimization model of common interest and a multi-agent cooperative GT-based model. The Hanjiang River Basin is chosen as a case study, where there are conflicts among different interest agents in this basin. The results show that the proposed bi-level model could attain the same improvement of common interest by 8%, with the conventional optimal model. However, different from the conventional optimal model, since the individual interests have been considered in the bi-level optimization model, the willingness of cooperation of individuals has risen from 20% to 80%. With a slight decrease by 3% of only one agent, the increases of interest of other agents are 14%, 18%, 7%, and 14%, respectively, when using the bi-level optimization model. The conclusion could be drawn that the proposed model is superior to the conventional optimal model. Moreover, this study provides scientific support for the large spatial scale water resource allocation model.

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Li, Shiyong, Wenzhe Li, Huan Liu e Wei Sun. "A Stackelberg Game Approach toward Migration of Enterprise Applications to the Cloud". Mathematics 9, n. 19 (22 settembre 2021): 2348. http://dx.doi.org/10.3390/math9192348.

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With the development of cloud computing, more and more cloud resources are rented or purchased by users. Using an economics approach to achieve cloud resource management has been thought of as a good choice for an enterprise user to complete an application’s migration and deployment into the public cloud. During an application’s migration process, it is important but very challenging to achieve the satisfaction of both the enterprise user and the public cloud provider at the same time. In this paper, we apply an economics approach to investigate the migration optimization problem during the migration process of applications from the enterprise user’s data center to the remote public cloud. We consider the application migration time of the enterprise user and the energy consumption of physical machines, and establish a single static round optimization problem for both the enterprise user and the cloud provider on the premise of satisfying the quality of experience (QoE) based on the Stackelberg game, where the public cloud provider is leader and the enterprise user is follower. Then we propose a novel algorithm to find the optimal physical machine placement for application migration. After that, we further consider that an enterprise user needs to migrate several applications, and extend the single-round static game to the multi-round dynamic game, where the energy consumption costs of the physical machines are reduced by adjusting the states of the physical machines in each round. We finally illustrate the performance of our scheme through some simulation results.

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Yu, Qianwen, Zehao Sun, Junyuan Shen, Xia Xu e Xiangnan Chen. "Interactive Allocation of Water Pollutant Initial Emission Rights in a Basin under Total Amount Control: A Leader-Follower Hierarchical Decision Model". International Journal of Environmental Research and Public Health 20, n. 2 (13 gennaio 2023): 1511. http://dx.doi.org/10.3390/ijerph20021511.

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The initial emission rights allocation is the key measure to achieve the goal of total amount control and deepen the emission trading system. Although many studies have focused on the modeling of initial emission rights allocation, such as using game theory and multi-objective optimization methods, few studies have observed the hierarchical relationship of mutual interference and restriction between watershed management agency and local governments in each subarea during allocation. This relationship directly affects the rationality of the results of regional emission rights allocation. In this study, a leader-follower hierarchical decision model (LFHDM) for allocating initial emission rights in a basin is developed. Based on the bilevel programming approach, the model simulates the interactive decision-making process between the watershed management agency of the upper-level model (LFHDM-U) and the local government of the lower-level model (LFHDM-L) in the allocation under total amount control. A case study of China’s Yellow River Basin is conducted to demonstrate the feasibility and practicality of the model. Findings reveal that, compared with the single-level model, the developed LFHDM has higher satisfaction with the allocation scheme. Under different scenarios, the overall satisfaction of the configuration schemes of COD and NH3-N in each province and autonomous region remains above 0.9. In addition, the allocation volumes of COD and NH3-N in each province of the Yellow River Basin in planning year increase with the enhancement of allowable assimilative capacity of water bodies, but the interval gap of satisfaction with allocation schemes gradually narrows. It shows that when the allowable assimilation capacity of a water body is low, the decision-making of the allocation scheme needs to be more cautious. Moreover, for the Yellow River Basin, apart from Qinghai and Sichuan, the task of reducing water pollutants in other provinces in the next few years is very arduous. The average reduction of total COD and NH3-N in the basin is about 48% and 46%, respectively.

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Zhang, Yu, Shih-Sen Chang e Tao Chen. "Existence and Generic Stability of Strong Noncooperative Equilibria of Vector-Valued Games". Mathematics 9, n. 24 (7 dicembre 2021): 3158. http://dx.doi.org/10.3390/math9243158.

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In this paper, we obtain an existence theorem of general strong noncooperative equilibrium point of vector-valued games, in which every player maximizes all goals. We also obtain an existence theorem of strong equilibrium point of vector-valued games with single-leader–multi-follower framework by using the upper semicontinuous of parametric strong noncooperative equilibrium point set of the followers. Moreover, we obtain some results on the generic stability of general strong noncooperative equilibrium point vector-valued games.

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Basilico, Nicola, Stefano Coniglio, Nicola Gatti e Alberto Marchesi. "Bilevel programming methods for computing single-leader-multi-follower equilibria in normal-form and polymatrix games". EURO Journal on Computational Optimization 8, n. 1 (18 maggio 2019): 3–31. http://dx.doi.org/10.1007/s13675-019-00114-8.

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Li, Yanqiang, Lijuan Li, Yang Xia, Daifeng Zhang e Yong Wang. "Multi-leader single-follower stackelberg game task offloading and resource allocation based on selection optimization in Internet of Vehicles". IEEE Access, 2023, 1. http://dx.doi.org/10.1109/access.2023.3280412.

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Dong, Tingting, Xiaotong Sun, Qi Luo, Jian Wang e Yafeng Yin. "The Dual Effects of Team Contest Design on On-Demand Service Work Schedules". Service Science, 8 marzo 2023. http://dx.doi.org/10.1287/serv.2023.0320.

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Emerging on-demand service platforms (OSPs) have recently embraced teamwork as a strategy for stimulating workers’ productivity and mediating temporal supply and demand imbalances. This research investigates the team contest scheme design problem considering work schedules. Introducing teams on OSPs creates a hierarchical single-leader multi-follower game. The leader (platform) establishes rewards and intrateam revenue-sharing rules for distributing workers’ payoffs. Each follower (team) competes with others by coordinating the schedules of its team members to maximize the total expected utility. The concurrence of interteam competition and intrateam coordination causes dual effects, which are captured by an equilibrium analysis of the followers’ game. To align the platform’s interest with workers’ heterogeneous working-time preferences, we propose a profit-maximizing contest scheme consisting of a winner’s reward and time-varying payments. A novel algorithm that combines Bayesian optimization, duality, and a penalty method solves the optimal scheme in the nonconvex equilibrium-constrained problem. Our results indicate that teamwork is a useful strategy with limitations. Under the proposed scheme, team contest always benefits workers. Intrateam coordination helps teams strategically mitigate the negative externalities caused by overcompetition among workers. For the platform, the optimal scheme can direct teams’ schedules toward more profitable market equilibria when workers have inaccurate perceptions of the market. History: This paper has been accepted for the Service Science Special Issue on Innovation in Transportation-Enabled Urban Services. Funding: This work was supported by the National Science Foundation [Grant FW-HTF-P 2222806]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/serv.2023.0320 .

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Lim, Jisoon, e Neda Masoud. "Dynamic Usage Allocation and Pricing for Curb Space Operation". Transportation Science, 6 giugno 2024. http://dx.doi.org/10.1287/trsc.2024.0507.

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The importance of curbside management is quickly growing in a modernized urban setting. Dynamic allocation of curb space to different usages and dynamic pricing for those usages can help meet the growing demand for curb space more effectively and promote user turnover. To model curbside operations, we formulate a Stackelberg leader-follower game between a leader operating curbside spaces, who sets space allocation and pricing of each curbside usage, and multi-followers, one for each type of curbside usage, who accept the proposed prices or reject them in favor of outside options. The proposed model offers flexible adaptability to manage curb space usages characterized by high turnover rates, such as parking and ride-sourcing pickup and drop-off, alongside accommodating usages that require more permanent infrastructure allocation, such as micromobility stations. Furthermore, the proposed model is able to capture the sensitivity of users to both prices, which are determined solely by the operator, and the occupancy levels of the curb space, which are determined by the complex interactions between the curbside operator and the users. We model a Stackelberg leader-follower game as a bilevel nonlinear optimization problem and reconstruct the problem into a single-level convex program by applying the Karush-Kuhn-Tucker conditions, objective function transformation, and constraint linearization. Then, we develop a solution algorithm that leverages valid inequalities produced via Benders decomposition. We validate the practicability of the model and draw insights into curbside management using numerical experiments. History: This paper has been accepted for the Transportation Sci. Special Issue on the ISTTT25 Conference. Funding: This work was supported by the National Science Foundation, Division of Civil, Mechanical and Manufacturing Innovation [Grant 2046372]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0507 .

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Chakraborty, A., Tarun Maiti e B. C. Giri. "Consignment stock policy in a closed-loop supply chain". RAIRO - Operations Research, 16 giugno 2020. http://dx.doi.org/10.1051/ro/2020064.

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The main feature of sustainable supply Chain Management is reuse of End of Life (EOL) products to reduce the environmental pollution. This paper considers the Consignment Stock (CS) policy for a Closed-Loop Supply Chain (CLSC). To achieve the economic goal, this study presents a multi-echelon supply chain with a single manufacturer, a single retailer and a third-party service provider. The objective is to optimize this three-level CLSC under a Stackelberg game scenario. The other objective is to identify the environmental impact of remanufacturing EOL products. In this CLSC, the manufacturer acts as the Stackelberg leader and the retailer, the third party are the followers. Under manufacturer's leadership, the retailer and the third party acquire three different decision strategies - I, II, and III. In decision strategy I, the retailer acts as the leader and the third party acts as a follower, whereas in decision strategy II, they obtain a Nash game strategy. In the decision strategy III, they act as one unit and decide their decisions centrally. Numerical example and sensitivity analysis are used to illustrate optimal results of different decision strategies and also check the behaviour of key model-parameters. The best outcomes are found in decision strategy I. The main findings of our study show that when upper level player has more power then the supply chain gives best outcomes.

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Grimm, Veronika, Daniel Nowak, Lars Schewe, Martin Schmidt, Alexandra Schwartz e Gregor Zöttl. "A tractable multi-leader multi-follower peak-load-pricing model with strategic interaction". Mathematical Programming, 13 dicembre 2021. http://dx.doi.org/10.1007/s10107-021-01708-0.

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AbstractWhile single-level Nash equilibrium problems are quite well understood nowadays, less is known about multi-leader multi-follower games. However, these have important applications, e.g., in the analysis of electricity and gas markets, where often a limited number of firms interacts on various subsequent markets. In this paper, we consider a special class of two-level multi-leader multi-follower games that can be applied, e.g., to model strategic booking decisions in the European entry-exit gas market. For this nontrivial class of games, we develop a solution algorithm that is able to compute the complete set of Nash equilibria instead of just individual solutions or a bigger set of stationary points. Additionally, we prove that for this class of games, the solution set is finite and provide examples for instances without any Nash equilibria in pure strategies. We apply the algorithm to a case study in which we compute strategic booking and nomination decisions in a model of the European entry-exit gas market system. Finally, we use our algorithm to provide a publicly available test library for the considered class of multi-leader multi-follower games. This library contains problem instances with different economic and mathematical properties so that other researchers in the field can test and benchmark newly developed methods for this challenging class of problems.

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Aussel, Didier, Cécile Egea e Martin Schmidt. "A tutorial on solving single‐leader‐multi‐follower problems using SOS1 reformulations". International Transactions in Operational Research, 26 maggio 2024. http://dx.doi.org/10.1111/itor.13466.

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AbstractIn this tutorial, we consider single‐leader‐multi‐follower games in which the models of the lower‐level players have polyhedral feasible sets and convex objective functions. This situation allows for classic Karush–Kuhn–Tucker reformulations of the separate lower‐level problems, which lead to challenging single‐level reformulations of Mathematical Programing with Complementarity Constraints (MPCC) type. The main contribution of this tutorial is to present a ready‐to‐use reformulation of this MPCC using special‐ordered‐sets of type 1 (SOS1) conditions. These conditions are readily available in all modern mixed‐integer linear optimization solvers that solve the single‐leader‐multi‐follower problem to optimality. After formally stating the problem class under consideration as well as deriving its reformulations, we present explicit Python code that shows how these techniques can be realized using the solver Gurobi. Finally, we also show the effect of the SOS1‐based reformulation using the real‐world example of industrial eco‐park modeling.

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Borges, Pedro, Claudia Sagastizábal e Mikhail Solodov. "Decomposition Algorithms for Some Deterministic and Two-Stage Stochastic Single-Leader Multi-Follower Games". Computational Optimization and Applications, 5 gennaio 2021. http://dx.doi.org/10.1007/s10589-020-00257-0.

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Xi, Haoning, Didier Aussel, Wei Liu, S. Travis Waller e David Rey. "Single-leader multi-follower games for the regulation of two-sided Mobility-as-a-Service markets". European Journal of Operational Research, giugno 2022. http://dx.doi.org/10.1016/j.ejor.2022.06.041.

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Articoli di riviste sul tema "Single-Leader-Multi-Follower game"

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