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Keywords = coalition game theory

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20 pages, 1606 KiB  
Article
Brain Tumour Segmentation Using Choquet Integrals and Coalition Game
by Makhlouf Derdour, Mohammed El Bachir Yahiaoui, Moustafa Sadek Kahil, Mohamed Gasmi and Mohamed Chahine Ghanem
Information 2025, 16(7), 615; https://doi.org/10.3390/info16070615 - 17 Jul 2025
Viewed by 230
Abstract
Artificial Intelligence (AI) and computer-aided diagnosis (CAD) have revolutionised various aspects of modern life, particularly in the medical domain. These technologies enable efficient solutions for complex challenges, such as accurately segmenting brain tumour regions, which significantly aid medical professionals in monitoring and treating [...] Read more.
Artificial Intelligence (AI) and computer-aided diagnosis (CAD) have revolutionised various aspects of modern life, particularly in the medical domain. These technologies enable efficient solutions for complex challenges, such as accurately segmenting brain tumour regions, which significantly aid medical professionals in monitoring and treating patients. This research focuses on segmenting glioma brain tumour lesions in MRI images by analysing them at the pixel level. The aim is to develop a deep learning-based approach that enables ensemble learning to achieve precise and consistent segmentation of brain tumours. While many studies have explored ensemble learning techniques in this area, most rely on aggregation functions like the Weighted Arithmetic Mean (WAM) without accounting for the interdependencies between classifier subsets. To address this limitation, the Choquet integral is employed for ensemble learning, along with a novel evaluation framework for fuzzy measures. This framework integrates coalition game theory, information theory, and Lambda fuzzy approximation. Three distinct fuzzy measure sets are computed using different weighting strategies informed by these theories. Based on these measures, three Choquet integrals are calculated for segmenting different components of brain lesions, and their outputs are subsequently combined. The BraTS-2020 online validation dataset is used to validate the proposed approach. Results demonstrate superior performance compared with several recent methods, achieving Dice Similarity Coefficients of 0.896, 0.851, and 0.792 and 95% Hausdorff distances of 5.96 mm, 6.65 mm, and 20.74 mm for the whole tumour, tumour core, and enhancing tumour core, respectively. Full article
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28 pages, 2701 KiB  
Article
Optimal Scheduling of Hybrid Games Considering Renewable Energy Uncertainty
by Haihong Bian, Kai Ji, Yifan Zhang, Xin Tang, Yongqing Xie and Cheng Chen
World Electr. Veh. J. 2025, 16(7), 401; https://doi.org/10.3390/wevj16070401 - 17 Jul 2025
Viewed by 177
Abstract
As the integration of renewable energy sources into microgrid operations deepens, their inherent uncertainty poses significant challenges for dispatch scheduling. This paper proposes a hybrid game-theoretic optimization strategy to address the uncertainty of renewable energy in microgrid scheduling. An energy trading framework is [...] Read more.
As the integration of renewable energy sources into microgrid operations deepens, their inherent uncertainty poses significant challenges for dispatch scheduling. This paper proposes a hybrid game-theoretic optimization strategy to address the uncertainty of renewable energy in microgrid scheduling. An energy trading framework is developed, involving integrated energy microgrids (IEMS), shared energy storage operators (ESOS), and user aggregators (UAS). A mixed game model combining master–slave and cooperative game theory is constructed in which the ESO acts as the leader by setting electricity prices to maximize its own profit, while guiding the IEMs and UAs—as followers—to optimize their respective operations. Cooperative decisions within the IEM coalition are coordinated using Nash bargaining theory. To enhance the generality of the user aggregator model, both electric vehicle (EV) users and demand response (DR) users are considered. Additionally, the model incorporates renewable energy output uncertainty through distributionally robust chance constraints (DRCCs). The resulting two-level optimization problem is solved using Karush–Kuhn–Tucker (KKT) conditions and the Alternating Direction Method of Multipliers (ADMM). Simulation results verify the effectiveness and robustness of the proposed model in enhancing operational efficiency under conditions of uncertainty. Full article
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33 pages, 5362 KiB  
Article
A Method for Trust-Based Collaborative Smart Device Selection and Resource Allocation in the Financial Internet of Things
by Bo Wang, Jiesheng Wang and Mingchu Li
Sensors 2025, 25(13), 4082; https://doi.org/10.3390/s25134082 - 30 Jun 2025
Viewed by 228
Abstract
With the rapid development of the Financial Internet of Things (FIoT), many intelligent devices have been deployed in various business scenarios. Due to the unique characteristics of these devices, they are highly vulnerable to malicious attacks, posing significant threats to the system’s stability [...] Read more.
With the rapid development of the Financial Internet of Things (FIoT), many intelligent devices have been deployed in various business scenarios. Due to the unique characteristics of these devices, they are highly vulnerable to malicious attacks, posing significant threats to the system’s stability and security. Moreover, the limited resources available in the FIoT, combined with the extensive deployment of AI algorithms, can significantly reduce overall system availability. To address the challenge of resisting malicious behaviors and attacks in the FIoT, this paper proposes a trust-based collaborative smart device selection algorithm that integrates both subjective and objective trust mechanisms with dynamic blacklists and whitelists, leveraging domain knowledge and game theory. It is essential to evaluate real-time dynamic trust levels during system execution to accurately assess device trustworthiness. A dynamic blacklist and whitelist transformation mechanism is also proposed to capture the evolving behavior of collaborative service devices and update the lists accordingly. The proposed algorithm enhances the anti-attack capabilities of smart devices in the FIoT by combining adaptive trust evaluation with blacklist and whitelist strategies. It maintains a high task success rate in both single and complex attack scenarios. Furthermore, to address the challenge of resource allocation for trusted smart devices under constrained edge resources, a coalition game-based algorithm is proposed that considers both device activity and trust levels. Experimental results demonstrate that the proposed method significantly improves task success rates and resource allocation performance compared to existing approaches. Full article
(This article belongs to the Special Issue Network Security and IoT Security: 2nd Edition)
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25 pages, 7829 KiB  
Article
Consider Demand Response and Power-Sharing Source-Storage-Load Three-Level Game Models
by Fuyi Zou, Hui He, Xiang Liao, Ke Liu, Shuo Ouyang, Li Mo and Wei Huang
Sustainability 2025, 17(10), 4270; https://doi.org/10.3390/su17104270 - 8 May 2025
Viewed by 398
Abstract
With the increasing connection between integrated natural gas, thermal energy, and electric power systems, the integrated energy system (IES) needs to coordinate the internal unit scheduling and meet the different load demands of customers. However, when the energy subjects involved in scheduling are [...] Read more.
With the increasing connection between integrated natural gas, thermal energy, and electric power systems, the integrated energy system (IES) needs to coordinate the internal unit scheduling and meet the different load demands of customers. However, when the energy subjects involved in scheduling are engaged in conflicts of interest, aspects such as hierarchical status relationships and cooperative and competitive relationships must be considered. Therefore, this paper studies the problem of achieving optimal energy scheduling for multiple subjects of source, storage, and load under the same distribution network while ensuring that their benefits are not impaired. First, this paper establishes a dual master-slave game model with a shared energy storage system (SESS), IES, and the alliance of prosumers (APs) as the main subjects. Second, based on the Nash negotiation theory and considering the sharing of electric energy among prosumers, the APs model is equated into two sub-problems of coalition cost minimization and cooperative benefit distribution to ensure that the coalition members distribute the cooperative benefits equitably. Further, the Stackelberg-Stackelberg-Nash three-layer game model is established, and the dichotomous distributed optimization algorithm combined with the alternating direction multiplier method (ADMM) is used to solve this three-layer game model. Finally, in the simulation results of the arithmetic example, the natural gas consumption is reduced by 9.32%, the economic efficiency of IES is improved by 3.95%, and the comprehensive energy purchase cost of APs is reduced by 12.16%, the proposed model verifies the sustainability co-optimization and mutual benefits of source, storage and load multi-interested subjects. Full article
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25 pages, 337 KiB  
Article
Applications of the Shapley Value to Financial Problems
by Olamide Ayodele, Sunday Timileyin Ayodeji and Kayode Oshinubi
Int. J. Financial Stud. 2025, 13(2), 80; https://doi.org/10.3390/ijfs13020080 - 7 May 2025
Viewed by 665
Abstract
Managing risk, matching resources efficiently, and ensuring fair allocation are fundamental challenges in both finance and decision-making processes. In many scenarios, participants contribute unequally to collective outcomes, raising the question of how to distribute costs, benefits, or opportunities in a justifiable and optimal [...] Read more.
Managing risk, matching resources efficiently, and ensuring fair allocation are fundamental challenges in both finance and decision-making processes. In many scenarios, participants contribute unequally to collective outcomes, raising the question of how to distribute costs, benefits, or opportunities in a justifiable and optimal manner. This paper applies the Shapley value—a solution concept from cooperative game theory—as a principled tool in the following two specific financial settings: first, in tax cooperation games; and second, in assignment markets. In tax cooperation games, we use the Shapley value to determine the equitable tax burden distribution among three firms, A, B, and C, which operate in two countries, Italy and Poland. Our model ensures that countries participating in coalitions face a lower degree of tax evasion compared to non-members, and that cooperating firms benefit from discounted tax liabilities. This structure incentivizes coalition formation and reveals the economic advantage of joint participation. In assignment markets, we use the Shapley value to find the optimal pairing in a four-buyers and four-sellers housing market. Our findings show that the Shapley value provides a rigorous framework for capturing the relative importance of participants in the coalition, leading to more balanced tax allocations and fairer market transactions. Our theoretical insights with computational techniques highlights the Shapley value’s effectiveness in addressing complex allocation challenges across financial management domains. Full article
29 pages, 15643 KiB  
Article
Network Visualization of Cooperative Games
by Carlos I. Pérez-Sechi, Javier Castro, Daniel Gómez, Daniel Martín, Rosa Espínola and Inmaculada Gutiérrez
Appl. Sci. 2025, 15(7), 3825; https://doi.org/10.3390/app15073825 - 31 Mar 2025
Viewed by 683
Abstract
Over the last five decades, the modeling of characteristic functions has been the key focus of cooperative game theory research. Solutions for distributing goods among players have been extensively explored, while less emphasis has been placed on examining player interactions. This paper emphasizes [...] Read more.
Over the last five decades, the modeling of characteristic functions has been the key focus of cooperative game theory research. Solutions for distributing goods among players have been extensively explored, while less emphasis has been placed on examining player interactions. This paper emphasizes the importance of player relationships, with the help of the ‘player interaction index’ to capture coalition formation needs. By representing interactions through a graph, this study deepens the understanding of player relationships and synergies. It elaborates a graphical representation using network analysis to visualize player interactions, enhancing the understanding of the dynamics within the game. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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17 pages, 264 KiB  
Article
A Resolution Under Interval Uncertainty
by Yan-An Hwang and Yu-Hsien Liao
Mathematics 2025, 13(5), 762; https://doi.org/10.3390/math13050762 - 26 Feb 2025
Viewed by 484
Abstract
Traditional transferable utility (TU) games assume precise real-valued utilities for coalition outcomes, but real-world situations often involve uncertainty or imprecision. Interval TU games extend the classical framework by representing utilities and payoffs as closed intervals, leveraging interval arithmetic to address inherent ambiguities in [...] Read more.
Traditional transferable utility (TU) games assume precise real-valued utilities for coalition outcomes, but real-world situations often involve uncertainty or imprecision. Interval TU games extend the classical framework by representing utilities and payoffs as closed intervals, leveraging interval arithmetic to address inherent ambiguities in data. This paper reviews the theoretical foundations of interval TU games and explores allocating solutions under uncertainty. Central to this study is the adaptation of consistency, a fundamental property in game-theoretical resolutions, to the interval framework. Drawing on concepts such as the pseudo equal allocations of non-separable costs and the pseudo weighted allocations of non-separable costs, we characterize these allocation resolutions through a specific reduction and related consistency. By bridging classical TU games with interval generalizations, this study offers a robust foundation for analyzing allocations under uncertainty and outlines avenues for future research in theoretical and applied game theory. Full article
20 pages, 278 KiB  
Article
Extending the Transhuman Person: Religious Practices as Cognitive Technological Enhancements
by Tobias Tanton
Religions 2025, 16(3), 272; https://doi.org/10.3390/rel16030272 - 22 Feb 2025
Cited by 1 | Viewed by 1098
Abstract
Transhumanism embraces the use of technology to enhance human capabilities. In keeping with traditional theories of cognition, transhumanists typically assume that mental capacities are organism-bound (or brain-bound), and enhancement is thus achieved exclusively by modifying the human organism. However, 4E cognition challenges this [...] Read more.
Transhumanism embraces the use of technology to enhance human capabilities. In keeping with traditional theories of cognition, transhumanists typically assume that mental capacities are organism-bound (or brain-bound), and enhancement is thus achieved exclusively by modifying the human organism. However, 4E cognition challenges this assumption. Instead, understanding the mind as extended or scaffolded highlights how cognitive processes recruit environmental resources to perform their tasks. Therefore, as Andy Clark argues, cognitive enhancement is no longer restricted to modifications of the biological organism but is also achieved by using cognitive tools or niches that allow brain–body–world coalitions to perform more efficient or more sophisticated cognitive functions. Hence, humans are ‘natural-born cyborgs’ who have long been using environmental resources to enhance cognitive abilities. In this article, I extend this analysis to religion. Drawing on recent work on 4E cognition in religious practices, I argue that religious practices can themselves be understood as ‘cognitive technologies’ that count as enhancements. These insights from cognitive science serve to reframe the dialog between Christian theology and transhumanism: (1) enhancements are reframed as belonging to a long history of self-modification, rather than being the sole purview of the future, (2) humans should be understood as intrinsically technological, and (3) theologians are already in the enhancement game and, conversely, transhumanists should consider religious practices. Full article
(This article belongs to the Special Issue Situating Religious Cognition)
27 pages, 991 KiB  
Article
Equal Division Contribution Values of Trapezoidal Fuzzy Numbers and Their Application to Profit Allocation in Cold Chain Logistics for Agricultural Products
by Jungan Zhan, Rong Fan, Minghao Liu, Jiacai Liu and Wenjian Zhao
Symmetry 2025, 17(2), 210; https://doi.org/10.3390/sym17020210 - 29 Jan 2025
Viewed by 633
Abstract
With the acceleration of fresh food e-commerce development, cold chain logistics for agricultural products has increasingly become a research hotspot. However, limited by the number of orders accepted by enterprises, many cold chain transportation vehicles for agricultural products struggle to reach a full [...] Read more.
With the acceleration of fresh food e-commerce development, cold chain logistics for agricultural products has increasingly become a research hotspot. However, limited by the number of orders accepted by enterprises, many cold chain transportation vehicles for agricultural products struggle to reach a full load. This undoubtedly increases transportation costs for agricultural product cold chain logistics enterprises. In order to reduce the cost of transportation and increase the profit of enterprises, this paper will adopt the strategy of building enterprise coalition based on cooperative game theory. By increasing the loading rate of transportation vehicles, it will increase the profit of enterprises. First, utilizing the minimization of overall dissatisfaction among players in profit allocation after coalition participation as the objective function, a model of the equal division contribution values of the trapezoidal fuzzy number will be constructed, which will be used as the profit allocation model for the players. Then, the solution of the model will be provided, and the properties including symmetry are analyzed. Second, by improving the loading rate of cold chain transport vehicles as the key and combining various parameters in the transportation stage of agricultural product cold chain logistics, the coalition profit will be calculated. Finally, using the solution of the equal division contribution value of the trapezoidal fuzzy number in the cooperative game as the allocation strategy, the obtained profit will be distributed to each enterprise participating in the coalition. The results show that when dealing with cooperative profit allocation problems in similar scenarios, the solutions of the equal division contribution value of the trapezoidal fuzzy number are highly reliable and adaptable. The method presented in this paper can not only increase the profit of enterprises but also minimize the overall dissatisfaction of all enterprises with the allocation result. Full article
(This article belongs to the Section Computer)
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14 pages, 484 KiB  
Article
The Axiomatic Characterization of the Grey Shapley Value
by Mehmet Gençtürk, Mahmut Sami Öztürk and Osman Palancı
Axioms 2025, 14(1), 51; https://doi.org/10.3390/axioms14010051 - 10 Jan 2025
Viewed by 633
Abstract
One of the most significant solution concepts in cooperative grey game theory is the grey Shapley value. This value is a fascinating one among the models and methods of operations research, and has been the subject of extensive study by other researchers. The [...] Read more.
One of the most significant solution concepts in cooperative grey game theory is the grey Shapley value. This value is a fascinating one among the models and methods of operations research, and has been the subject of extensive study by other researchers. The objective of this study is to characterize and redefine this value in cooperative games where coalition values are grey numbers. In this study, the grey Shapley value is characterized by the following axioms: G-gain loss, G-null player, and G-differential marginality. Finally, this study concludes with an investigation of some applications involving production costs. This study is based on an investigation of the costs incurred when milk producers collaborate. Full article
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29 pages, 13369 KiB  
Article
Cooperative Behavior of Prosumers in Integrated Energy Systems
by Natalia Aizenberg, Evgeny Barakhtenko and Gleb Mayorov
Mathematics 2024, 12(24), 4005; https://doi.org/10.3390/math12244005 - 20 Dec 2024
Viewed by 691
Abstract
The technical complexity of organizing energy systems’ operation has recently been compounded by the complexity of reconciling the interests of individual entities involved in interactions. This study proposes a possible solution to the problem of modeling their relationships within a large system. Our [...] Read more.
The technical complexity of organizing energy systems’ operation has recently been compounded by the complexity of reconciling the interests of individual entities involved in interactions. This study proposes a possible solution to the problem of modeling their relationships within a large system. Our solution takes into account multiple levels of interactions, imperfect information, and conflicting interests. We present a mathematical statement of the problem of optimal interactions between the centralized system and prosumers in the integrated energy system (IES) with due consideration of the layered architecture of the IES. The paper also contributes a model for arranging the interactions between centralized and distributed energy sources for cases when IES prosumers form coalitions. The implementation of this model is based on multi-agent techniques and cooperative game theory tools. In order to arrive at a rational arrangement of the interactions of prosumers in the IES, the model implements different approaches to the allocation of the coalition’s total payoff (the Shapley value, Modiclus, PreNucleolus solution concepts). Furthermore, we propose a criterion for deciding on the “best” imputation. We contribute a multi-agent system that implements the proposed model and use a test IES setup to validate the model by simulations. The results of the simulations ensure optimal interactions between the entities involved in the energy supply process within the IES and driven by their own interests. The results also elucidate the conditions that make it feasible for prosumers to form coalitions. Full article
(This article belongs to the Special Issue Mathematical Modeling and Applications in Industrial Organization)
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27 pages, 6325 KiB  
Article
Handling Exponentially Growing Strategies in Spatial Cooperative Games: The Case of the European Union
by Mehmet Küçükmehmetoğlu, Yasin Fahjan and Muhammed Ziya Paköz
Algorithms 2024, 17(12), 554; https://doi.org/10.3390/a17120554 - 4 Dec 2024
Viewed by 857
Abstract
This paper introduces a comprehensive cooperative game theory framework to measure the significance of location and neighborhood relations in conjunction with the magnitude of players/parties. The significances of these relations are measured over the EU geography. In this case, there are (i) the [...] Read more.
This paper introduces a comprehensive cooperative game theory framework to measure the significance of location and neighborhood relations in conjunction with the magnitude of players/parties. The significances of these relations are measured over the EU geography. In this case, there are (i) the test of availability of a core solution that satisfies all associated parties/players; (ii) the measurement of players’/parties’ rational minimal and maximal return expectations from the grand coalition regarding their all individual and sub-group strategies and associated return rationalities; (iii) the determination of the critical players/parties in the grand coalition. The study’s main contributions are the provision of a methodology that identifies spatially/geographically critical players/parties and the design of an algorithm for handling exponentially growing strategies alongside increasing numbers of players/parties. In sum, a comprehensive cooperative game theory framework is introduced to measure the significance of location and neighborhood relations in conjunction with the magnitude of the players/parties. The case of the EU has revealed the union’s geographically critical countries, with Germany being found to be the most influential. Full article
(This article belongs to the Section Algorithms for Multidisciplinary Applications)
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22 pages, 1124 KiB  
Article
Improved Banzhaf Value Based on Participant’s Triangular Fuzzy Number-Weighted Excess Contributions and Its Application in Manufacturing Supply Chain Coalitions
by Jiacai Liu, Shiying Liu, Rongji Lai and Qingfan Lin
Symmetry 2024, 16(12), 1593; https://doi.org/10.3390/sym16121593 - 29 Nov 2024
Cited by 2 | Viewed by 1082
Abstract
Intense market competition has driven small- and medium-sized enterprises (SMEs) in the manufacturing sector to collaborate and form supply chain coalitions, which can improve the information flow and resource sharing and significantly enhance supply chain management efficiency. However, the distribution of cooperative benefits [...] Read more.
Intense market competition has driven small- and medium-sized enterprises (SMEs) in the manufacturing sector to collaborate and form supply chain coalitions, which can improve the information flow and resource sharing and significantly enhance supply chain management efficiency. However, the distribution of cooperative benefits poses a core challenge for the long-term stability of coalitions. This paper addresses the impact of dynamic changes in complex business environments by utilizing triangular fuzzy numbers to represent the value of coalition, effectively depicting the uncertainty and ambiguity in the cooperation process. Compared to traditional models (which do not use triangular fuzzy numbers), this model is better suited to dynamic changes, offering flexible response mechanisms that ensure adaptability and fairness in the decision-making process. In addition, considering the influence of each member’s weight in the coalition, the fuzzy comprehensive evaluation method is used to determine the weights. With the goal of minimizing the dissatisfaction of enterprises in benefit distribution, a least square contribution with triangular fuzzy numbers is constructed to replace the marginal contribution of the classical Banzhaf value, and an improved Banzhaf value based on the player’s triangular fuzzy number-weighted excess contribution is proposed to arrive at a fair and reasonable benefit allocation strategy in order to enhance the long-term stability and cooperative benefits of coalition. By analyzing an example of the supply chain coalition, the effectiveness of the proposed improved Banzhaf value is verified, which satisfies the uniqueness, the individual rationality, and the group rationality. It not only promotes the level of risk management and decision making under the uncertainty conditions of complex business, but also deepens the theoretical foundation of cooperative game theory and expands its possibilities in practical applications and future development. Full article
(This article belongs to the Section Mathematics)
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17 pages, 2611 KiB  
Article
A Coordinated Bidding Strategy of Wind Power Producers and DR Aggregators Using a Cooperative Game Approach
by Xuemei Dai, Shiyuan Zheng, Haoran Chen and Wenjun Bi
Appl. Sci. 2024, 14(22), 10699; https://doi.org/10.3390/app142210699 - 19 Nov 2024
Cited by 1 | Viewed by 939
Abstract
The purpose of this paper is to analyze the profitability of wind energy and demand response (DR) resources participating in the energy and frequency regulation markets. Since wind power producers (WPPs) must reduce their output to provide up-regulation and DR aggregators (DRAs) have [...] Read more.
The purpose of this paper is to analyze the profitability of wind energy and demand response (DR) resources participating in the energy and frequency regulation markets. Since wind power producers (WPPs) must reduce their output to provide up-regulation and DR aggregators (DRAs) have to purchase additional power to facilitate down-regulation, this may result in revenue loss. If WPPs coordinate with DRAs, these two costs could be reduced. Thus, it would be profitable for WPPs and DRAs to form a coalition to participate in the regulation market. To better utilize the frequency response characteristics of wind and DR resources, this paper proposes a cooperation scheme to optimize the bidding strategy of the coalition. Furthermore, cooperative game theory methods, including Nucleolus- and Shapley-value-based models, are employed to fairly allocate additional benefits among WPPs and DRAs. The uncertainties associated with wind power and the behavior of DR customers are modeled through stochastic programming. In the optimization process, the decision-maker’s attitude toward risks is considered using conditional value at risk (CVaR). Case studies demonstrate that the proposed bidding strategy can improve the performance of the coalition and lead to higher benefits for both WPPs and DRAs. Specifically, the expected revenue of the coordinated strategies increased by 12.1% compared to that of uncoordinated strategies. Full article
(This article belongs to the Special Issue State-of-the-Art of Power Systems)
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21 pages, 716 KiB  
Article
FedBeam: Reliable Incentive Mechanisms for Federated Learning in UAV-Enabled Internet of Vehicles
by Gangqiang Hu, Donglin Zhu, Jiaying Shen, Jialing Hu, Jianmin Han and Taiyong Li
Drones 2024, 8(10), 567; https://doi.org/10.3390/drones8100567 - 10 Oct 2024
Cited by 1 | Viewed by 2067
Abstract
Unmanned aerial vehicles (UAVs) can be utilized as airborne base stations to deliver wireless communication and federated learning (FL) training services for ground vehicles. However, most existing studies assume that vehicles (clients) and UAVs (model owners) offer services voluntarily. In reality, participants (FL [...] Read more.
Unmanned aerial vehicles (UAVs) can be utilized as airborne base stations to deliver wireless communication and federated learning (FL) training services for ground vehicles. However, most existing studies assume that vehicles (clients) and UAVs (model owners) offer services voluntarily. In reality, participants (FL clients and model owners) are selfish and will not engage in training without compensation. Meanwhile, due to the heterogeneity of participants and the presence of free-riders and Byzantine behaviors, the quality of vehicles’ model updates can vary significantly. To incentivize participants to engage in model training and ensure reliable outcomes, this paper designs a reliable incentive mechanism (FedBeam) based on game theory. Specifically, we model the cooperation problem between model owners and clients as a two-layer Stackelberg game and prove the existence and uniqueness of the Stackelberg equilibrium (SE). For the cooperation among model owners, we formulate the problem as a coalition game and based on this, analyze and design a coalition formation algorithm to derive the Pareto optimal social utility. Additionally, to achieve reliable FL model updates, we design a weighted-beta (Wbeta) reputation update mechanism to incentivize FL clients to provide high-quality model updates. The experimental results show that compared to the baselines, the proposed incentive mechanism improves social welfare by 17.6% and test accuracy by 5.5% on simulated and real datasets, respectively. Full article
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