Distributed Nash Equilibrium Seeking for General Networked Games With Bounded Disturbances

This paper is concerned with anti-disturbance Nash equilibrium seeking for games with partial information.First,reduced-order disturbance observer-based algorithms are proposed to achieve Nash equilibrium seeking for games with firstorder and second-order players,respectively.In the developed algorithms,the observed disturbance values are included in control signals to eliminate the influence of disturbances,based on which a gradient-like optimization method is implemented for each player.Second,a signum function based distributed algorithm is proposed to attenuate disturbances for games with secondorder integrator-type players.To be more specific,a signum function is involved in the proposed seeking strategy to dominate disturbances,based on which the feedback of the velocity-like states and the gradients of the functions associated with players achieves stabilization of system dynamics and optimization of players'objective functions.Through Lyapunov stability analysis,it is proven that the players'actions can approach a small region around the Nash equilibrium by utilizing disturbance observerbased strategies with appropriate control gains.Moreover,exponential(asymptotic)convergence can be achieved when the signum function based control strategy(with an adaptive control gain)is employed.The performance of the proposed algorithms is tested by utilizing an integrated simulation platform of virtual robot experimentation platform(V-REP)and MATLAB.

Stackelberg Game for Wireless Powered and Backscattering Enabled Sensor Networks

This paper investigates a wireless powered and backscattering enabled sensor network based on the non-linear energy harvesting model, where the power beacon(PB) delivers energy signals to wireless sensors to enable their passive backscattering and active transmission to the access point(AP). We propose an efficient time scheduling scheme for network performance enhancement, based on which each sensor can always harvest energy from the PB over the entire block except its time slots allocated for passive and active information delivery. Considering the PB and wireless sensors are from two selfish service providers, we use the Stackelberg game to model the energy interaction among them. To address the non-convexity of the leader-level problem, we propose to decompose the original problem into two subproblems and solve them iteratively in an alternating manner. Specifically, the successive convex approximation, semi-definite relaxation(SDR) and variable substitution techniques are applied to find a nearoptimal solution. To evaluate the performance loss caused by the interaction between two providers, we further investigate the social welfare maximization problem. Numerical results demonstrate that compared to the benchmark schemes, the proposed scheme can achieve up to 35.4% and 38.7% utility gain for the leader and the follower, respectively.

Distributed Optimal Variational GNE Seeking in Merely Monotone Games

In this paper, the optimal variational generalized Nash equilibrium(v-GNE) seeking problem in merely monotone games with linearly coupled cost functions is investigated, in which the feasible strategy domain of each agent is coupled through an affine constraint. A distributed algorithm based on the hybrid steepest descent method is first proposed to seek the optimal v-GNE. Then, an accelerated algorithm with relaxation is proposed and analyzed, which has the potential to further improve the convergence speed to the optimal v-GNE. Some sufficient conditions in both algorithms are obtained to ensure the global convergence towards the optimal v-GNE. To illustrate the performance of the algorithms, numerical simulation is conducted based on a networked Nash-Cournot game with bounded market capacities.

Design and pricing of maintenance service contract based on Nash non-cooperative game approach

Nowadays manufacturers are facing fierce challenge.Apart from the products,providing customers with multiple maintenance options in the service contract becomes more popular,since it can help to improve customer satisfaction,and ultimately promote sales and maximize profit for the manufacturer.By considering the combinations of corrective maintenance and preventive maintenance,totally three types of maintenance service contracts are designed.Moreover,attractive incentive and penalty mechanisms are adopted in the contracts.On this basis,Nash non-cooperative game is applied to analyze the revenue for both the manufacturer and customers,and so as to optimize the pricing mechanism of maintenance service contract and achieve a win-win situation.Numerical experiments are conducted.The results show that by taking into account the incentive and penalty mechanisms,the revenue can be improved for both the customers and manufacturer.Moreover,with the increase of repair rate and improvement factor in the preventive maintenance,the revenue will increase gradually for both the parties.

Stackelberg Game-Based Optimal Dispatch for PEDF Park and Power Grid Interaction under Multiple Incentive Mechanisms

The integration of photovoltaic,energy storage,direct current,and flexible load(PEDF)technologies in building power systems is an importantmeans to address the energy crisis and promote the development of green buildings.The friendly interaction between the PEDF systems and the power grid can promote the utilization of renewable energy and enhance the stability of the power grid.For this purpose,this work introduces a framework of multiple incentive mechanisms for a PEDF park,a building energy system that implements PEDF technologies.The incentive mechanisms proposed in this paper include both economic and noneconomic aspects,which is the most significant innovation of this paper.By modeling the relationship between a PEDF park and the power grid into a Stackelberg game,we demonstrate the effectiveness of these incentive measures in promoting the friendly interaction between the two entities.In this game model,the power grid determines on the prices of electricity trading and incentive subsidy,aiming to maximize its revenue while reducing the peak load of the PEDF park.On the other hand,the PEDF park make its dispatch plan according to the prices established by the grid,in order to reduce electricity consumption expense,improve electricity utility,and enhance the penetration rate of renewable energy.The results show that the proposed incentive mechanisms for the PEDF park can help to optimize energy consumption and promote sustainable energy practices.

Research on Operation Optimization of Energy Storage Power Station and Integrated Energy Microgrid Alliance Based on Stackelberg Game

With the development of renewable energy technologies such as photovoltaics and wind power,it has become a research hotspot to improve the consumption rate of new energy and reduce energy costs through the deployment of energy storage.To solve the problem of the interests of different subjects in the operation of the energy storage power stations(ESS)and the integrated energy multi-microgrid alliance(IEMA),this paper proposes the optimization operation method of the energy storage power station and the IEMA based on the Stackelberg game.In the upper layer,ESS optimizes charging and discharging decisions through a dynamic pricing mechanism.In the lower layer,IEMA optimizes the output of various energy conversion coupled devices within the IEMA,as well as energy interaction and demand response(DR),based on the energy interaction prices provided by ESS.The results demonstrate that the optimization strategy proposed in this paper not only effectively balances the benefits of the IEMA and ESS but also enhances energy consumption rates and reduces IEMA energy costs.

Nash Equilibrium of a Fixed-Sum Two-Player Game

It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.

车联网中基于三方Stackelberg博弈的动态多媒体定价方案

在当前车联网的应用场景下,中继车辆数据转发的积极性低下与存储空间有限,导致用户体验质量(QoE)降低,为此提出基于三方Stackelberg博弈的动态多媒体定价方案.为了激励中继车辆参与转发多媒体内容,提出多媒体内容定价框架,其中中继车辆获得全额佣金后向路侧单元(RSU)支付部分佣金.设计基于Stackelberg博弈的动态定价模型,根据中继车辆、用户车辆与RSU三方的存储空间利用率、内容数据大小和成本因素,建立各自的效用函数,并将其转化为三方四阶段Stackelberg定价模型.通过反向归纳法证明纳什均衡的存在,实现三方之间的动态定价以得到各自最优策略.仿真结果表明,所提方案有效解决了中继车辆存储空间过载问题,并提高了中继车辆积极性,且在提升用户QoE方面较传统方案具有优势.

面向无线边缘网络的分层Stackelberg博弈群体激励方法

现有分布式机器学习模型的相关激励机制大多基于单层服务器架构,难以适应当前异构无线计算场景,同时存在计算资源分配不平衡、通信成本高昂等问题.针对上述问题,创新地提出一种面向无线边缘网络的分层Stackelberg博弈群体激励方法(Hierarchical Stackelberg game Swarm Learning Incentive method for wireless edge network,HSISL),创新地将Stackelberg博弈机制引入群体学习模型中,依据各参与方性能差异,云端聚合平台、边缘簇节点、边缘计算节点三方进行动态博弈,通过双定价公平激励过程,共同制定个性化分层资源分配策略,得到模型训练的最优纳什解,有效引导边缘计算模型进行正向加速.通过理论与实验分析,HSISL能够有效提升模型公平性与训练效率,其在MNIST数据集上的准确率可达96.06%.

互补品供应链Stackelberg博弈下纵向决策研究

以两条均由一个制造商和一个零售商构成的互补品供应链为研究对象,探讨互补品供应链采用不同决策方式时的链间Stackelberg博弈和链内Stackelberg博弈问题,研究市场规模、成本等参数对市场价格、需求、利润的影响。进一步地,对链间Stackelberg博弈下的四种决策方式(集中-集中、集中-分散、分散-集中、分散-分散)下的均衡解进行比较分析。研究表明:互补产品生产成本与需求、利润负相关;自身价格与互补产品成本负相关;集中决策是互补品主导供应链的占优策略;对于跟随者供应链而言,采取集中决策还是分散决策方式,首先取决于主导者供应链的决策方式,其次取决于产品之间的互补程度;集中-集中决策方式是互补品供应链的帕累托均衡解。因此,互补品供应链内部成员之间可设计一种增量利润分享机制,确保供应链集中决策的稳定性;互补品供应链之间应注重两个方面:一是相互合作共同降低产品成本,实现降本增效;二是以某条供应链产品进行低价引流,促进消费者对互补产品的需求,进而实现互补品供应链利润最大化。

基于Stackelberg博弈的停车场管理策略

为了解决城市停车难问题,基于Stackelberg博弈论提出了停车场运营者与交通管理者共同决策的城市停车场管理策略。针对停车者、停车场运营者和交通管理者的交互关系,从博弈论角度分析了这三方参与者之间的影响,并建立了这三方参与者的相应效用函数;以交通管理者与停车场运营者利益主体矛盾最小化为目标,基于Stackelberg博弈建立了这三方的博弈模型,确定了实时停车场进出管理原则;基于数值仿真将差分进化算法与Kriging代理模型进行联立对博弈模型进行求解,得到相应停车预约管理方案及三方效用;通过数值仿真将基于Stackelberg博弈得到的方案与停车场运营者利益最大化方案进行对比分析。研究结果表明:在主线流量大、中、小三种情景下,基于Stackelberg博弈方案是各方利益矛盾最小的方案。

双碳目标下基于Stackelberg和合作博弈的虚拟电厂双层优化调度

在中国的双碳目标下,大规模新能源发电接入虚拟电厂时,将导致电力市场交易中的高额惩罚成本。为此,设计了虚拟电厂参与日前市场竞标的双层博弈模型,以双层收益最大化为目标对虚拟电厂进行调度优化。首先,利用场景生成与削减技术考虑风力发电商和电动汽车聚合商的不确定性,设计了由风力发电商、电动汽车聚合商和燃气轮机合作组成的虚拟电厂下层电量竞标模型,以及虚拟电厂控制中心的上层电价竞标模型。其次,基于两个子模型之间的主从递阶关系,利用卡罗需库-恩塔-克(KKT)条件将双层模型转化为一个混合互补问题,通过求解获得优化方案,并基于Shapley值法对合作方进行利润分配。数值算例表明,设计的模型能有效减少碳排放和降低风电惩罚成本,同时增加参与者的收益。

IWSNs防移动干扰节点的两层协作Stackelberg博弈

针对工业无线传感器网络物理层移动干扰攻击节点的攻击问题,研究sink节点和簇头节点共同抵御攻击的两层协作博弈模型。在簇头节点中选择最佳协作节点,共同抵御移动干扰攻击节点;以网络安全速率为优化目标,将sink节点、最佳协作节点和攻击节点之间的合作竞争关系建模为两层协作Stackelberg博弈模型,采用逆向归纳法求解博弈均衡解。仿真实验结果表明,与未采用协作节点的方案相比,采用的最佳协作节点选择方案对移动攻击节点的抵御效果更佳,且与其他协作博弈功率控制模型相比,两层协作Stackelberg博弈模型可有效提高工业无线传感器网络的安全速率。

基于Stackelberg博弈的电炉企业供应链渠道选择模型

为了提升电炉企业供应链渠道的风险抵抗力,设计一种基于Stackelberg博弈的电炉企业供应链渠道选择模型。在Stackelberg博弈中,分析电炉企业供应链成员的Stackelberg博弈条件,作出相关假设;将Stackelberg博弈基本元素与电炉企业供应链元素一一对应,计算实际市场需求量和收益函数,确定电炉企业渠道选择的影响因素,建立物流企业供应链渠道选择模型;设计电炉企业供应链渠道选择步骤,选择最优的电炉企业供应链渠道。实验结果表明:研究方法选择的供应链渠道在内部风险和外部风险条件均获得较高收益,具有较优的抗风险能力。

A Novel Stackelberg-Game-Based Energy Storage Sharing Scheme Under Demand Charge

Demand response(DR)using shared energy storage systems(ESSs)is an appealing method to save electricity bills for users under demand charge and time-of-use(TOU)price.A novel Stackelberg-game-based ESS sharing scheme is proposed and analyzed in this study.In this scheme,the interactions between selfish users and an operator are characterized as a Stackelberg game.Operator holds a large-scale ESS that is shared among users in the form of energy transactions.It sells energy to users and sets the selling price first.It maximizes its profit through optimal pricing and ESS dispatching.Users purchase some energy from operator for the reduction of their demand charges after operator's selling price is announced.This game-theoretic ESS sharing scheme is characterized and analyzed by formulating and solving a bi-level optimization model.The upper-level optimization maximizes operator's profit and the lower-level optimization minimizes users'costs.The bi-level model is transformed and linearized into a mixed-integer linear programming(MILP)model using the mathematical programming with equilibrium constraints(MPEC)method and model linearizing techniques.Case studies with actual data are carried out to explore the economic performances of the proposed ESS sharing scheme.

Stackelberg Game-Based Resource Allocation with Blockchain for Cold-Chain Logistics System

Cold-chain logistics system(CCLS)plays the role of collecting and managing the logistics data of frozen food.However,there always exist problems of information loss,data tampering,and privacy leakage in traditional centralized systems,which influence frozen food security and people’s health.The centralized management form impedes the development of the cold-chain logistics industry and weakens logistics data availability.This paper first introduces a distributed CCLS based on blockchain technology to solve the centralized management problem.This system aggregates the production base,storage,transport,detection,processing,and consumer to form a cold-chain logistics union.The blockchain ledger guarantees that the logistics data cannot be tampered with and establishes a traceability mechanism for food safety incidents.Meanwhile,to improve the value of logistics data,a Stackelberg game-based resource allocation model has been proposed between the logistics data resource provider and the consumer.The competition between resource price and volume balances the resource supplement and consumption.This model can help to achieve an optimal resource price when the Stackelberg game obtains Nash equilibrium.The two participants also can maximize their revenues with the optimal resource price and volume by utilizing the backward induction method.Then,the performance evaluations of transaction throughput and latency show that the proposed distributed CCLS is more secure and stable.The simulations about the variation trend of data price and amount,optimal benefits,and total benefits comparison of different forms show that the resource allocation model is more efficient and practical.Moreover,the blockchain-based CCLS and Stackelberg game-based resource allocation model also can promote the value of logistic data and improve social benefits.

Research on the bi-layer low carbon optimization strategy of integrated energy system based on Stackelberg master slave game

With increasing reforms related to integrated energy systems(IESs),each energy subsystem,as a participant based on bounded rationality,significantly influences the optimal scheduling of the entire IES through mutual learning and imitation.A reasonable multiagent joint operation strategy can help this system meet its low-carbon objectives.This paper proposes a bilayer low-carbon optimal operational strategy for an IES based on the Stackelberg master-slave game and multiagent joint operation.The studied IES includes cogeneration,power-to-gas,and carbon capture systems.Based on the Stackelberg master-slave game theory,sellers are used as leaders in the upper layer to set the prices of electricity and heat,while energy producers,energy storage providers,and load aggregators are used as followers in the lower layer to adjust the operational strategy of the system.An IES bilayer optimization model based on the Stackelberg master-slave game was developed.Finally,the Karush-Kuhn-Tucker(KKT)condition and linear relaxation technology are used to convert the bilayer game model to a single layer.CPLEX,which is a mathematical program solver,is used to solve the equilibrium problem and the carbon emission trading cost of the system when the benefits of each subject reach maximum and to analyze the impact of different carbon emission trading prices and growth rates on the operational strategy of the system.As an experimental demonstration,we simulated an IES coupled with an IEEE 39-node electrical grid system,a six-node heat network system,and a six-node gas network system.The simulation results confirm the effectiveness and feasibility of the proposed model.

基于Stackelberg博弈的电动汽车充电管理策略

电动汽车的充电效率和充电成本是电动汽车电源管理的重要问题,也是影响电动汽车推广的关键因素。对此,提出一种基于Stackelberg博弈模型的收费控制策略。在博弈中,电网、零售商和用户都参与决策,充电策略可以灵活地满足电网、零售商和用户的不同需求,采用逆归纳法得到博弈模型的均衡解。通过仿真、无序充电过程和基于静态分时电价的充电控制方法对其效益进行比较,分析博弈模型中参数对收费过程的影响,验证了该方法的有效性。

Cooperative Anti-Jamming and Interference Mitigation for UAV Networks: A Local Altruistic Game Approach

To improve the anti-jamming and interference mitigation ability of the UAV-aided communication systems, this paper investigates the channel selection optimization problem in face of both internal mutual interference and external malicious jamming. A cooperative anti-jamming and interference mitigation method based on local altruistic is proposed to optimize UAVs’ channel selection. Specifically, a Stackelberg game is modeled to formulate the confrontation relationship between UAVs and the jammer. A local altruistic game is modeled with each UAV considering the utilities of both itself and other UAVs. A distributed cooperative anti-jamming and interference mitigation algorithm is proposed to obtain the Stackelberg equilibrium. Finally, the convergence of the proposed algorithm and the impact of the transmission power on the system loss value are analyzed, and the anti-jamming performance of the proposed algorithm can be improved by around 64% compared with the existing algorithms.

A multi-UAV deployment method for border patrolling based on Stackelberg game

To strengthen border patrol measures, unmanned aerial vehicles(UAVs) are gradually used in many countries to detect illegal entries on borders. However, how to efficiently deploy limited UAVs to patrol on borders of large areas remains challenging. In this paper, we first model the problem of deploying UAVs for border patrol as a Stackelberg game. Two players are considered in this game: The border patrol agency is the leader,who optimizes the patrol path of UAVs to detect the illegal immigrant. The illegal immigrant is the follower, who selects a certain area of the border to pass through at a certain time after observing the leader’s strategy. Second, a compact linear programming problem is proposed to tackle the exponential growth of the number of leader’s strategies. Third, a method is proposed to reduce the size of the strategy space of the follower. Then, we provide some theoretic results to present the effect of parameters of the model on leader’s utilities. Experimental results demonstrate the positive effect of limited starting and ending areas of UAV’s patrolling conditions and multiple patrolling altitudes on the leader ’s utility, and show that the proposed solution outperforms two conventional patrol strategies and has strong robustness.