This paper presents a mode-switching collaborative defense strategy for spacecraft pursuit-evasiondefense scenarios.In these scenarios,the pursuer tries to avoid the defender while capturing the evader,while the evade...This paper presents a mode-switching collaborative defense strategy for spacecraft pursuit-evasiondefense scenarios.In these scenarios,the pursuer tries to avoid the defender while capturing the evader,while the evader and defender form an alliance to prevent the pursuer from achieving its goal.First,the behavioral modes of the pursuer,including attack and avoidance modes,were established using differential game theory.These modes are then recognized by an interactive multiple model-matching algorithm(IMM),that uses several smooth variable structure filters to match the modes of the pursuer and update their probabilities in real time.Based on the linear-quadratic optimization theory,combined with the results of strategy identification,a two-way cooperative optimal strategy for the defender and evader is proposed,where the evader aids the defender to intercept the pursuer by performing luring maneuvers.Simulation results show that the interactive multi-model algorithm based on several smooth variable structure filters perform well in the strategy identification of the pursuer,and the cooperative defense strategy based on strategy identification has good interception performance when facing pursuers,who are able to flexibly adjust their game objectives.展开更多
When the maneuverability of a pursuer is not significantly higher than that of an evader,it will be difficult to intercept the evader with only one pursuer.Therefore,this article adopts a two-to-one differential game ...When the maneuverability of a pursuer is not significantly higher than that of an evader,it will be difficult to intercept the evader with only one pursuer.Therefore,this article adopts a two-to-one differential game strategy,the game of kind is generally considered to be angle-optimized,which allows unlimited turns,but these practices do not take into account the effect of acceleration,which does not correspond to the actual situation,thus,based on the angle-optimized,the acceleration optimization and the acceleration upper bound constraint are added into the game for consideration.A two-to-one differential game problem is proposed in the three-dimensional space,and an improved multi-objective grey wolf optimization(IMOGWO)algorithm is proposed to solve the optimal game point of this problem.With the equations that describe the relative motions between the pursuers and the evader in the three-dimensional space,a multi-objective function with constraints is given as the performance index to design an optimal strategy for the differential game.Then the optimal game point is solved by using the IMOGWO algorithm.It is proved based on Markov chains that with the IMOGWO,the Pareto solution set is the solution of the differential game.Finally,it is verified through simulations that the pursuers can capture the escapee,and via comparative experiments,it is shown that the IMOGWO algorithm performs well in terms of running time and memory usage.展开更多
This paper considers the value iteration algorithms of stochastic zero-sum linear quadratic games with unkown dynamics.On-policy and off-policy learning algorithms are developed to solve the stochastic zero-sum games,...This paper considers the value iteration algorithms of stochastic zero-sum linear quadratic games with unkown dynamics.On-policy and off-policy learning algorithms are developed to solve the stochastic zero-sum games,where the system dynamics is not required.By analyzing the value function iterations,the convergence of the model-based algorithm is shown.The equivalence of several types of value iteration algorithms is established.The effectiveness of model-free algorithms is demonstrated by a numerical example.展开更多
A centralized-distributed scheduling strategy for distribution networks based on multi-temporal and hierarchical cooperative game is proposed to address the issues of difficult operation control and energy optimizatio...A centralized-distributed scheduling strategy for distribution networks based on multi-temporal and hierarchical cooperative game is proposed to address the issues of difficult operation control and energy optimization interaction in distribution network transformer areas,as well as the problem of significant photovoltaic curtailment due to the inability to consume photovoltaic power locally.A scheduling architecture combiningmulti-temporal scales with a three-level decision-making hierarchy is established:the overall approach adopts a centralized-distributed method,analyzing the operational characteristics and interaction relationships of the distribution network center layer,cluster layer,and transformer area layer,providing a“spatial foundation”for subsequent optimization.The optimization process is divided into two stages on the temporal scale:in the first stage,based on forecasted electricity load and demand response characteristics,time-of-use electricity prices are utilized to formulate day-ahead optimization strategies;in the second stage,based on the charging and discharging characteristics of energy storage vehicles and multi-agent cooperative game relationships,rolling electricity prices and optimal interactive energy solutions are determined among clusters and transformer areas using the Nash bargaining theory.Finally,a distributed optimization algorithm using the bisection method is employed to solve the constructed model.Simulation results demonstrate that the proposed optimization strategy can facilitate photovoltaic consumption in the distribution network and enhance grid economy.展开更多
We study the influence of conformity on the evolution of cooperative behavior in games under the learning method of sampling on networks.A strategy update rule based on sampling is introduced into the stag hunt game,w...We study the influence of conformity on the evolution of cooperative behavior in games under the learning method of sampling on networks.A strategy update rule based on sampling is introduced into the stag hunt game,where agents draw samples from their neighbors and then update their strategies based on conformity or inference according to the situation in the sample.Based on these assumptions,we present the state transition equations in the dynamic evolution of population cooperation,conduct simulation analysis on lattice networks and scale-free networks,and discuss how this mechanism affects the evolution of cooperation and how cooperation evolves under different levels of conformity in the network.Our simulation results show that blindly imitating the strategies of neighbors does not necessarily lead to rapid consensus in the population.Instead,rational inference through samples can better promote the evolution of the same strategy among all agents in the population.Moreover,the simulation results also show that a smaller sample size cannot reflect the true situation of the neighbors,which has a large randomness,and the size of the benefits obtained in cooperation determines the direction of the entire population towards cooperation or defection.This work incorporates the conforming behavior of agents into the game,uses the method of sampling for strategy updates and enriches the theory of evolutionary games with a more realistic significance.展开更多
This paper introduces a lane-changing strategy aimed at trajectory planning and tracking control for intelligent vehicles navigating complex driving environments.A fifth-degree polynomial is employed to generate a set...This paper introduces a lane-changing strategy aimed at trajectory planning and tracking control for intelligent vehicles navigating complex driving environments.A fifth-degree polynomial is employed to generate a set of potential lane-changing trajectories in the Frenet coordinate system.These trajectories are evaluated using non-cooperative game theory,considering the interaction between the target vehicle and its surroundings.Models considering safety payoffs,speed payoffs,comfort payoffs,and aggressiveness are formulated to obtain a Nash equilibrium solution.This way,collision avoidance is ensured,and an optimal lane change trajectory is planned.Three game scenarios are discussed,and the optimal trajectories obtained are compared using the NGSIM dataset.Comparison of trajectory tracking effects by themodel predictive control(MPC)and linear quadratic regulator(LQR).Finally,the left lane change,right lane change,and abort lane change operations are verified in the autonomous driving simulation platform.Simulation and experimental results show that the strategy can plan appropriate lane change trajectory and accomplish tracking in complex environments.展开更多
In this paper,we investigate the distributed Nash equilibrium(NE)seeking problem for aggregative games with multiple uncertain Euler–Lagrange(EL)systems over jointly connected and weight-balanced switching networks.T...In this paper,we investigate the distributed Nash equilibrium(NE)seeking problem for aggregative games with multiple uncertain Euler–Lagrange(EL)systems over jointly connected and weight-balanced switching networks.The designed distributed controller consists of two parts:a dynamic average consensus part that asymptotically reproduces the unknown NE,and an adaptive reference-tracking module responsible for steering EL systems’positions to track a desired trajectory.The generalized Barbalat’s Lemma is used to overcome the discontinuity of the closed-loop system caused by the switching networks.The proposed algorithm is illustrated by a sensor network deployment problem.展开更多
This paper considers risk-sensitive linear-quadratic mean-field games.By the so-called direct approach via dynamic programming,the authors determine the feedback Nash equilibrium in an N-player game.Subsequently,the a...This paper considers risk-sensitive linear-quadratic mean-field games.By the so-called direct approach via dynamic programming,the authors determine the feedback Nash equilibrium in an N-player game.Subsequently,the authors design a set of decentralized strategies by passing to the mean-field limit.The authors prove that the set of decentralized strategies constitutes an O(1/N)-Nash equilibrium when applied by the N players,and hence obtain so far the tightest equilibrium error bounds for this class of models.展开更多
The videogame industry has always put visual components at the forefront in its design and analytical processes while following a visuocentric approach.This paper contends that a new perspective is needed to appreciat...The videogame industry has always put visual components at the forefront in its design and analytical processes while following a visuocentric approach.This paper contends that a new perspective is needed to appreciate how auditory atmospherics play a vital yet underestimated role in creating immersive and captivating gaming experiences.This study demonstrates how sound can create player presence and evoke emotions to guide them through video game environments confirming sound design as essential for developing immersive virtual worlds.According to existing research the paper investigates how detailed soundscapes enhance player immersion and improve the total gaming experience.The paper investigates how auditory elements affect psychological states and emotions through their influence on immersion levels,emotional reactions,cognitive abilities and examines potential health consequences.The paper describes the technical implementation of immersive audio within game development software while projecting the evolution of game audio through innovations in spatial audio technology and procedural sound creation supported by AI-driven sound design and biometric integration.This paper proposes a comprehensive multi-sensory game design strategy that positions auditory atmospherics as an essential core element for the progression of interactive entertainment.展开更多
This paper studies a class of linear quadratic mean field games where the coefficients of quadratic cost functions depend on both the mean and the variance of the population’s state distribution through its quantile ...This paper studies a class of linear quadratic mean field games where the coefficients of quadratic cost functions depend on both the mean and the variance of the population’s state distribution through its quantile function.Such a formulation allows for modelling agents that are sensitive to not only the population average but also the population variance.The potential mean field game equilibria are identified.Their calculation involves solving two nonlinearly coupled differential equations:one is a Riccati equation and the other the variance evolution equation.Sufficient conditions for the existence and uniqueness of a mean field equilibrium are established.Finally,numerical results are presented to illustrate the behavior of two coupled differential equations and the performance of the mean field game solution.展开更多
This paper presents a dynamic game framework to analyze the role of large banks in interbank markets.By extending existing models,a large bank is incorporated as a dynamic decision-maker interacting with multiple smal...This paper presents a dynamic game framework to analyze the role of large banks in interbank markets.By extending existing models,a large bank is incorporated as a dynamic decision-maker interacting with multiple small banks.Using the mean-field game methodology and convex analysis,best-response trading strategies are derived,leading to an approximate equilibrium for the interbank market.The influence of the large bank is investigated on the market stability by examining individual default probabilities and systemic risk,through the use of Monte Carlo simulations.The proposed findings reveal that,when the size of the major bank is not excessively large,it can positively contribute to market stability.However,there is also the potential for negative spillover effects in the event of default,leading to an increase in systemic risk.The magnitude of this impact is further influenced by the size and trading rate of the major bank.Overall,this study provides valuable insights into the management of systemic risk in interbank markets.展开更多
This paper concerns two-player zero-sum stochastic differential games with nonanticipative strategies against closed-loop controls in the case where the coefficients of mean-field stochastic differential equations and...This paper concerns two-player zero-sum stochastic differential games with nonanticipative strategies against closed-loop controls in the case where the coefficients of mean-field stochastic differential equations and cost functional depend on the joint distribution of the state and the control.In our game,both the(lower and upper)value functions and the(lower and upper)second-order Bellman–Isaacs equations are defined on the Wasserstein space P_(2)(R^(n))which is an infinite dimensional space.The dynamic programming principle for the value functions is proved.If the(upper and lower)value functions are smooth enough,we show that they are the classical solutions to the second-order Bellman–Isaacs equations.On the other hand,the classical solutions to the(upper and lower)Bellman–Isaacs equations are unique and coincide with the(upper and lower)value functions.As an illustrative application,the linear quadratic case is considered.Under the Isaacs condition,the explicit expressions of optimal closed-loop controls for both players are given.Finally,we introduce the intrinsic notion of viscosity solution of our second-order Bellman–Isaacs equations,and characterize the(upper and lower)value functions as their viscosity solutions.展开更多
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 a...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.展开更多
This study aimed to identify the reasons for transferring athletes to local medical facilities during the Olympic and Paralympic Games.Data on 567 injuries and other illnesses of athletes treated at the on-site clinic...This study aimed to identify the reasons for transferring athletes to local medical facilities during the Olympic and Paralympic Games.Data on 567 injuries and other illnesses of athletes treated at the on-site clinics were collected from the Tokyo 2020 Organizing Committee.Of these,84 athletes who required outpatient care during the Games were registered for this survey.During the Olympic and Paralympic Games,66(8.3/1000)and 18(7.2/1000)athletes,respectively,consulted external medical facilities.In the Olympic Games,the reasons for these visits included 48 cases(72.7%)of injuries,13(19.7%)cases of illnesses,and 5(7.6%)cases of heat stroke illness(HSI).Of these patients,56(84.9%)were treated as outpatients and 10(15.1%)were hospitalized,while three of these patients required hospitalization for>7 days.On the other hand,in the Paralympics Games,there were 7(38.8%)cases of injuries,9(50.0%)other illnesses,1(5.6%)case of HSI,and 1(5.6%)other cases,of which 11(61.1%)were treated as outpatients and 7(38.9%)were hospitalized,but none was hospitalized for>7 days.Injuries accounted for 70%of the total cases at the 2021 Olympic Games,but only three(0.05%)were severe cases that required hospitalization for more than 1 week.In contrast,in the Paralympic Games,other illnesses accounted for approximately half of the total cases.This study provides details on the extent of injuries and other illnesses that were transferred to outside facilities,which has not been documented in previous games.展开更多
The rapid development of the anti-missile weapon technology brings new challenges to the cooperative penetration strategy solution and the guidance law design for Hypersonic Vehicles(HVs).This paper studies the coordi...The rapid development of the anti-missile weapon technology brings new challenges to the cooperative penetration strategy solution and the guidance law design for Hypersonic Vehicles(HVs).This paper studies the coordinated game penetration guidance problem for multiple hypersonic vehicles faced with space threat areas.A scheme for seeking cooperative game penetration guidance strategy under safety critical control framework is presented.In this scheme,a multiHV cooperative game model is proposed in a minimum optimization form which can simplify the solving process and accelerate the computing speed.Then,a second-order control barrier function is developed to transform the implicit nonlinear constraints of the proposed model into linear ones.In order to obtain better performance of guidance strategy,a composite guidance law under the safety critical control framework is presented to allocate guidance strategies appropriately in the whole process.It is shown that the proposed scheme can guarantee successful penetration while avoiding threat areas.Finally,a comparative simulation with a two-on-three game is conducted to verify the effectiveness of the proposed method.展开更多
The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainl...The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainly concentrate on the cooperative pursuit of multiple players in two-dimensional pursuit-evasion games. However, these approaches can hardly be applied to practical situations where players usually move in three-dimensional space with a three-degree-of-freedom control. In this paper,we make the first attempt to investigate the equilibrium strategy of the realistic pursuit-evasion game, in which the pursuer follows a three-degree-of-freedom control, and the evader moves freely. First, we describe the pursuer's three-degree-of-freedom control and the evader's relative coordinate. We then rigorously derive the equilibrium strategy by solving the retrogressive path equation according to the Hamilton-Jacobi-Bellman-Isaacs(HJBI) method, which divides the pursuit-evasion process into the navigation and acceleration phases. Besides, we analyze the maximum allowable speed for the pursuer to capture the evader successfully and provide the strategy with which the evader can escape when the pursuer's speed exceeds the threshold. We further conduct comparison tests with various unilateral deviations to verify that the proposed strategy forms a Nash equilibrium.展开更多
Regional integrated energy system(RIES)cluster,i.e.,multi-source integration and multi-region coordination,is an effective approach for increasing energy utilization efficiency.The hierarchical architecture and limite...Regional integrated energy system(RIES)cluster,i.e.,multi-source integration and multi-region coordination,is an effective approach for increasing energy utilization efficiency.The hierarchical architecture and limited information sharing of RIES cluster make it difficult for traditional game theory to accurately describe their game behavior.Thus,a hierarchical game approach considering bounded rationality is proposed in this paper to balance the interests of optimizing RIES cluster under privacy protection.A Stackelberg game with the cluster operator(CO)as the leader and multiple RIES as followers is developed to simultaneously optimize leader benefit and RIES utilization efficiency.Concurrently,a slight altruistic function is introduced to simulate the game behavior of each RIES agent on whether to cooperate or not.By introducing an evolutionary game based on bounded rationality in the lower layer,the flaw of the assumption that participants are completely rational can be avoided.Specially,for autonomous optimal dispatching,each RIES is treated as a prosumer,fexibly switching its market participation role to achieve cluster coordination optimization.Case studies on a RIES cluster verify effectiveness of the proposed approach.展开更多
Benefiting from the development of Federated Learning(FL)and distributed communication systems,large-scale intelligent applications become possible.Distributed devices not only provide adequate training data,but also ...Benefiting from the development of Federated Learning(FL)and distributed communication systems,large-scale intelligent applications become possible.Distributed devices not only provide adequate training data,but also cause privacy leakage and energy consumption.How to optimize the energy consumption in distributed communication systems,while ensuring the privacy of users and model accuracy,has become an urgent challenge.In this paper,we define the FL as a 3-layer architecture including users,agents and server.In order to find a balance among model training accuracy,privacy-preserving effect,and energy consumption,we design the training process of FL as game models.We use an extensive game tree to analyze the key elements that influence the players’decisions in the single game,and then find the incentive mechanism that meet the social norms through the repeated game.The experimental results show that the Nash equilibrium we obtained satisfies the laws of reality,and the proposed incentive mechanism can also promote users to submit high-quality data in FL.Following the multiple rounds of play,the incentive mechanism can help all players find the optimal strategies for energy,privacy,and accuracy of FL in distributed communication systems.展开更多
Modern power grid is fast emerging as a complex cyber-physical power system(CPPS)integrating physical current-carrying components and processes with cyber-embedded computing,which faces increasing cy-berspace security...Modern power grid is fast emerging as a complex cyber-physical power system(CPPS)integrating physical current-carrying components and processes with cyber-embedded computing,which faces increasing cy-berspace security threats and risks.In this paper,the state(i.e.,voltage)offsets resulting from false data injection(FDI)attacks and the bus safety characterization are applied to quantify the attack consequences.The state offsets are obtained by the state estimation method,and the bus safety characterization considers the power net-work topology as well as the vulnerability and connection relationship of buses.Considering the indeterminacy of attacker’s resource consumption and reward,a zero-sum game-theoretical model from the defender’s perspective with incomplete information is explored for the optimal allocation of limited defensive resources.The attacker aims to falsify measurements without triggering threshold alarms to break through the protection,leading to load shedding,over-voltage or under-voltage.The defender attempts to ensure the estimation results to be as close to the actual states as possible,and guarantee the system’s safety and efficient defensive resource utilization.The proposed solution is extensively evaluated through simu-lations using the IEEE 33-bus test network and real-time digital simulator(RTDS)based testbed experiments of the IEEE 14-bus network.The results demonstrate the effec-tiveness of the proposed game-theoretical approach for optimal defensive resource allocation in CPPS when lim-ited resources are available when under FDI attacks.Index Terms—Optimal strategy,game theory,Nash equilibrium,CPPS,FDI attack.展开更多
Malicious attacks against data are unavoidable in the interconnected,open and shared Energy Internet(EI),Intrusion tolerant techniques are critical to the data security of EI.Existing intrusion tolerant techniques suf...Malicious attacks against data are unavoidable in the interconnected,open and shared Energy Internet(EI),Intrusion tolerant techniques are critical to the data security of EI.Existing intrusion tolerant techniques suffered from problems such as low adaptability,policy lag,and difficulty in determining the degree of tolerance.To address these issues,we propose a novel adaptive intrusion tolerance model based on game theory that enjoys two-fold ideas:(1)it constructs an improved replica of the intrusion tolerance model of the dynamic equation evolution game to induce incentive weights;and (2)it combines a tournament competition model with incentive weights to obtain optimal strategies for each stage of the game process.Extensive experiments are conducted in the IEEE 39-bus system,whose results demonstrate the feasibility of the incentive weights,confirm the proposed strategy strengthens the system’s ability to tolerate aggression,and improves the dynamic adaptability and response efficiency of the aggression-tolerant system in the case of limited resources.展开更多
基金the Science and Technology Department,Heilongjiang Province under Grant Agreement No JJ2022LH0315。
文摘This paper presents a mode-switching collaborative defense strategy for spacecraft pursuit-evasiondefense scenarios.In these scenarios,the pursuer tries to avoid the defender while capturing the evader,while the evader and defender form an alliance to prevent the pursuer from achieving its goal.First,the behavioral modes of the pursuer,including attack and avoidance modes,were established using differential game theory.These modes are then recognized by an interactive multiple model-matching algorithm(IMM),that uses several smooth variable structure filters to match the modes of the pursuer and update their probabilities in real time.Based on the linear-quadratic optimization theory,combined with the results of strategy identification,a two-way cooperative optimal strategy for the defender and evader is proposed,where the evader aids the defender to intercept the pursuer by performing luring maneuvers.Simulation results show that the interactive multi-model algorithm based on several smooth variable structure filters perform well in the strategy identification of the pursuer,and the cooperative defense strategy based on strategy identification has good interception performance when facing pursuers,who are able to flexibly adjust their game objectives.
基金National Natural Science Foundation of China(NSFC61773142,NSFC62303136)。
文摘When the maneuverability of a pursuer is not significantly higher than that of an evader,it will be difficult to intercept the evader with only one pursuer.Therefore,this article adopts a two-to-one differential game strategy,the game of kind is generally considered to be angle-optimized,which allows unlimited turns,but these practices do not take into account the effect of acceleration,which does not correspond to the actual situation,thus,based on the angle-optimized,the acceleration optimization and the acceleration upper bound constraint are added into the game for consideration.A two-to-one differential game problem is proposed in the three-dimensional space,and an improved multi-objective grey wolf optimization(IMOGWO)algorithm is proposed to solve the optimal game point of this problem.With the equations that describe the relative motions between the pursuers and the evader in the three-dimensional space,a multi-objective function with constraints is given as the performance index to design an optimal strategy for the differential game.Then the optimal game point is solved by using the IMOGWO algorithm.It is proved based on Markov chains that with the IMOGWO,the Pareto solution set is the solution of the differential game.Finally,it is verified through simulations that the pursuers can capture the escapee,and via comparative experiments,it is shown that the IMOGWO algorithm performs well in terms of running time and memory usage.
基金supported by the National Natural Science Foundation of China under Grant Nos.62122043,62192753,62433020,T2293770Natural Science Foundation of Shandong Province for Distinguished Young Scholars under Grant No.ZR2022JQ31.
文摘This paper considers the value iteration algorithms of stochastic zero-sum linear quadratic games with unkown dynamics.On-policy and off-policy learning algorithms are developed to solve the stochastic zero-sum games,where the system dynamics is not required.By analyzing the value function iterations,the convergence of the model-based algorithm is shown.The equivalence of several types of value iteration algorithms is established.The effectiveness of model-free algorithms is demonstrated by a numerical example.
基金funded by the Jilin Province Science and Technology Development Plan Project(20230101344JC).
文摘A centralized-distributed scheduling strategy for distribution networks based on multi-temporal and hierarchical cooperative game is proposed to address the issues of difficult operation control and energy optimization interaction in distribution network transformer areas,as well as the problem of significant photovoltaic curtailment due to the inability to consume photovoltaic power locally.A scheduling architecture combiningmulti-temporal scales with a three-level decision-making hierarchy is established:the overall approach adopts a centralized-distributed method,analyzing the operational characteristics and interaction relationships of the distribution network center layer,cluster layer,and transformer area layer,providing a“spatial foundation”for subsequent optimization.The optimization process is divided into two stages on the temporal scale:in the first stage,based on forecasted electricity load and demand response characteristics,time-of-use electricity prices are utilized to formulate day-ahead optimization strategies;in the second stage,based on the charging and discharging characteristics of energy storage vehicles and multi-agent cooperative game relationships,rolling electricity prices and optimal interactive energy solutions are determined among clusters and transformer areas using the Nash bargaining theory.Finally,a distributed optimization algorithm using the bisection method is employed to solve the constructed model.Simulation results demonstrate that the proposed optimization strategy can facilitate photovoltaic consumption in the distribution network and enhance grid economy.
基金Project supported by the National Natural Science Foundation of China(Grant No.72031009)the National Social Science Foundation of China(Grant No.20&ZD058)。
文摘We study the influence of conformity on the evolution of cooperative behavior in games under the learning method of sampling on networks.A strategy update rule based on sampling is introduced into the stag hunt game,where agents draw samples from their neighbors and then update their strategies based on conformity or inference according to the situation in the sample.Based on these assumptions,we present the state transition equations in the dynamic evolution of population cooperation,conduct simulation analysis on lattice networks and scale-free networks,and discuss how this mechanism affects the evolution of cooperation and how cooperation evolves under different levels of conformity in the network.Our simulation results show that blindly imitating the strategies of neighbors does not necessarily lead to rapid consensus in the population.Instead,rational inference through samples can better promote the evolution of the same strategy among all agents in the population.Moreover,the simulation results also show that a smaller sample size cannot reflect the true situation of the neighbors,which has a large randomness,and the size of the benefits obtained in cooperation determines the direction of the entire population towards cooperation or defection.This work incorporates the conforming behavior of agents into the game,uses the method of sampling for strategy updates and enriches the theory of evolutionary games with a more realistic significance.
基金supported by the Science and Technology Program of Shandong Higher Education Institutions(Grant J18KA048).
文摘This paper introduces a lane-changing strategy aimed at trajectory planning and tracking control for intelligent vehicles navigating complex driving environments.A fifth-degree polynomial is employed to generate a set of potential lane-changing trajectories in the Frenet coordinate system.These trajectories are evaluated using non-cooperative game theory,considering the interaction between the target vehicle and its surroundings.Models considering safety payoffs,speed payoffs,comfort payoffs,and aggressiveness are formulated to obtain a Nash equilibrium solution.This way,collision avoidance is ensured,and an optimal lane change trajectory is planned.Three game scenarios are discussed,and the optimal trajectories obtained are compared using the NGSIM dataset.Comparison of trajectory tracking effects by themodel predictive control(MPC)and linear quadratic regulator(LQR).Finally,the left lane change,right lane change,and abort lane change operations are verified in the autonomous driving simulation platform.Simulation and experimental results show that the strategy can plan appropriate lane change trajectory and accomplish tracking in complex environments.
基金supported by the Research Grants Council of the Hong Kong Special Administration Region under the Grant No.14201621。
文摘In this paper,we investigate the distributed Nash equilibrium(NE)seeking problem for aggregative games with multiple uncertain Euler–Lagrange(EL)systems over jointly connected and weight-balanced switching networks.The designed distributed controller consists of two parts:a dynamic average consensus part that asymptotically reproduces the unknown NE,and an adaptive reference-tracking module responsible for steering EL systems’positions to track a desired trajectory.The generalized Barbalat’s Lemma is used to overcome the discontinuity of the closed-loop system caused by the switching networks.The proposed algorithm is illustrated by a sensor network deployment problem.
基金supported by Natural Sciences and Engineering Research Council(NSERC)of Canada.
文摘This paper considers risk-sensitive linear-quadratic mean-field games.By the so-called direct approach via dynamic programming,the authors determine the feedback Nash equilibrium in an N-player game.Subsequently,the authors design a set of decentralized strategies by passing to the mean-field limit.The authors prove that the set of decentralized strategies constitutes an O(1/N)-Nash equilibrium when applied by the N players,and hence obtain so far the tightest equilibrium error bounds for this class of models.
文摘The videogame industry has always put visual components at the forefront in its design and analytical processes while following a visuocentric approach.This paper contends that a new perspective is needed to appreciate how auditory atmospherics play a vital yet underestimated role in creating immersive and captivating gaming experiences.This study demonstrates how sound can create player presence and evoke emotions to guide them through video game environments confirming sound design as essential for developing immersive virtual worlds.According to existing research the paper investigates how detailed soundscapes enhance player immersion and improve the total gaming experience.The paper investigates how auditory elements affect psychological states and emotions through their influence on immersion levels,emotional reactions,cognitive abilities and examines potential health consequences.The paper describes the technical implementation of immersive audio within game development software while projecting the evolution of game audio through innovations in spatial audio technology and procedural sound creation supported by AI-driven sound design and biometric integration.This paper proposes a comprehensive multi-sensory game design strategy that positions auditory atmospherics as an essential core element for the progression of interactive entertainment.
基金supported by NSERC(Canada)under Grant Nos.RGPIN-2024-06612(SG)and RGPIN 2022-05402(RM).
文摘This paper studies a class of linear quadratic mean field games where the coefficients of quadratic cost functions depend on both the mean and the variance of the population’s state distribution through its quantile function.Such a formulation allows for modelling agents that are sensitive to not only the population average but also the population variance.The potential mean field game equilibria are identified.Their calculation involves solving two nonlinearly coupled differential equations:one is a Riccati equation and the other the variance evolution equation.Sufficient conditions for the existence and uniqueness of a mean field equilibrium are established.Finally,numerical results are presented to illustrate the behavior of two coupled differential equations and the performance of the mean field game solution.
基金supported by the Natural Sciences and Engineering Research Council of Canada(NSERC)under Grant No.RGPIN-2022-05337the Social Sciences and Humanities Research Council of Canada under GrantNo.430-2022-00544.
文摘This paper presents a dynamic game framework to analyze the role of large banks in interbank markets.By extending existing models,a large bank is incorporated as a dynamic decision-maker interacting with multiple small banks.Using the mean-field game methodology and convex analysis,best-response trading strategies are derived,leading to an approximate equilibrium for the interbank market.The influence of the large bank is investigated on the market stability by examining individual default probabilities and systemic risk,through the use of Monte Carlo simulations.The proposed findings reveal that,when the size of the major bank is not excessively large,it can positively contribute to market stability.However,there is also the potential for negative spillover effects in the event of default,leading to an increase in systemic risk.The magnitude of this impact is further influenced by the size and trading rate of the major bank.Overall,this study provides valuable insights into the management of systemic risk in interbank markets.
基金supported by Natural Science Foundation of Shandong Province(Grant Nos.ZR2020MA032,ZR2022MA029)National Natural Science Foundation of China(Grant Nos.12171279,72171133)+1 种基金The second named author was supported by National Key R&D Program of China(Grant No.2022YFA1006102)National Natural Science Foundation of China(Grant No.11831010)。
文摘This paper concerns two-player zero-sum stochastic differential games with nonanticipative strategies against closed-loop controls in the case where the coefficients of mean-field stochastic differential equations and cost functional depend on the joint distribution of the state and the control.In our game,both the(lower and upper)value functions and the(lower and upper)second-order Bellman–Isaacs equations are defined on the Wasserstein space P_(2)(R^(n))which is an infinite dimensional space.The dynamic programming principle for the value functions is proved.If the(upper and lower)value functions are smooth enough,we show that they are the classical solutions to the second-order Bellman–Isaacs equations.On the other hand,the classical solutions to the(upper and lower)Bellman–Isaacs equations are unique and coincide with the(upper and lower)value functions.As an illustrative application,the linear quadratic case is considered.Under the Isaacs condition,the explicit expressions of optimal closed-loop controls for both players are given.Finally,we introduce the intrinsic notion of viscosity solution of our second-order Bellman–Isaacs equations,and characterize the(upper and lower)value functions as their viscosity solutions.
基金supported in part by the National Natural Science Foundation of China (No.62271253,61901523,62001381)Fundamental Research Funds for the Central Universities (No.NS2023018)+2 种基金the National Aerospace Science Foundation of China under Grant 2023Z021052002the open research fund of National Mobile Communications Research Laboratory,Southeast University (No.2023D09)Postgraduate Research & Practice Innovation Program of NUAA (No.xcxjh20220402)。
文摘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.
文摘This study aimed to identify the reasons for transferring athletes to local medical facilities during the Olympic and Paralympic Games.Data on 567 injuries and other illnesses of athletes treated at the on-site clinics were collected from the Tokyo 2020 Organizing Committee.Of these,84 athletes who required outpatient care during the Games were registered for this survey.During the Olympic and Paralympic Games,66(8.3/1000)and 18(7.2/1000)athletes,respectively,consulted external medical facilities.In the Olympic Games,the reasons for these visits included 48 cases(72.7%)of injuries,13(19.7%)cases of illnesses,and 5(7.6%)cases of heat stroke illness(HSI).Of these patients,56(84.9%)were treated as outpatients and 10(15.1%)were hospitalized,while three of these patients required hospitalization for>7 days.On the other hand,in the Paralympics Games,there were 7(38.8%)cases of injuries,9(50.0%)other illnesses,1(5.6%)case of HSI,and 1(5.6%)other cases,of which 11(61.1%)were treated as outpatients and 7(38.9%)were hospitalized,but none was hospitalized for>7 days.Injuries accounted for 70%of the total cases at the 2021 Olympic Games,but only three(0.05%)were severe cases that required hospitalization for more than 1 week.In contrast,in the Paralympic Games,other illnesses accounted for approximately half of the total cases.This study provides details on the extent of injuries and other illnesses that were transferred to outside facilities,which has not been documented in previous games.
基金supported by the Natural Science Foundation of Jiangsu Province,China(No.BK20220945)。
文摘The rapid development of the anti-missile weapon technology brings new challenges to the cooperative penetration strategy solution and the guidance law design for Hypersonic Vehicles(HVs).This paper studies the coordinated game penetration guidance problem for multiple hypersonic vehicles faced with space threat areas.A scheme for seeking cooperative game penetration guidance strategy under safety critical control framework is presented.In this scheme,a multiHV cooperative game model is proposed in a minimum optimization form which can simplify the solving process and accelerate the computing speed.Then,a second-order control barrier function is developed to transform the implicit nonlinear constraints of the proposed model into linear ones.In order to obtain better performance of guidance strategy,a composite guidance law under the safety critical control framework is presented to allocate guidance strategies appropriately in the whole process.It is shown that the proposed scheme can guarantee successful penetration while avoiding threat areas.Finally,a comparative simulation with a two-on-three game is conducted to verify the effectiveness of the proposed method.
基金supported in part by the Strategic Priority Research Program of Chinese Academy of Sciences(XDA27030100)National Natural Science Foundation of China(72293575, 11832001)。
文摘The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainly concentrate on the cooperative pursuit of multiple players in two-dimensional pursuit-evasion games. However, these approaches can hardly be applied to practical situations where players usually move in three-dimensional space with a three-degree-of-freedom control. In this paper,we make the first attempt to investigate the equilibrium strategy of the realistic pursuit-evasion game, in which the pursuer follows a three-degree-of-freedom control, and the evader moves freely. First, we describe the pursuer's three-degree-of-freedom control and the evader's relative coordinate. We then rigorously derive the equilibrium strategy by solving the retrogressive path equation according to the Hamilton-Jacobi-Bellman-Isaacs(HJBI) method, which divides the pursuit-evasion process into the navigation and acceleration phases. Besides, we analyze the maximum allowable speed for the pursuer to capture the evader successfully and provide the strategy with which the evader can escape when the pursuer's speed exceeds the threshold. We further conduct comparison tests with various unilateral deviations to verify that the proposed strategy forms a Nash equilibrium.
基金supported by the National Key R&D Program(No.2020YFB0905900)the National Natural Science Foundation of China(No.52277098)。
文摘Regional integrated energy system(RIES)cluster,i.e.,multi-source integration and multi-region coordination,is an effective approach for increasing energy utilization efficiency.The hierarchical architecture and limited information sharing of RIES cluster make it difficult for traditional game theory to accurately describe their game behavior.Thus,a hierarchical game approach considering bounded rationality is proposed in this paper to balance the interests of optimizing RIES cluster under privacy protection.A Stackelberg game with the cluster operator(CO)as the leader and multiple RIES as followers is developed to simultaneously optimize leader benefit and RIES utilization efficiency.Concurrently,a slight altruistic function is introduced to simulate the game behavior of each RIES agent on whether to cooperate or not.By introducing an evolutionary game based on bounded rationality in the lower layer,the flaw of the assumption that participants are completely rational can be avoided.Specially,for autonomous optimal dispatching,each RIES is treated as a prosumer,fexibly switching its market participation role to achieve cluster coordination optimization.Case studies on a RIES cluster verify effectiveness of the proposed approach.
基金sponsored by the National Key R&D Program of China(No.2018YFB2100400)the National Natural Science Foundation of China(No.62002077,61872100)+4 种基金the Major Research Plan of the National Natural Science Foundation of China(92167203)the Guangdong Basic and Applied Basic Research Foundation(No.2020A1515110385)the China Postdoctoral Science Foundation(No.2022M710860)the Zhejiang Lab(No.2020NF0AB01)Guangzhou Science and Technology Plan Project(202102010440).
文摘Benefiting from the development of Federated Learning(FL)and distributed communication systems,large-scale intelligent applications become possible.Distributed devices not only provide adequate training data,but also cause privacy leakage and energy consumption.How to optimize the energy consumption in distributed communication systems,while ensuring the privacy of users and model accuracy,has become an urgent challenge.In this paper,we define the FL as a 3-layer architecture including users,agents and server.In order to find a balance among model training accuracy,privacy-preserving effect,and energy consumption,we design the training process of FL as game models.We use an extensive game tree to analyze the key elements that influence the players’decisions in the single game,and then find the incentive mechanism that meet the social norms through the repeated game.The experimental results show that the Nash equilibrium we obtained satisfies the laws of reality,and the proposed incentive mechanism can also promote users to submit high-quality data in FL.Following the multiple rounds of play,the incentive mechanism can help all players find the optimal strategies for energy,privacy,and accuracy of FL in distributed communication systems.
基金supported by the National Key Research and Development Program of China(No.2023YFB 3107603)the“Pioneer”and“Leading Goose”R&D Program of Zhejiang(No.2022C01239)+2 种基金the Special Support Plan for Zhejiang Province High-level Talents(No.2022R52012)the National Natural Science Foundation of China(No.52177119)the Funda-mental Research Funds for the Central Universities(Zhejiang University NGICS Platform).
文摘Modern power grid is fast emerging as a complex cyber-physical power system(CPPS)integrating physical current-carrying components and processes with cyber-embedded computing,which faces increasing cy-berspace security threats and risks.In this paper,the state(i.e.,voltage)offsets resulting from false data injection(FDI)attacks and the bus safety characterization are applied to quantify the attack consequences.The state offsets are obtained by the state estimation method,and the bus safety characterization considers the power net-work topology as well as the vulnerability and connection relationship of buses.Considering the indeterminacy of attacker’s resource consumption and reward,a zero-sum game-theoretical model from the defender’s perspective with incomplete information is explored for the optimal allocation of limited defensive resources.The attacker aims to falsify measurements without triggering threshold alarms to break through the protection,leading to load shedding,over-voltage or under-voltage.The defender attempts to ensure the estimation results to be as close to the actual states as possible,and guarantee the system’s safety and efficient defensive resource utilization.The proposed solution is extensively evaluated through simu-lations using the IEEE 33-bus test network and real-time digital simulator(RTDS)based testbed experiments of the IEEE 14-bus network.The results demonstrate the effec-tiveness of the proposed game-theoretical approach for optimal defensive resource allocation in CPPS when lim-ited resources are available when under FDI attacks.Index Terms—Optimal strategy,game theory,Nash equilibrium,CPPS,FDI attack.
基金supported by the National Natural Science Foundation of China(Nos.51977113,62293500,62293501 and 62293505).
文摘Malicious attacks against data are unavoidable in the interconnected,open and shared Energy Internet(EI),Intrusion tolerant techniques are critical to the data security of EI.Existing intrusion tolerant techniques suffered from problems such as low adaptability,policy lag,and difficulty in determining the degree of tolerance.To address these issues,we propose a novel adaptive intrusion tolerance model based on game theory that enjoys two-fold ideas:(1)it constructs an improved replica of the intrusion tolerance model of the dynamic equation evolution game to induce incentive weights;and (2)it combines a tournament competition model with incentive weights to obtain optimal strategies for each stage of the game process.Extensive experiments are conducted in the IEEE 39-bus system,whose results demonstrate the feasibility of the incentive weights,confirm the proposed strategy strengthens the system’s ability to tolerate aggression,and improves the dynamic adaptability and response efficiency of the aggression-tolerant system in the case of limited resources.
