This paper is concerned with distributed Nash equi librium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achi...This paper is concerned with distributed Nash equi librium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achieve the optimization o players' objective functions while restricting their actions within required non-empty, convex and compact domains. In addition, a leader-following consensus protocol, in which quantized informa tion flows are utilized, is employed for information sharing among players. More specifically, logarithmic quantizers and uniform quantizers are investigated under both undirected and connected communication graphs and strongly connected digraphs, respec tively. Through Lyapunov stability analysis, it is shown that play ers' actions can be steered to a neighborhood of the Nash equilib rium with logarithmic and uniform quantizers, and the quanti fied convergence error depends on the parameter of the quan tizer for both undirected and directed cases. A numerical exam ple is given to verify the theoretical results.展开更多
为了优化区域交通信号配时方案,提升区域通行效率,文章提出一种基于改进多智能体Nash Q Learning的区域交通信号协调控制方法。首先,采用离散化编码方法,通过划分单元格将连续状态信息转化为离散形式。其次,在算法中融入长短时记忆网络(...为了优化区域交通信号配时方案,提升区域通行效率,文章提出一种基于改进多智能体Nash Q Learning的区域交通信号协调控制方法。首先,采用离散化编码方法,通过划分单元格将连续状态信息转化为离散形式。其次,在算法中融入长短时记忆网络(Long Short Term Memory,LSTM)模块,用于从状态数据中挖掘更多的隐藏信息,丰富Q值表中的状态数据。最后,基于微观交通仿真软件SUMO(Simulation of Urban Mobility)的仿真测试结果表明,相较于原始Nash Q Learning交通信号控制方法,所提方法在低、中、高流量下车辆的平均等待时间分别减少了11.5%、16.2%和10.0%,平均排队长度分别减少了9.1%、8.2%和7.6%,平均停车次数分别减少了18.3%、16.1%和10.0%。结果证明了该算法具有更好的控制效果。展开更多
Nowadays manufacturers are facing fierce challenge.Apart from the products,providing customers with multiple maintenance options in the service contract becomes more popular,since it can help to improve customer satis...Nowadays manufacturers are facing fierce challenge.Apart from the products,providing customers with multiple maintenance options in the service contract becomes more popular,since it can help to improve customer satisfaction,and ultimately promote sales and maximize profit for the manufacturer.By considering the combinations of corrective maintenance and preventive maintenance,totally three types of maintenance service contracts are designed.Moreover,attractive incentive and penalty mechanisms are adopted in the contracts.On this basis,Nash non-cooperative game is applied to analyze the revenue for both the manufacturer and customers,and so as to optimize the pricing mechanism of maintenance service contract and achieve a win-win situation.Numerical experiments are conducted.The results show that by taking into account the incentive and penalty mechanisms,the revenue can be improved for both the customers and manufacturer.Moreover,with the increase of repair rate and improvement factor in the preventive maintenance,the revenue will increase gradually for both the parties.展开更多
It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems kn...It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.展开更多
随着新时代的蓬勃发展,电商领域取得了历史性突破,但也伴随着许多不确定性问题显现。随机广义Nash均衡是非合作博弈的重要概念,在现代经济学的研究中具有重要地位。本文从随机广义Nash均衡的角度来分析电商领域中的实际问题,将电商领域...随着新时代的蓬勃发展,电商领域取得了历史性突破,但也伴随着许多不确定性问题显现。随机广义Nash均衡是非合作博弈的重要概念,在现代经济学的研究中具有重要地位。本文从随机广义Nash均衡的角度来分析电商领域中的实际问题,将电商领域中的问题等价于对应的随机广义Nash均衡问题。同时,采用样本平均近似法(SAA)处理随机因素,利用Nikaido-Isoda函数和改进的差分进化算法进行求解。最后,给出一个关于电商平台对应生产厂商产品生产数量问题的实例。结果显示,利用随机广义Nash均衡和差分进化算法来解决电商领域中的实际问题具有可行性,对电商平台的进一步发展具有研究意义。With the booming development of the new era, the field of e-commerce has made a historic breakthrough, but it is also accompanied by many revealed uncertainty problems. Stochastic Generalized Nash Equilibrium is an important concept of non-cooperative game, which occupies an important position in the study of modern economics. In this paper, we analyze the practical problems in the field of e-commerce from the perspective of Stochastic Generalized Nash Equilibrium, and equate the problems in the field of e-commerce with the corresponding Stochastic Generalized Nash Equilibrium problems. Meanwhile, the Sample Average Approximation (SAA) method is adopted to deal with the stochastic factors, and the Nikaido-Isoda function and the improved differential evolutionary algorithm are used for the solution. Finally, an example is given of the problem of the number of products produced by the corresponding manufacturer of the e-commerce platform. The results show that it is possible to use stochastic generalized Nash equilibrium and differential evolution algorithms to solve practical problems in the field of e-commerce, which has research implications for the further development of e-commerce platforms.展开更多
基金supported by the National Natural Science Foundation of China (NSFC)(62222308, 62173181, 62073171, 62221004)the Natural Science Foundation of Jiangsu Province (BK20200744, BK20220139)+3 种基金Jiangsu Specially-Appointed Professor (RK043STP19001)the Young Elite Scientists Sponsorship Program by CAST (2021QNRC001)1311 Talent Plan of Nanjing University of Posts and Telecommunicationsthe Fundamental Research Funds for the Central Universities (30920032203)。
文摘This paper is concerned with distributed Nash equi librium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achieve the optimization o players' objective functions while restricting their actions within required non-empty, convex and compact domains. In addition, a leader-following consensus protocol, in which quantized informa tion flows are utilized, is employed for information sharing among players. More specifically, logarithmic quantizers and uniform quantizers are investigated under both undirected and connected communication graphs and strongly connected digraphs, respec tively. Through Lyapunov stability analysis, it is shown that play ers' actions can be steered to a neighborhood of the Nash equilib rium with logarithmic and uniform quantizers, and the quanti fied convergence error depends on the parameter of the quan tizer for both undirected and directed cases. A numerical exam ple is given to verify the theoretical results.
文摘为了优化区域交通信号配时方案,提升区域通行效率,文章提出一种基于改进多智能体Nash Q Learning的区域交通信号协调控制方法。首先,采用离散化编码方法,通过划分单元格将连续状态信息转化为离散形式。其次,在算法中融入长短时记忆网络(Long Short Term Memory,LSTM)模块,用于从状态数据中挖掘更多的隐藏信息,丰富Q值表中的状态数据。最后,基于微观交通仿真软件SUMO(Simulation of Urban Mobility)的仿真测试结果表明,相较于原始Nash Q Learning交通信号控制方法,所提方法在低、中、高流量下车辆的平均等待时间分别减少了11.5%、16.2%和10.0%,平均排队长度分别减少了9.1%、8.2%和7.6%,平均停车次数分别减少了18.3%、16.1%和10.0%。结果证明了该算法具有更好的控制效果。
基金supported by the National Natural Science Foundation of China(71671035)。
文摘Nowadays manufacturers are facing fierce challenge.Apart from the products,providing customers with multiple maintenance options in the service contract becomes more popular,since it can help to improve customer satisfaction,and ultimately promote sales and maximize profit for the manufacturer.By considering the combinations of corrective maintenance and preventive maintenance,totally three types of maintenance service contracts are designed.Moreover,attractive incentive and penalty mechanisms are adopted in the contracts.On this basis,Nash non-cooperative game is applied to analyze the revenue for both the manufacturer and customers,and so as to optimize the pricing mechanism of maintenance service contract and achieve a win-win situation.Numerical experiments are conducted.The results show that by taking into account the incentive and penalty mechanisms,the revenue can be improved for both the customers and manufacturer.Moreover,with the increase of repair rate and improvement factor in the preventive maintenance,the revenue will increase gradually for both the parties.
文摘It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.
文摘随着新时代的蓬勃发展,电商领域取得了历史性突破,但也伴随着许多不确定性问题显现。随机广义Nash均衡是非合作博弈的重要概念,在现代经济学的研究中具有重要地位。本文从随机广义Nash均衡的角度来分析电商领域中的实际问题,将电商领域中的问题等价于对应的随机广义Nash均衡问题。同时,采用样本平均近似法(SAA)处理随机因素,利用Nikaido-Isoda函数和改进的差分进化算法进行求解。最后,给出一个关于电商平台对应生产厂商产品生产数量问题的实例。结果显示,利用随机广义Nash均衡和差分进化算法来解决电商领域中的实际问题具有可行性,对电商平台的进一步发展具有研究意义。With the booming development of the new era, the field of e-commerce has made a historic breakthrough, but it is also accompanied by many revealed uncertainty problems. Stochastic Generalized Nash Equilibrium is an important concept of non-cooperative game, which occupies an important position in the study of modern economics. In this paper, we analyze the practical problems in the field of e-commerce from the perspective of Stochastic Generalized Nash Equilibrium, and equate the problems in the field of e-commerce with the corresponding Stochastic Generalized Nash Equilibrium problems. Meanwhile, the Sample Average Approximation (SAA) method is adopted to deal with the stochastic factors, and the Nikaido-Isoda function and the improved differential evolutionary algorithm are used for the solution. Finally, an example is given of the problem of the number of products produced by the corresponding manufacturer of the e-commerce platform. The results show that it is possible to use stochastic generalized Nash equilibrium and differential evolution algorithms to solve practical problems in the field of e-commerce, which has research implications for the further development of e-commerce platforms.
