Optimization is critical in various fields like smart vehicles, and transportation. Federated Learning (FL) has emerged as an effective approach in the coordination of autonomous vehicles, but traditional methods such as FedAvg can create performance disparities across clients. This paper addresses this fairness issue through the $q$-Fair Federated Learning ($q$-FFL) framework, adjusting model performance across clients using a tunable fairness parameter. We propose a modified FedAvg algorithm for $q$-FFL that maintains comparable convergence rates, ensuring more balanced client outcomes. Additionally, we explore incentive mechanisms in FL using a Stackelberg game model, incorporating a fairness coefficient to encourage equitable participation. Building on prior works, we redefine client utility functions to address communication and computation costs, ensuring fair resource allocation. The proposed framework achieves both global and local fairness, maintaining a unique Nash equilibrium in the modified game setting.

This study investigates optimal decisions in a green supply chain consisting of a manufacturer and a leading retailer considering the green marketing and fairness preferences of member firms. Four Stackelberg game decision models are constructed in which the manufacturer and the re-tailer engage in green marketing separately when the manufacturer has no and has fairness preferences. The impacts of fairness preferences and green marketing on the optimal decision in the green supply chain are comparatively analyzed. The study finds that member firms perform green marketing regardless of the presence or absence of fairness preferences and that such be-havior increases the wholesale price, retail price, and market demand of low-carbon products as well as the profits of member firms and the supply chain. A more interesting finding is that the profit growth of member firms and the supply chain due to the manufacturer’s green marketing is more pronounced than that due to the retailer’s green marketing. When the retailer and the manufacturer engage in conduct green marketing, the manufacturer's fairness preferences have different effects on the wholesale price, retail price, market demand, level of green marketing efforts, member enterprises and profits of supply chain. Therefore, firms should consider the impact of green marketing and fairness preferences to make pricing and performance decisions, so as to achieve efficient operation of the whole supply chain and avoid double marginal effects. Finally, the above conclusions are verified through numerical simulation, providing a reference for the decision-making of member firms in the green supply chain.

This article has two objectives. Firstly, we will use the vector variational-like inequalities problems to achieve local approximate (weakly) efficient solutions of Vector Optimization Problem within the novel field of the Hadamard manifolds. Previously, we will introduce the concepts of generalized approximate geodesic convex functions and illustrate them with examples. We will see the minimum requirements under which critical points, solutions of Stampacchia and Minty weak variational-like inequalities and local approximate weakly efficient solutions can be identified, extending previous results from the literature for linear Euclidean spaces. Secondly, we will show an economical application, using again solutions of the variational problems to identify with Stackelberg equilibrium points on Hadamard manifolds and under geodesic convexity assumptions.

Unmanned Aerial Vehicles (UAVs) severing as the relay is an effective technology method to extend the coverage. It can also alleviate the congestion and increase the throughput, especially applied in UAV networks. However, since the energy of UAVs is limited and the resources in UAV networks are scarce, how to optimize the network delay performance under these constraints should be well investigated. Besides, the relationship among different resources, e.g. power and bandwidth, is coupled which makes the optimization more complex. This article investigates the problem of joint power and bandwidth allocation in UAV backhaul networks, which considers both the delay performance and the resource utilization efficiency. Considering the heterogeneous locations characteristics of different UAVs, we formulate the optimization problem as a Stackelberg game. The relay UAV acts as the leader and extended UAVs act as followers. Their utility functions take both the delay durance and the resource consumption into account. To capture the competitive relationship among followers, the sub-game is proved to be an exact potential game and exists Nash equilibriums (NE). The Stackelberg Equilibrium (SE) is proved afterwards. We utilize a hierarchical learning algorithm (HLA) to find out the best resource allocation strategies, which also reduces the computational complexity. Simulation results demonstrate the effectiveness of the proposed method.

The chemical industry is an integral part of the world economy and a substantial income source for developing countries. However, existing regulations or the enforcement of these regulations, on controlling atmospheric pollutants sometimes may be insufficient, leading to the deterioration of surrounding ecosystems and to a quality decrease of the atmospheric environment. Previous works in this domain fail to generate executable solutions for inspection agencies due to practical challenges. In addressing these challenges, we introduce a so-called Chemical Plant Environment Protection Game (CPEP) to generate reasonable schedules of high-accuracy air quality monitoring stations for inspection agencies. First, Stackelberg Security Games (SSGs) are incorporated together with source estimation methods into this research. Second, high-accuracy air quality monitoring stations as well as gas sensors are modeled into the CPEP. Third, simplified data analysis on the regularly discharging of chemical plants is utilized to construct the CPEP. Finally, an illustrative case study is used to investigate the effectiveness of the CPEP Game, and a realistic case study is conducted to illustrate how the models and algorithms being proposed in this paper, work. Results show that playing a CPEP Game can reduce operational costs of high-accuracy air quality monitoring stations; moreover, playing the game leads to more compliance from the chemical plants towards the inspection agencies.