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.

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.

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.

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.

基于Stackelberg Game诱导策略的网络调度算法

首先建立了网络Stackelberg Game模型,分析了该模型下Nash均衡的存在性,给出了网络的队最优解。在网络资源管理中,引入基于Stackelberg Game的网络诱导策略,利用动态博弈和多次逐步诱导的方法,提出了一种网络由一般状态到最优运行状态的动态调度算法。队最优解保证了网络在最优运行状态下的稳定性。数值仿真验证了该算法的有效性。

Multi-Stage Hierarchical Channel Allocation in UAV-Assisted D2D Networks:A Stackelberg Game Approach

UAV-assisted D2D networks can provide auxiliary communication for areas with poor communication facilities by using the characteristics of easy deployment of unmanned aerial vehicle(UAV),then it becomes a promising technology.However,the coexistence of UAV and D2D aggravates the conflict of spectrum resources.In addition,when the UAV performs the communication service,it will inevitably cause the location change,which will make the original channel allocation no longer applicable.Inspired by the influence of frequent channel switching on channel allocation,we define the communication utility as a tradeoff between the throughput and channel switching cost.In the considered model,we investigate the multi-stage hierarchical spectrum access problem with maximizing aggregate communication utilities in UAV-assisted D2D networks.In particular,due to the hierarchical feature of the considered network,we adopt Stackelberg game to formulate this spectrum access problem where both the throughput and channel switching cost are considered.We prove that the proposed game has a stable Stackelberg equilibrium(SE),and the heterogeneous network based channel allocation(HN-CA)algorithm is proposed to achieve the desired solution.Simulation results verify the validity of the proposed game and show the effectiveness of the HN-CA algorithm.

Optimal flexibility dispatch of demand side resources with high penetration of renewables:a Stackelberg game method

To promote the utilization of renewable energy,such as photovoltaics,this paper proposes an optimal flexibility dispatch method for demand-side resources(DSR)based on the Stackelberg game theory.First,the concept of the generalized DSR is analyzed and flexibility models for various DSR are constructed.Second,owing to the characteristics of small capacity but large-scale,an outer approximation is proposed to describe the aggregate flexibility of DSR.Then,the optimal flexibility dispatch model of DSR based on the Stackelberg game is established and a decentralized solution algorithm is designed to obtain the Stackelberg equilibrium.Finally,the actual data are utilized for the case study and the results show that,compared to the traditional centralized optimization method,the proposed optimal flexibility dispatch method can not only reduce the net load variability of the DSR aggregator but is beneficial for all DSR owners,which is more suitable for practical applications.

SDN assisted Stackelberg Game model for LTE-WiFi offloading in 5G networks

The data traffic that is accumulated at the Macro Base Station(MBS)keeps on increasing as almost all the people start using mobile phones.The MBS cannot accommodate all user’s demands,and attempts to offload some users to the nearby small cells so that the user could get the expected service.For the MBS to offload data traffic to an Access Point(AP),it should offer an optimal economic incentive in a way its utility is maximized.Similarly,the APs should choose an optimal traffic to admit load for the price that it gets from MBS.To balance this tradeoff between the economic incentive and the admittance load to achieve optimal offloading,Software Defined Networking(SDN)assisted Stackelberg Game(SaSG)model is proposed.In this model,the MBS selects the users carefully to aggregate the service with AP,so that the user experiencing least service gets aggregated first.The MBS uses the Received Signal Strength Indicator(RSSI)value of the users as the main parameter for aggregating a particular user for a contract period with LTE and WiFi.Each player involved in the game tries to maximize their payoff utilities,and thus,while incorporating those utilities in real-time scenario,we obtain maximum throughput per user which experiences best data service without any lack in Quality of Experience(QoE).Thus,the proposed SaSG model proves better when compared with other game theory models,and hence an optimal data offloading is achieved.

Put Others Before Itself:A Multi-Leader One-Follower Anti-Jamming Stackelberg Game Against Tracking Jammer

This paper mainly investigates the coordinated anti-jamming channel access problems in multiuser scenarios where there exists a tracking jammer who senses the spectrum and traces the channel with maximal receiving power.To cope with the challenges brought by the tracking jammer,a multi-leader onefollower anti-jamming Stackelberg(MOAS)game is formulated,which is able to model the complex interactions between users and the tracking jammer.In the proposed game,users act as leaders,chose their channel access strategies and transmit firstly.The tracking jammer acts as the follower,whose objective is to find the optimal jamming strategy at each time slot.Besides,the existence of Stackelberg equilibriums(SEs)is proved,which means users reach Nash Equilibriums(NEs)for each jamming strategy while the jammer finds its best response jamming strategy for the current network access case.An active attraction based anti-jamming channel access(3ACA)algorithm is designed to reach SEs,where jammed users keep their channel access strategies unchanged to create access chances for other users.To enhance the fairness of the system,users will adjust their strategies and relearn after certain time slots to provide access chances for those users who sacrifice themselves to attract the tracking jammer.

Guarding Legal Communication with Smart Jammer:Stackelberg Game Based Power Control Analysis

This paper investigates a power control problem in a jamming system,where a separate smart jammer is deployed to ensure the communication security of the legal user.However,due to power leakage,the smart jammer may incur unintentional interference to legal users.The key is how to suppress illegal communication while limit the negative impact on legal user.A jamming counter measure Stackelberg game is formulated to model the jamming power control dynamic of the system.The smart jammer acts as a leader to sense and interfere illegal communications of the illegal user,while the illegal user acts as a follower.In the game,the impact of uncertain channel information is taken into account.According to whether illegal user considers the uncertain channel information,we investigate two scenarios,namely,illegal user can obtain statistical distribution and accurate information of interference channel gain and its own cost,respectively.This work not only proposes a jamming counter measure iterative algorithm to update parameters,but also gives two solutions to obtain the Stackelberg equilibrium(SE).The power convergence behaviours under two scenarios are analyzed and compared.Additionally,brute force is used to verify the accuracy of the SE value further.

ACHIEVING OPTIMAL ADVERSARIAL ACCURACY FOR ADVERSARIAL DEEP LEARNING USING STACKELBERG GAMES

The purpose of adversarial deep learning is to train robust DNNs against adversarial attacks,and this is one of the major research focuses of deep learning.Game theory has been used to answer some of the basic questions about adversarial deep learning,such as those regarding the existence of a classifier with optimal robustness and the existence of optimal adversarial samples for a given class of classifiers.In most previous works,adversarial deep learning was formulated as a simultaneous game and the strategy spaces were assumed to be certain probability distributions in order for the Nash equilibrium to exist.However,this assumption is not applicable to practical situations.In this paper,we give answers to these basic questions for the practical case where the classifiers are DNNs with a given structure;we do that by formulating adversarial deep learning in the form of Stackelberg games.The existence of Stackelberg equilibria for these games is proven.Furthermore,it is shown that the equilibrium DNN has the largest adversarial accuracy among all DNNs with the same structure,when Carlini-Wagner s margin loss is used.The trade-off between robustness and accuracy in adversarial deep learning is also studied from a game theoretical perspective.

Secure Transmission in Satellite-UAV Integrated System Against Eavesdropping and Jamming:A Two-Level Stackelberg Game Model

Aiming at the physical layer security(PLS)secure transmission existing in the information backhaul link of the satellite-UAV integrated(SUI)network,a two-layer Stackelberg game model(TSGM)that can resist full-duplex(FD)eavesdropping and jamming attacks is proposed.The confrontation relationship between the UAV network and the attacker is established as the first layer Stackelberg game.The source UAV adjusts its own transmission power strategy according to the attacker’s jamming strategy to resist malicious jamming attacks.The internal competition and cooperation relationship in UAV network is modeled as the second layer Stackelberg game,and the optimal cooperative UAV transmits jamming signal to the attacker to resist malicious eavesdropping attacks.Aiming at the“selfishness”of UAV nodes,a price incentive mechanism is established to encourage UAV to actively participate in cooperation,so as to maximize the advantages of cooperative communication.For the proposed TSGM,we construct the utility function and analyze the closed equilibrium solution of the game model,and design a three-stage optimal response iterative(TORI)algorithm to solve the game equilibrium.The simulation results show that the proposed TSGM can effectively increase the utility of the source UAV and improve the enthusiasm of cooperation compared with other power control models.

基于Stackelberg Game模型的网络性能研究

通过对多局域世界模型(Multi-Local-World Model,MLWM)的分析,抽取出一个基本的拓扑子结构,并将主从博弈的思想引入到网络流量控制中,建立了一个基于网络拓扑的Stackelberg博弈模型.在该模型下,分析了Nash均衡的存在性与唯一性,求出了Nash均衡时最佳的链路价格和流量,给出了网络最佳运行状态的一种定量描述,最后分析了网络拓扑参数对网络最佳运行状态的影响,研究了该模型下网络拓扑变化引起的网络性能的演化特性.

Cognitive RAN Slicing Resource Allocation Based on Stackelberg Game

The cognitive network has become a promising method to solve the spectrum resources shortage problem.Especially for the optimization of network slicing resources in the cognitive radio access network(RAN),we are interested in the profit of the mobile virtual network operator(MVNO)and the utility of secondary users(SUs).In cognitive RAN,we aim to find the optimal scheme for the MVNO to efficiently allocate slice resources to SUs.Since the MVNO and SUs are selfish and the game between the MVNO and SUs is difficult to reach equilibrium,we consider modeling this scheme as a Stackelberg game.Leveraging mathematical programming with equilibrium constraints(MPEC)and Karush-Kuhn-Tucker(KKT)conditions,we can obtain a single-level optimization problem,and then prove that the problem is a convex optimization problem.The simulation results show that the proposed method is superior to the noncooperative game.While guaranteeing the Quality of Service(QoS)of primary users(PUs)and SUs,the proposed method can balance the profit of the MVNO and the utility of SUs.

Dual Power Allocation Optimization Based on Stackelberg Game in Heterogeneous Network with Hybrid Energy Supplies

In heterogeneous network with hybrid energy supplies including green energy and on-grid energy, it is imperative to increase the utilization of green energy as well as to improve the utilities of users and networks. As the difference of hybrid energy source in stability and economy, thus, this paper focuses on the network with hybrid energy source, and design the utility of each user in the hybrid energy source system from the perspective of stability, economy and environment pollution. A dual power allocation algorithm based on Stackelberg game to maximize the utilities of users and networks is proposed. In addition, an iteration method is proposed which enables all players to reach the Stackelberg equilibrium(SE). Simulation results validate that players can reach the SE and the utilities of users and networks can be maximization, and the green energy can be efficiently used.

A Multi-Objective Coordinated Charging and Discharging Strategy for Electric Vehicles Based on Stackelberg Game

For the negative impact of large-scale electric vehicles (EVs) disorderly charging on the power grid, a multi-objective optimization strategy for coordinated charging and discharging of EVs based on Stackelberg game is proposed. As the leader, the grid company aims to stabilize load fluctuations and formulate a reasonable electricity price strategy to guide EVs to participate in vehicle-to-grid (V2G);As followers, EV users optimize their charging plans based on electricity price information with the objective of reducing costs and obtaining good comfort. This paper uses the MOPSO algorithm to solve the proposed multi-objective Stackelberg problem, and calculates the optimization results under various preferences, which proves the effectiveness of the proposed model and method.

Bi-level Multi-leader Multi-follower Stackelberg Game Model for Multi-energy Retail Package Optimization

In the competitive energy market,energy retailers are facing the uncertainties of both energy price and demand,which requires them to formulate reasonable energy purchasing and selling strategies for improving their competitiveness in this market.Particularly,the attractive multi-energy retail packages are the key for retailers to increase their benefit.Therefore,combined with incentive means and price signals,five types of multi-energy retail packages such as peak-valley time-of-use(TOU)price package and day-night bundled price package are designed in this paper for retailers.The iterative interactions between retailers and end-users are modeled using a bi-level model of stochastic optimization based on multi-leader multi-follower(MLMF)Stackelberg game,in which retailers are leaders and end-users are followers.Retailers make decisions to maximize the profit considering the conditional value at risk(CVaR)while end-users optimize the satisfaction of both energy comfort and economy.Besides,a distributed algorithm is proposed to obtain the Nash equilibrium of above MLMF Stackelberg game model while the particle swarm optimization(PSO)algorithm and CPLEX solver are applied to solve the optimization model for each participant(retailer or end-user).Numeral results show that the designed retail packages can increase the overall profit of retailers,and the overall satisfaction of industrial users is the highest while that of residential users is the lowest after game interaction.

Hierarchical Control Strategy for Load Regulation Based on Stackelberg Game Theory Considering Randomness

Demand response has been recognized as a valuable functionality of power systems for mitigating power imbalances.This paper proposes a hierarchical control strategy among the distribution system operator(DSO),load aggregators(LAs),and thermostatically controlled loads(TCLs);the strategy includes a scheduling layer and an executive layer to provide load regulation.In the scheduling layer,the DSO(leader)offers compensation price(CP)strategies,and the LAs(followers)respond to CP strategies with available regulation power(ARP)strategies.Profits of the DSO and LAs are modeled according to their behaviors during the load regulation process.Stackelberg game is adopted to capture interactions among the players and leader and to obtain the optimal strategy for each participant to achieve utility.Moreover,considering inevitable random factors in practice,e.g.,renewable generation and behavior of users,two different stochastic models based on sample average approximation(SAA)and parameter modification are formulated with improved scheduling accuracy.In the executive layer,distributed TCLs are triggered based on strategies determined in the scheduling layer.A self-triggering method that does not violate user privacy is presented,where TCLs receive external signals from the LA and independently determine whether to alter their operation statuses.Numerical simulations are performed on the modified IEEE-24 bus system to verify effectiveness of the proposed strategy.

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.