Search Results (108)

This paper investigates a multiple unmanned aerial vehicle (UAV) enabled network for supporting emergency communication services, where each drone acts as a base station (also called the drone small cell (DSC)). The novelty of this paper is that a mean field game (MFG)-based strategy is conceived for jointly controlling the three-dimensional (3D) locations of these drones to guarantee the distortion requirement of lossy communications, while considering the inter-cell interference and the flight energy consumption of drones. More explicitly, we derive the Hamilton–Jacobi–Bellman (HJB) and Fokker–Planck–Kolmogorov (FPK) equations, and propose an algorithm where both the Lax–Friedrichs scheme and the Lagrange relaxation are invoked for solving the HJB and FPK equations with 3D control vectors and state vectors. The numerical results show that the proposed algorithm can achieve a higher access rate with a similar flight energy consumption. Full article

The proportion of grid-connected renewable energy, represented by wind and photovoltaic power, continues to rise. The intermittence and volatility of the power output of renewable energy bring serious challenges to the secure and stable operation of the power system. Adopting a market-based approach to promote the active participation of producers in frequency regulation and other auxiliary service markets besides the energy market is the only way to comprehensively solve the problems of power system security, stability, and economic benefits. Therefore, for the future bidding decision scenario of large-scale renewable energy generators participating in the energy–frequency regulation market, a bi-level game-theoretic bidding model based on mean-field game and non-cooperative game theory is proposed. The inner level is a mean-field game among large-scale renewable energy generators of the same type, and the outer level is a non-cooperative game among different types of generators. A combination of fixed-point iteration and finite-difference method is employed to solve the proposed bi-level bidding decision model. Case analysis indicates that the proposed model can effectively realize the bidding decision optimization for large-scale renewable energy generators in the energy–frequency regulation market. Furthermore, in comparison to traditional proportional bidding model, the proposed model enables renewable energy generators to secure higher profits in the energy–frequency regulation market. Full article

As an emerging and lively research field, game designers are employing Dynamic Difficulty Adjustment (DDA) in Game Artificial Intelligence (Game AI) to improve player experience. Traditional DDA methods focus little on player churn, which cannot always lead to enhanced player engagement. Hence, we propose the Engagement-oriented Dynamic Difficulty Adjustment (EDDA) to meet the urgent need for a highly general and customizable solution in the game industry. EDDA directly considers players’ churn trend to ensure player engagement during gameplay. Its real-time monitoring algorithm and common parameter set are effective in quantifying and preventing player churn. We developed a prototype system integrating seven major game genres to verify the difficulty, gameplay time, and scores of the Game Engagement Questionnaire (GEQ) in multiple dimensions. EDDA has the largest mean and median of all genres in the above metrics with the highest confidence level and effect size, which demonstrates its generality and availability in improving player experience. It is fair to say that EDDA not only provides game designers with targeted player churn monitoring and intervention means, but also offers a deeper level of thinking for the generalized application of DDA and other Game AI technologies. Full article

In recent years, rapid progress in autonomous driving has been achieved through advances in sensing, control, and earning. However, as the complexity of traffic scenarios increases, ensuring safe interaction among vehicles remains a formidable challenge. Recent works combining artificial potential fields (APFs) with game-theoretic methods have shown promise in modeling vehicle interactions and avoiding collisions. However, these approaches often suffer from overly conservative decisions or fail to capture the nonlinear dynamics of real-world driving. To address these imitations, we propose a novel framework that integrates mean field game (MFG) theory with model predictive control (MPC) and quadratic programming (QP). Our approach everages the aggregate behavior of surrounding vehicles to predict interactive effects and embeds these predictions into an MPC-QP scheme for real-time control. Simulation results in complex driving scenarios demonstrate that our method achieves multiple autonomous driving tasks while ensuring collision-free operation. Furthermore, the proposed framework outperforms popular game-based benchmarks in terms of achieving driving tasks and producing fewer collisions. Full article

Background: Agility is crucial in game sports, requiring both motor and cognitive skills. Athletes must perceive and process information to adapt movements, yet traditional agility tests often lack cognitive and multidirectional demands. Additionally, modern test systems are mostly stationary. This study evaluated the novel and portable “Functional Agility Square Test” (FAST) for validity, reliability, and usefulness. Methods: To assess discriminant validity, 22 game sports (GS) and 22 non-game sports (NGS) athletes participated in one session. Test–retest reliability was examined with 36 GS athletes (20 female) across three sessions. Participants performed cognitive (FAST_COG), preplanned (FAST_MOT), and randomized (FAST_SAT) reactive change-of-direction tasks, each repeated three times per session. Results: Results showed significantly lower response times (RTs) in GS compared to NGS (p < 0.05). Mean RTs indicated moderate relative reliability (ICC 0.50–0.74), while medians showed moderate to good reliability (ICC 0.59–0.83). Usefulness was evident from the first session (FAST_MOT) or from the third session (FAST_SAT) based on median RTs. Conclusions: Thus, the FAST seems to be valid, reliable, and sensitive for GS-based agility assessment. Its portable setup enables ecologically valid field testing. Future research should further increase task complexity to better simulate game conditions. Full article

This paper investigates Mean Field Game methods to solve missile interception strategies in three-dimensional space, with a focus on analyzing the pursuit–evasion problem in many-to-many scenarios. By extending traditional missile interception models, an efficient solution is proposed to avoid dimensional explosion and communication burdens, particularly for large-scale, multi-missile systems. The paper presents a system of stochastic differential equations with control constraints, describing the motion dynamics between the missile (pursuer) and the target (evader), and defines the associated cost function, considering proximity group distributions with other missiles and targets. Next, Hamilton–Jacobi–Bellman equations for the pursuers and evaders are derived, and the uniqueness of the distributional solution is proved. Furthermore, using the $ϵ$-Nash equilibrium framework, it is demonstrated that, under the MFG model, participants can deviate from the optimal strategy within a certain tolerance, while still minimizing the cost. Finally, the paper summarizes the derivation process of the optimal strategy and proves that, under reasonable assumptions, the system can achieve a uniquely stable equilibrium, ensuring the stability of the strategies and distributions of both the pursuers and evaders. The research provides a scalable solution to high-risk, multi-agent control problems, with significant practical applications, particularly in fields such as missile defense systems. Full article

Robustness is an important issue in deep learning, and Bayesian neural networks (BNNs) provide means of robustness analysis, while the minimax method is a conservative choice in the classical Bayesian field. Recently, researchers have applied the closed-loop idea to neural networks via the minimax method and proposed the closed-loop neural networks. In this paper, we study more conservative BNNs with the minimax method, which formulates a two-player game between a deterministic neural network and a sampling stochastic neural network. From this perspective, we reveal the connection between the closed-loop neural and the BNNs. We test the models on some simple data sets and study their robustness under noise perturbation, etc. Full article

Acquired brain injury (ABI) is one of the leading causes of disability worldwide. Immersive virtual reality (IVR) is an emerging tool in the field of neurological rehabilitation that has shown promising results, although it has been little studied in patients with ABI. The main objective of this study was to explore the feasibility of a TEVI-DCA program as a rehabilitation tool for people with ABI. In this study, 14 people with ABI were recruited (mean age of 52.43 years (range from 35 to 65 years), 57.1% men) and took part in a twice-weekly IVR therapy program. The intervention was feasible and safe. The participants completed the program with no adverse effects (no symptoms on the Simulator Sickness Questionnaire), and experienced high usability (System Usability Scale > 80%) and outstandingly positive post-game experiences (Game Experience Questionnaire 2.56/4). In addition, the participants significantly improved several of their physical and cognitive capacities, showing increased strength (handgrip p = 0.042), reduced fall risk (Tinetti test p < 0.001), an increase in the physical component of the quality of life (PCS-SF-8 p = 0.006), and improved executive functions (Wisconsin Card Sorting Test p = 0.005). These findings demonstrate that the TEVI-DCA program appears to be a feasible therapeutic tool for people with ABI, as it has shown maximum adherence, with an absence of adverse events, and was shown to lead to improvements in physical–cognitive aspects, although further studies are needed to corroborate the findings of this study. Full article

This paper investigates the role of fiscal incentives in promoting the transition to a green economy using a dynamic mean-field game framework. By modeling firms as representative agents undergoing an environmentally sustainable transition, we analyze two distinct types of incentive structure: fixed incentives and incentives based on the average behavior of firms. The findings underscore the importance of balancing incentive structures to avoid economic inefficiencies and ensure a smooth ecological transition. Full article

To explore the coupling relationship between information propagation behaviors and evolution dynamics in swarm systems, this paper establishes the SEBAR model based on mean field theory with a macroscopic view of information dissemination. Then, the balance points and basic reproduction number are calculated and a proof of equilibrium stability from the point of view of system stability is given. In addition, the influence of model parameters on propagation behaviors is also analyzed. To stimulate the emergence of cooperative behaviors in a swarm system, a repeated “prisoner’s dilemma” game based on controllable individuals is proposed under the framework of bionic “soft control”. The combination of information propagation and game strategies is used to realize information regulation. The simulation results show that the proposed models and methods can reflect the information communication patterns and evolution characteristics. It also illustrates the viability and effectiveness of regulating information through the evolutionary game. Full article

This study examines the subjective attributes that coaches consider most important for identifying and developing the talent of junior élite football players. It also explores whether players’ physical fitness efficiency moderates these attributes and influences playing time during the regular season. Forty-three junior élite football players and four Italian Serie A club coaches participated in the study, contributing their unique perspectives and experiences. Players’ physical fitness was assessed using the Yo-Yo Intermittent Recovery Level 1 test, while coaches rated players’ abilities through a structured questionnaire. A significant positive relationship was found between ’understanding of the game and position on the field’ and total playing time (t = 3.498, p < 0.01, β = 0.953). Physical efficiency further strengthened this relationship when players’ fitness levels were average (b = 0.624, p < 0.001) and one standard deviation above the mean (b = 0.891, p < 0.001). These findings highlight the importance of tactical awareness in earning playing time and suggest that physical fitness enhances the effect of cognitive abilities on performance. This study provides insights into how coaches assess talent and underscores the value of integrating physical and tactical development in youth football, providing a testament to the power of collaboration in advancing our understanding of talent identification in sports. Full article

This review paper examines the current landscape of electricity market modelling, specifically focusing on stochastic approaches, transitioning from Mean Field Games (MFGs) to Neural Network (NN) modelling. The central objective is to scrutinize and synthesize evolving modelling strategies within power systems, facilitating technological advancements in the contemporary electricity market. This paper emphasizes the assessment of model efficacy, particularly in the context of MFG and NN applications. Our findings shed light on the diversity of models, offering practical insights into their strengths and limitations, thereby providing a valuable resource for researchers, policy makers, and industry practitioners. The review guides navigating and leveraging the latest stochastic modelling techniques for enhanced decision making and improved market operations. Full article

Multi-population mean-field game is a critical subclass of mean-field games (MFGs). It is a theoretically feasible multi-agent model for simulating and analyzing the game between multiple heterogeneous populations of interacting massive agents. Due to the factors of game complexity, dimensionality disaster and disturbances should be taken into account simultaneously to solve the multi-population high-dimensional stochastic MFG problem, which is a great challenge. We present CA-Net, a coupled alternating neural network approach for tractably solving multi-population high-dimensional MFGs. First, we provide a universal modeling framework for large-scale heterogeneous multi-agent game systems, which is strictly expressed as a multi-population MFG problem. Next, we generalize the potential variational primal–dual structure that MFGs exhibit, then phrase the multi-population MFG problem as a convex–concave saddle-point problem. Last but not least, we design a generative adversarial network (GAN) with multiple generators and multiple discriminators—the solving network—which parameterizes the value functions and the density functions of multiple populations by two sets of neural networks, respectively. In multi-group quadcopter trajectory-planning numerical experiments, the convergence results of HJB residuals, control, and average speed show the effectiveness of the CA-Net algorithm, and the comparison with baseline methods—cluster game, HJB-NN, Lax–Friedrichs, ML, and APAC-Net—shows the progressiveness of our solution method. Full article

In unmanned aerial vehicle (UAV)-assisted device-to-device (D2D) caching networks, the uncertainty from unpredictable content demands and variable user positions poses a significant challenge for traditional optimization methods, often making them impractical. Multi-agent deep reinforcement learning (MADRL) offers significant advantages in optimizing multi-agent system decisions and serves as an effective and practical alternative. However, its application in large-scale dynamic environments is severely limited by the curse of dimensionality and communication overhead. To resolve this problem, we develop a scalable heterogeneous multi-agent mean-field actor-critic (SH-MAMFAC) framework. The framework treats ground users (GUs) and UAVs as distinct agents and designs cooperative rewards to convert the resource allocation problem into a fully cooperative game, enhancing global network performance. We also implement a mixed-action mapping strategy to handle discrete and continuous action spaces. A mean-field MADRL framework is introduced to minimize individual agent training loads while enhancing total cache hit probability (CHP). The simulation results show that our algorithm improves CHP and reduces transmission delay. A comparative analysis with existing mainstream deep reinforcement learning (DRL) algorithms shows that SH-MAMFAC significantly reduces training time and maintains high CHP as GU count grows. Additionally, by comparing with SH-MAMFAC variants that do not include trajectory optimization or power control, the proposed joint design scheme significantly reduces transmission delay. Full article

In this article, we present the mathematical foundations of generative machine intelligence and link them with mean-field-type game theory. The key interaction mechanism is self-attention, which exhibits aggregative properties similar to those found in mean-field-type game theory. It is not necessary to have an infinite number of neural units to handle mean-field-type terms. For instance, the variance reduction in error within generative machine intelligence is a mean-field-type problem and does not involve an infinite number of decision-makers. Based on this insight, we construct mean-field-type transformers that operate on data that are not necessarily identically distributed and evolve over several layers using mean-field-type transition kernels. We demonstrate that the outcomes of these mean-field-type transformers correspond exactly to the mean-field-type equilibria of a hierarchical mean-field-type game. Due to the non-convexity of the operators’ composition, gradient-based methods alone are insufficient. To distinguish a global minimum from other extrema—such as local minima, local maxima, global maxima, and saddle points—alternative methods that exploit hidden convexities of anti-derivatives of activation functions are required. We also discuss the integration of blockchain technologies into machine intelligence, facilitating an incentive design loop for all contributors and enabling blockchain token economics for each system participant. This feature is especially relevant to ensuring the integrity of factual data, legislative information, medical records, and scientifically published references that should remain immutable after the application of generative machine intelligence. Full article