In repeated zero-sum games,instead of constantly playing an equilibrium strategy of the stage game,learning to exploit the opponent given historical interactions could typically obtain a higher utility.However,when pl...In repeated zero-sum games,instead of constantly playing an equilibrium strategy of the stage game,learning to exploit the opponent given historical interactions could typically obtain a higher utility.However,when playing against a fully adaptive opponent,one would have dificulty identifying the opponent's adaptive dynamics and further exploiting its potential weakness.In this paper,we study the problem of optimizing against the adaptive opponent who uses no-regret learning.No-regret learning is a classic and widely-used branch of adaptive learning algorithms.We propose a general framework for online modeling no-regret opponents and exploiting their weakness.With this framework,one could approximate the opponent's no-regret learning dynamics and then develop a response plan to obtain a significant profit based on the inferences of the opponent's strategies.We employ two system identification architectures,including the recurrent neural network(RNN)and the nonlinear autoregressive exogenous model,and adopt an efficient greedy response plan within the framework.Theoretically,we prove the approximation capability of our RNN architecture at approximating specific no-regret dynamics.Empirically,we demonstrate that during interactions at a low level of non-stationarity,our architectures could approximate the dynamics with a low error,and the derived policies could exploit the no-regret opponent to obtain a decent utility.展开更多
In this paper, we consider multiobjective two-person zero-sum games with vector payoffs and vector fuzzy payoffs. We translate such games into the corresponding multiobjective programming problems and introduce the pe...In this paper, we consider multiobjective two-person zero-sum games with vector payoffs and vector fuzzy payoffs. We translate such games into the corresponding multiobjective programming problems and introduce the pessimistic Pareto optimal solution concept by assuming that a player supposes the opponent adopts the most disadvantage strategy for the self. It is shown that any pessimistic Pareto optimal solution can be obtained on the basis of linear programming techniques even if the membership functions for the objective functions are nonlinear. Moreover, we propose interactive algorithms based on the bisection method to obtain a pessimistic compromise solution from among the set of all pessimistic Pareto optimal solutions. In order to show the efficiency of the proposed method, we illustrate interactive processes of an application to a vegetable shipment problem.展开更多
There are a few studies that focus on solution methods for finding a Nash equilibrium of zero-sum games. We discuss the use of Karmarkar’s interior point method to solve the Nash equilibrium problems of a zero-sum ga...There are a few studies that focus on solution methods for finding a Nash equilibrium of zero-sum games. We discuss the use of Karmarkar’s interior point method to solve the Nash equilibrium problems of a zero-sum game, and prove that it is theoretically a polynomial time algorithm. We implement the Karmarkar method, and a preliminary computational result shows that it performs well for zero-sum games. We also mention an affine scaling method that would help us compute Nash equilibria of general zero-sum games effectively.展开更多
This paper investigates the multi-player non-zero-sum game problem for unknown linear continuous-time systems with unmeasurable states.By only accessing the data information of input and output,a data-driven learning ...This paper investigates the multi-player non-zero-sum game problem for unknown linear continuous-time systems with unmeasurable states.By only accessing the data information of input and output,a data-driven learning control approach is proposed to estimate N-tuple dynamic output feedback control policies which can form Nash equilibrium solution to the multi-player non-zero-sum game problem.In particular,the explicit form of dynamic output feedback Nash strategy is constructed by embedding the internal dynamics and solving coupled algebraic Riccati equations.The coupled policy-iteration based iterative learning equations are established to estimate the N-tuple feedback control gains without prior knowledge of system matrices.Finally,an example is used to illustrate the effectiveness of the proposed approach.展开更多
The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions.Th...The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions.Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.展开更多
In this paper,an accelerated value iteration(VI)algorithm is established to solve the zero-sum game problem with convergence guarantee.First,inspired by the successive over relaxation theory,the convergence rate of th...In this paper,an accelerated value iteration(VI)algorithm is established to solve the zero-sum game problem with convergence guarantee.First,inspired by the successive over relaxation theory,the convergence rate of the iterative value function sequence is accelerated significantly with the relaxation factor.Second,the convergence and monotonicity of the value function sequence are analyzed under different ranges of the relaxation factor.Third,two practical approaches,namely the integrated scheme and the relaxation function,are introduced into the accelerated VI algorithm to guarantee the convergence of the iterative value function sequence for zero-sum games.The integrated scheme consists of the accelerated stage and the convergence stage,and the relaxation function can adjust the value of the relaxation factor.Finally,including the autopilot controller,the fantastic performance of the accelerated VI algorithm is verified through two examples with practical physical backgrounds.展开更多
The existence and uniqueness of the solutions for one kind of forward- backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. ...The existence and uniqueness of the solutions for one kind of forward- backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.展开更多
Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate...Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate this impulse game problem with the modified objective function including interaction costs among the players in a discontinuous fashion,and subsequently,to derive a verification theorem for identifying the feedback Nash equilibrium strategy.展开更多
This paper studies a class of continuous-time two person zero-sum stochastic differential games characterized by linear It?’s differential equation with state-dependent noise and Markovian parameter jumps. Under the ...This paper studies a class of continuous-time two person zero-sum stochastic differential games characterized by linear It?’s differential equation with state-dependent noise and Markovian parameter jumps. Under the assumption of stochastic stabilizability, necessary and sufficient condition for the existence of the optimal control strategies is presented by means of a system of coupled algebraic Riccati equations via using the stochastic optimal control theory. Furthermore, the stochastic H∞ control problem for stochastic systems with Markovian jumps is discussed as an immediate application, and meanwhile, an illustrative example is presented.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
In this paper,a zero-sum game Nash equilibrium computation problem with event-triggered communication is investigated under an undirected weight-balanced multi-agent network.A novel distributed event-triggered project...In this paper,a zero-sum game Nash equilibrium computation problem with event-triggered communication is investigated under an undirected weight-balanced multi-agent network.A novel distributed event-triggered projection subgradient algorithm is developed to reduce the communication burden within the subnetworks.In the proposed algorithm,when the difference between the current state of the agent and the state of the last trigger time exceeds a given threshold,the agent will be triggered to communicate with its neighbours.Moreover,we prove that all agents converge to Nash equilibrium by the proposed algorithm.Finally,two simulation examples verify that our algorithm not only reduces the communication burden but also ensures that the convergence speed and accuracy are close to that of the time-triggered method under the appropriate threshold.展开更多
This paper attempts to study two-person nonzero-sum games for denumerable continuous-time Markov chains determined by transition rates,with an expected average criterion.The transition rates are allowed to be unbounde...This paper attempts to study two-person nonzero-sum games for denumerable continuous-time Markov chains determined by transition rates,with an expected average criterion.The transition rates are allowed to be unbounded,and the payoff functions may be unbounded from above and from below.We give suitable conditions under which the existence of a Nash equilibrium is ensured.More precisely,using the socalled "vanishing discount" approach,a Nash equilibrium for the average criterion is obtained as a limit point of a sequence of equilibrium strategies for the discounted criterion as the discount factors tend to zero.Our results are illustrated with a birth-and-death game.展开更多
The Stackelberg prediction game(SPG)is a bilevel optimization frame-work for modeling strategic interactions between a learner and a follower.Existing meth-ods for solving this problem with general loss functions are ...The Stackelberg prediction game(SPG)is a bilevel optimization frame-work for modeling strategic interactions between a learner and a follower.Existing meth-ods for solving this problem with general loss functions are computationally expensive and scarce.We propose a novel hyper-gradient type method with a warm-start strategy to address this challenge.Particularly,we first use a Taylor expansion-based approach to obtain a good initial point.Then we apply a hyper-gradient descent method with an ex-plicit approximate hyper-gradient.We establish the convergence results of our algorithm theoretically.Furthermore,when the follower employs the least squares loss function,our method is shown to reach an e-stationary point by solving quadratic subproblems.Numerical experiments show our algorithms are empirically orders of magnitude faster than the state-of-the-art.展开更多
The two-player nonzero-sum linear-exponential-quadratic stochastic differential game is studied.The game takes into account the players'attitudes to risk.The nonlinear transformations and change of probability mea...The two-player nonzero-sum linear-exponential-quadratic stochastic differential game is studied.The game takes into account the players'attitudes to risk.The nonlinear transformations and change of probability measure techniques are used to study the existence of both open-loop and closed-loop Nash equilibria for the game.Some examples are constructed to illustrate their differences.Furthermore,theoretical results are applied to solve the risk-sensitive portfolio game problem in the financial market and show the effects of risk attitudes and economic performance on equilibria.展开更多
成果名称:Shapley's Conjecture on the Cores of Abstract Market Games主要作者:曹志刚,秦承忠,杨晓光奖项类别:著作论文奖获奖等级:二等奖获奖论文《Shapley's Conjecture on the Cores of Abstract Market Games》发表于博...成果名称:Shapley's Conjecture on the Cores of Abstract Market Games主要作者:曹志刚,秦承忠,杨晓光奖项类别:著作论文奖获奖等级:二等奖获奖论文《Shapley's Conjecture on the Cores of Abstract Market Games》发表于博弈论领域顶级期刊《Games and Economic Behavior》2018年第2期。论文研究成果初步解决了诺贝尔经济学奖获得者罗伊德·沙普利(Lloyd S. Shapley)提出的抽象市场博弈核非空的猜想。展开更多
This paper presents a comprehensive overview of distributed Nash equilibrium(NE)seeking algorithms in non-cooperative games for multiagent systems(MASs),with a distinct emphasis on the dynamic control perspective.It s...This paper presents a comprehensive overview of distributed Nash equilibrium(NE)seeking algorithms in non-cooperative games for multiagent systems(MASs),with a distinct emphasis on the dynamic control perspective.It specifically focuses on the research addressing distributed NE seeking problems in which agents are governed by heterogeneous dynamics.The paper begins by introducing fundamental concepts of general non-cooperative games and the NE,along with definitions of specific game structures such as aggregative games and multi-cluster games.It then systematically reviews existing studies on distributed NE seeking for various classes of MASs from the viewpoint of agent dynamics,including first-order,second-order,high-order,linear,and Euler-Lagrange(EL)systems.Furthermore,the paper highlights practical applications of these theoretical advances in cooperative control scenarios involving autonomous systems with complex dynamics,such as autonomous surface vessels,autonomous aerial vehicles,and other autonomous vehicles.Finally,the paper outlines several promising directions for future research.展开更多
Background Autism spectrum disorder(ASD)is a pervasive developmental disorder characterized by difficulties in social communication and restricted,repetitive behaviors.Early intervention is essential to improve develo...Background Autism spectrum disorder(ASD)is a pervasive developmental disorder characterized by difficulties in social communication and restricted,repetitive behaviors.Early intervention is essential to improve developmental outcomes in children with ASD.Serious games,which combine educational objectives with game based interactions,have shown potential as tools for early intervention in patients with ASD.However,in China,the development of serious games specifically designed for children with ASD remains in its infancy,with significant gaps in technical frameworks and effective data management methods.Method This paper proposes a framework aimed at facilitating the development of multimodal serious games designed for ASD interventions.We demonstrated the feasibility of the framework by developing and integrating several components,such as web applications,mobile games,and augmented reality games.These tools are interconnected to achieve data connectivity and management.Additionally,adaptive mechanics were employed within the framework to analyze real-time player data,which allowed the game difficulty to be dynamically adjusted and provide a personalized experience for each child.Results The framework successfully integrated various multimodal games,ensuring that real-time data management supported personalized game experiences.This approach ensured that the interventions remained appropriately challenging while still achievable.Conclusion The results indicate that the proposed framework enhances collaboration among therapists,parents,and developers while also improving the effectiveness of ASD interventions.By delivering personalized gameplay experiences that are both challenging and achievable,the framework offers a scalable platform for the future development of serious games.展开更多
This paper proposes a novel impulsive thrust strategy guided by optimal continuous thrust strategy to address two-player orbital pursuit-evasion game under impulsive thrust control.The strategy seeks to enhance the in...This paper proposes a novel impulsive thrust strategy guided by optimal continuous thrust strategy to address two-player orbital pursuit-evasion game under impulsive thrust control.The strategy seeks to enhance the interpretability of impulsive thrust strategy by integrating it within the framework of differential game in traditional continuous systems.First,this paper introduces an impulse-like constraint,with periodical changes in thrust amplitude,to characterize the impulsive thrust control.Then,the game with the impulse-like constraint is converted into the two-point boundary value problem,which is solved by the combined shooting and deep learning method proposed in this paper.Deep learning and numerical optimization are employed to obtain the guesses for unknown terminal adjoint variables and the game terminal time.Subsequently,the accurate values are solved by the shooting method to yield the optimal continuous thrust strategy with the impulse-like constraint.Finally,the shooting method is iteratively employed at each impulse decision moment to derive the impulsive thrust strategy guided by the optimal continuous thrust strategy.Numerical examples demonstrate the convergence of the combined shooting and deep learning method,even if the strongly nonlinear impulse-like constraint is introduced.The effect of the impulsive thrust strategy guided by the optimal continuous thrust strategy is also discussed.展开更多
I was so excited to be a volunteer for the 2025 Asian Winter Games.It was a wonderful chance to meet people from all over Asia.During the Games,I helped players find their way around the stadium.I also answered questi...I was so excited to be a volunteer for the 2025 Asian Winter Games.It was a wonderful chance to meet people from all over Asia.During the Games,I helped players find their way around the stadium.I also answered questions from visitors.Everyone was friendly,and I felt happy to help them.展开更多
基金the Science and Technology Innovation 2030-"New Generation Artificial Intelligence"Major Project(No.2018AAA0100901)。
文摘In repeated zero-sum games,instead of constantly playing an equilibrium strategy of the stage game,learning to exploit the opponent given historical interactions could typically obtain a higher utility.However,when playing against a fully adaptive opponent,one would have dificulty identifying the opponent's adaptive dynamics and further exploiting its potential weakness.In this paper,we study the problem of optimizing against the adaptive opponent who uses no-regret learning.No-regret learning is a classic and widely-used branch of adaptive learning algorithms.We propose a general framework for online modeling no-regret opponents and exploiting their weakness.With this framework,one could approximate the opponent's no-regret learning dynamics and then develop a response plan to obtain a significant profit based on the inferences of the opponent's strategies.We employ two system identification architectures,including the recurrent neural network(RNN)and the nonlinear autoregressive exogenous model,and adopt an efficient greedy response plan within the framework.Theoretically,we prove the approximation capability of our RNN architecture at approximating specific no-regret dynamics.Empirically,we demonstrate that during interactions at a low level of non-stationarity,our architectures could approximate the dynamics with a low error,and the derived policies could exploit the no-regret opponent to obtain a decent utility.
文摘In this paper, we consider multiobjective two-person zero-sum games with vector payoffs and vector fuzzy payoffs. We translate such games into the corresponding multiobjective programming problems and introduce the pessimistic Pareto optimal solution concept by assuming that a player supposes the opponent adopts the most disadvantage strategy for the self. It is shown that any pessimistic Pareto optimal solution can be obtained on the basis of linear programming techniques even if the membership functions for the objective functions are nonlinear. Moreover, we propose interactive algorithms based on the bisection method to obtain a pessimistic compromise solution from among the set of all pessimistic Pareto optimal solutions. In order to show the efficiency of the proposed method, we illustrate interactive processes of an application to a vegetable shipment problem.
文摘There are a few studies that focus on solution methods for finding a Nash equilibrium of zero-sum games. We discuss the use of Karmarkar’s interior point method to solve the Nash equilibrium problems of a zero-sum game, and prove that it is theoretically a polynomial time algorithm. We implement the Karmarkar method, and a preliminary computational result shows that it performs well for zero-sum games. We also mention an affine scaling method that would help us compute Nash equilibria of general zero-sum games effectively.
基金Supported by National High Technology Research and Development Program of China （863 Program） （2006AA04Z183）, National Natural Science Foundation of China （60621001, 60534010, 60572070, 60774048, 60728307）, Program for Changjiang Scholars and Innovative Research Groups of China （60728307, 4031002）
基金supported by National Key R&D Program of China under Grant No.2021ZD0112600the National Natural Science Foundation of China under Grant No.62373058+3 种基金the Beijing Natural Science Foundation under Grant No.L233003National Science Fund for Distinguished Young Scholars of China under Grant No.62025301the Postdoctoral Fellowship Program of CPSF under Grant No.GZC20233407the Basic Science Center Programs of NSFC under Grant No.62088101。
文摘This paper investigates the multi-player non-zero-sum game problem for unknown linear continuous-time systems with unmeasurable states.By only accessing the data information of input and output,a data-driven learning control approach is proposed to estimate N-tuple dynamic output feedback control policies which can form Nash equilibrium solution to the multi-player non-zero-sum game problem.In particular,the explicit form of dynamic output feedback Nash strategy is constructed by embedding the internal dynamics and solving coupled algebraic Riccati equations.The coupled policy-iteration based iterative learning equations are established to estimate the N-tuple feedback control gains without prior knowledge of system matrices.Finally,an example is used to illustrate the effectiveness of the proposed approach.
基金Project supported by the National Natural Science Foundation of China (No.10371067) thePlanned Item for the Outstanding Young Teachers of Ministry of Education of China (No.2057) the Special Fund for Ph.D. Program of Ministry of Education of China ( No.20020422020) and the Fok Ying Tung Education Foundation for Young College Teachers(No.91064)
文摘The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions.Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.
基金supported in part by the National Natural Science Foundation of China under Grant 62222301,Grant 61890930-5,and Grant 62021003the National Science and Technology Major Project under Grant 2021ZD0112302 and Grant 2021ZD0112301the Beijing Natural Science Foundation under Grant JQ19013.
文摘In this paper,an accelerated value iteration(VI)algorithm is established to solve the zero-sum game problem with convergence guarantee.First,inspired by the successive over relaxation theory,the convergence rate of the iterative value function sequence is accelerated significantly with the relaxation factor.Second,the convergence and monotonicity of the value function sequence are analyzed under different ranges of the relaxation factor.Third,two practical approaches,namely the integrated scheme and the relaxation function,are introduced into the accelerated VI algorithm to guarantee the convergence of the iterative value function sequence for zero-sum games.The integrated scheme consists of the accelerated stage and the convergence stage,and the relaxation function can adjust the value of the relaxation factor.Finally,including the autopilot controller,the fantastic performance of the accelerated VI algorithm is verified through two examples with practical physical backgrounds.
基金国家自然科学基金，Outstanding Young Teachers of Ministry of Education of China，Special Fund for Ph.D.Program of Ministry of Education of China，Fok Ying Tung Education Foundation
文摘The existence and uniqueness of the solutions for one kind of forward- backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.
基金supported in part by the National Natural Science Foundation of China(62173051)the Fundamental Research Funds for the Central Universities(2024CDJCGJ012,2023CDJXY-010)+1 种基金the Chongqing Technology Innovation and Application Development Special Key Project(CSTB2022TIADCUX0015,CSTB2022TIAD-KPX0162)the China Postdoctoral Science Foundation(2024M763865)
文摘Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate this impulse game problem with the modified objective function including interaction costs among the players in a discontinuous fashion,and subsequently,to derive a verification theorem for identifying the feedback Nash equilibrium strategy.
文摘This paper studies a class of continuous-time two person zero-sum stochastic differential games characterized by linear It?’s differential equation with state-dependent noise and Markovian parameter jumps. Under the assumption of stochastic stabilizability, necessary and sufficient condition for the existence of the optimal control strategies is presented by means of a system of coupled algebraic Riccati equations via using the stochastic optimal control theory. Furthermore, the stochastic H∞ control problem for stochastic systems with Markovian jumps is discussed as an immediate application, and meanwhile, an illustrative example is presented.
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.
文摘In this paper,a zero-sum game Nash equilibrium computation problem with event-triggered communication is investigated under an undirected weight-balanced multi-agent network.A novel distributed event-triggered projection subgradient algorithm is developed to reduce the communication burden within the subnetworks.In the proposed algorithm,when the difference between the current state of the agent and the state of the last trigger time exceeds a given threshold,the agent will be triggered to communicate with its neighbours.Moreover,we prove that all agents converge to Nash equilibrium by the proposed algorithm.Finally,two simulation examples verify that our algorithm not only reduces the communication burden but also ensures that the convergence speed and accuracy are close to that of the time-triggered method under the appropriate threshold.
基金supported by National Science Foundation for Distinguished Young Scholars of China (Grant No. 10925107)Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2011)
文摘This paper attempts to study two-person nonzero-sum games for denumerable continuous-time Markov chains determined by transition rates,with an expected average criterion.The transition rates are allowed to be unbounded,and the payoff functions may be unbounded from above and from below.We give suitable conditions under which the existence of a Nash equilibrium is ensured.More precisely,using the socalled "vanishing discount" approach,a Nash equilibrium for the average criterion is obtained as a limit point of a sequence of equilibrium strategies for the discounted criterion as the discount factors tend to zero.Our results are illustrated with a birth-and-death game.
文摘The Stackelberg prediction game(SPG)is a bilevel optimization frame-work for modeling strategic interactions between a learner and a follower.Existing meth-ods for solving this problem with general loss functions are computationally expensive and scarce.We propose a novel hyper-gradient type method with a warm-start strategy to address this challenge.Particularly,we first use a Taylor expansion-based approach to obtain a good initial point.Then we apply a hyper-gradient descent method with an ex-plicit approximate hyper-gradient.We establish the convergence results of our algorithm theoretically.Furthermore,when the follower employs the least squares loss function,our method is shown to reach an e-stationary point by solving quadratic subproblems.Numerical experiments show our algorithms are empirically orders of magnitude faster than the state-of-the-art.
文摘The two-player nonzero-sum linear-exponential-quadratic stochastic differential game is studied.The game takes into account the players'attitudes to risk.The nonlinear transformations and change of probability measure techniques are used to study the existence of both open-loop and closed-loop Nash equilibria for the game.Some examples are constructed to illustrate their differences.Furthermore,theoretical results are applied to solve the risk-sensitive portfolio game problem in the financial market and show the effects of risk attitudes and economic performance on equilibria.
文摘成果名称:Shapley's Conjecture on the Cores of Abstract Market Games主要作者:曹志刚,秦承忠,杨晓光奖项类别:著作论文奖获奖等级:二等奖获奖论文《Shapley's Conjecture on the Cores of Abstract Market Games》发表于博弈论领域顶级期刊《Games and Economic Behavior》2018年第2期。论文研究成果初步解决了诺贝尔经济学奖获得者罗伊德·沙普利(Lloyd S. Shapley)提出的抽象市场博弈核非空的猜想。
基金National Natural Science Foundation of China(62325304).
文摘This paper presents a comprehensive overview of distributed Nash equilibrium(NE)seeking algorithms in non-cooperative games for multiagent systems(MASs),with a distinct emphasis on the dynamic control perspective.It specifically focuses on the research addressing distributed NE seeking problems in which agents are governed by heterogeneous dynamics.The paper begins by introducing fundamental concepts of general non-cooperative games and the NE,along with definitions of specific game structures such as aggregative games and multi-cluster games.It then systematically reviews existing studies on distributed NE seeking for various classes of MASs from the viewpoint of agent dynamics,including first-order,second-order,high-order,linear,and Euler-Lagrange(EL)systems.Furthermore,the paper highlights practical applications of these theoretical advances in cooperative control scenarios involving autonomous systems with complex dynamics,such as autonomous surface vessels,autonomous aerial vehicles,and other autonomous vehicles.Finally,the paper outlines several promising directions for future research.
基金Supported by the Public Welfare Technology Application Research Project of Zhejiang Province(No.LTGY23F020001)the Provincial Construction Programme for First-Class Online and Offline Blended Courses(No.Z202Y22513)the Higher Education Teaching Reform Research Programme of Communication University of Zhejiang“Research on Contextualized Teaching Mode for the New Generation of Engineering Students Based on Convergence Media”。
文摘Background Autism spectrum disorder(ASD)is a pervasive developmental disorder characterized by difficulties in social communication and restricted,repetitive behaviors.Early intervention is essential to improve developmental outcomes in children with ASD.Serious games,which combine educational objectives with game based interactions,have shown potential as tools for early intervention in patients with ASD.However,in China,the development of serious games specifically designed for children with ASD remains in its infancy,with significant gaps in technical frameworks and effective data management methods.Method This paper proposes a framework aimed at facilitating the development of multimodal serious games designed for ASD interventions.We demonstrated the feasibility of the framework by developing and integrating several components,such as web applications,mobile games,and augmented reality games.These tools are interconnected to achieve data connectivity and management.Additionally,adaptive mechanics were employed within the framework to analyze real-time player data,which allowed the game difficulty to be dynamically adjusted and provide a personalized experience for each child.Results The framework successfully integrated various multimodal games,ensuring that real-time data management supported personalized game experiences.This approach ensured that the interventions remained appropriately challenging while still achievable.Conclusion The results indicate that the proposed framework enhances collaboration among therapists,parents,and developers while also improving the effectiveness of ASD interventions.By delivering personalized gameplay experiences that are both challenging and achievable,the framework offers a scalable platform for the future development of serious games.
基金funded by the National Natural Science Foundation of China(No.U21B6001)。
文摘This paper proposes a novel impulsive thrust strategy guided by optimal continuous thrust strategy to address two-player orbital pursuit-evasion game under impulsive thrust control.The strategy seeks to enhance the interpretability of impulsive thrust strategy by integrating it within the framework of differential game in traditional continuous systems.First,this paper introduces an impulse-like constraint,with periodical changes in thrust amplitude,to characterize the impulsive thrust control.Then,the game with the impulse-like constraint is converted into the two-point boundary value problem,which is solved by the combined shooting and deep learning method proposed in this paper.Deep learning and numerical optimization are employed to obtain the guesses for unknown terminal adjoint variables and the game terminal time.Subsequently,the accurate values are solved by the shooting method to yield the optimal continuous thrust strategy with the impulse-like constraint.Finally,the shooting method is iteratively employed at each impulse decision moment to derive the impulsive thrust strategy guided by the optimal continuous thrust strategy.Numerical examples demonstrate the convergence of the combined shooting and deep learning method,even if the strongly nonlinear impulse-like constraint is introduced.The effect of the impulsive thrust strategy guided by the optimal continuous thrust strategy is also discussed.
文摘I was so excited to be a volunteer for the 2025 Asian Winter Games.It was a wonderful chance to meet people from all over Asia.During the Games,I helped players find their way around the stadium.I also answered questions from visitors.Everyone was friendly,and I felt happy to help them.
