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.

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.

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.

Linear-quadratic generalized Stackelberg games with jump-diffusion processes and related forward-backward stochastic differential equations

A kind of linear-quadratic Stackelberg games with the multilevel hierarchy driven by both Brownian motion and Poisson processes is considered.The Stackelberg equilibrium is presented by linear forward-backward stochastic differential equations(FBSDEs)with Poisson processes(FBSDEPs)in a closed form.By the continuity method,the unique solvability of FBSDEPs with a multilevel self-similar domination-monotonicity structure is obtained.

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.

Mean-field type FBSDEs in a domination-monotonicity framework and LQ multi-level Stackelberg games

Motivated by various mean-field type linear-quadratic(MF-LQ,for short)multilevel Stackelberg games,we propose a kind of multi-level self-similar randomized dominationmonotonicity structures.When the coefficients of a class of mean-field type forwardbackward stochastic differential equations(MF-FBSDEs,for short)satisfy this kind of structures,we prove the existence,the uniqueness,an estimate and the continuous dependence on the coefficients of solutions.Further,the theoretical results are applied to construct unique Stackelberg equilibria for forward and backward MF-LQ multi-level Stackelberg games,respectively.

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.

Attention Markets of Blockchain-Based Decentralized Autonomous Organizations

The attention is a scarce resource in decentralized autonomous organizations(DAOs),as their self-governance relies heavily on the attention-intensive decision-making process of“proposal and voting”.To prevent the negative effects of pro-posers’attention-capturing strategies that contribute to the“tragedy of the commons”and ensure an efficient distribution of attention among multiple proposals,it is necessary to establish a market-driven allocation scheme for DAOs’attention.First,the Harberger tax-based attention markets are designed to facilitate its allocation via continuous and automated trading,where the individualized Harberger tax rate(HTR)determined by the pro-posers’reputation is adopted.Then,the Stackelberg game model is formulated in these markets,casting attention to owners in the role of leaders and other competitive proposers as followers.Its equilibrium trading strategies are also discussed to unravel the intricate dynamics of attention pricing.Moreover,utilizing the single-round Stackelberg game as an illustrative example,the existence of Nash equilibrium trading strategies is demonstrated.Finally,the impact of individualized HTR on trading strategies is investigated,and results suggest that it has a negative correlation with leaders’self-accessed prices and ownership duration,but its effect on their revenues varies under different conditions.This study is expected to provide valuable insights into leveraging attention resources to improve DAOs’governance and decision-making process.

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.

Mega-Constellations Based TT&C Resource Sharing: Keep Reliable Aeronautical Communication in an Emergency

With the development of the transportation industry, the effective guidance of aircraft in an emergency to prevent catastrophic accidents remains one of the top safety concerns. Undoubtedly, operational status data of the aircraft play an important role in the judgment and command of the Operational Control Center(OCC). However, how to transmit various operational status data from abnormal aircraft back to the OCC in an emergency is still an open problem. In this paper, we propose a novel Telemetry, Tracking,and Command(TT&C) architecture named Collaborative TT&C(CoTT&C) based on mega-constellation to solve such a problem. CoTT&C allows each satellite to help the abnormal aircraft by sharing TT&C resources when needed, realizing real-time and reliable aeronautical communication in an emergency. Specifically, we design a dynamic resource sharing mechanism for CoTT&C and model the mechanism as a single-leader-multi-follower Stackelberg game. Further, we give an unique Nash Equilibrium(NE) of the game as a closed form. Simulation results demonstrate that the proposed resource sharing mechanism is effective, incentive compatible, fair, and reciprocal. We hope that our findings can shed some light for future research on aeronautical communications in an emergency.

Incentive Feedback Stackelberg Strategy in Mean-Field Type Stochastic Difference Games

This paper designs an incentive Stackelberg strategy for the discrete-time stochastic systems with mean-field terms.Sufficient conditions for the existence of such a design are suggested.Moreover,the incentive strategy is obtained as a feedback form including the deviation of the state and its mathematical expectation.Also,the stability analysis is involved.It is found that the stability can be guaranteed by the follower.In addition,the specific algorithm is proposed and its effectiveness is checked by two examples.

A Blockchain-Based Game Approach to Multi-Microgrid Energy Dispatch

As the current global environment is deteriorating,distributed renewable energy is gradually becoming an important member of the energy internet.Blockchain,as a decentralized distributed ledger with decentralization,traceability and tamper-proof features,is an importantway to achieve efficient consumption andmulti-party supply of new energy.In this article,we establish a blockchain-based mathematical model of multiple microgrids and microgrid aggregators’revenue,consider the degree of microgrid users’preference for electricity thus increasing users’reliance on the blockchainmarket,and apply the one-master-multiple-slave Stackelberg game theory to solve the energy dispatching strategy when each market entity pursues the maximum revenue.The simulation results show that the blockchain-based dynamic game of the multi-microgrid market can effectively increase the revenue of both microgrids and aggregators and improve the utilization of renewable energy.

New Approach to Linear Stackelberg Problems with Multiple Leaders-followers

In this paper, we study linear static Stac kelberg problems with multiple leaders-followers in which each decision maker wi thin his group may or may not cooperate. An exact penalty function method is dev eloped. The duality gaps of the followers’ problems are appended to the leaders’ objective function with a penalty. The structure leads to the decomposition of the composite problem into a series of linear programmings leading to an efficie nt algorithm. We prove that local optimality is reached for an exact penalty fun ction and illustrate the method with three examples. The model in this paper ext ends the stackelberg leader-follower model.

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.