在Fudenberg and Tirole(1991,2002)关于纳什均衡的存在性和性质的技术性说明基础上,主要讨论完全信息的连续博弈。对照于刘宗谦(2004,2006)给出的、有限的完全信息静态博弈中的混合策略性质和均衡,它提出并证明连续博弈混合策略集上类...在Fudenberg and Tirole(1991,2002)关于纳什均衡的存在性和性质的技术性说明基础上,主要讨论完全信息的连续博弈。对照于刘宗谦(2004,2006)给出的、有限的完全信息静态博弈中的混合策略性质和均衡,它提出并证明连续博弈混合策略集上类似的一些性质,同样利用范一格里克斯伯格不动点定理证明了混合策略纳什均衡的存在性。为强调紧度量空间是可用有限集充分逼近的无限集的数学结构的应用,仿照Myerson(1991,2001)对无限策略集的讨论,它给出了有关的逼近定理的证明,从而也给出了连续博弈混合策略纳什均衡存在性的另一种证明。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
文摘在Fudenberg and Tirole(1991,2002)关于纳什均衡的存在性和性质的技术性说明基础上,主要讨论完全信息的连续博弈。对照于刘宗谦(2004,2006)给出的、有限的完全信息静态博弈中的混合策略性质和均衡,它提出并证明连续博弈混合策略集上类似的一些性质,同样利用范一格里克斯伯格不动点定理证明了混合策略纳什均衡的存在性。为强调紧度量空间是可用有限集充分逼近的无限集的数学结构的应用,仿照Myerson(1991,2001)对无限策略集的讨论,它给出了有关的逼近定理的证明,从而也给出了连续博弈混合策略纳什均衡存在性的另一种证明。
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.
