一般经济均衡的本质稳定性及Hadamard适定性

数学物理学报 ›› 2023, Vol. 43 ›› Issue (3): 930-938.

一般经济均衡的本质稳定性及Hadamard适定性

曾静^*(),彭家玉()

重庆工商大学数学与统计学院重庆400067

收稿日期:2022-06-22 修回日期:2023-02-06 出版日期:2023-06-26 发布日期:2023-06-01
通讯作者: 曾静 E-mail:zengjing1983@ctbu.edu.cn;pjjpjy@163.com
作者简介:彭家玉,E-mail: pjjpjy@163.com
基金资助:
国家自然科学基金(12001445);重庆市自然科学基金(基础研究与前沿探索专项)面上项目(cstc2019jcyj-msxmX0605);重庆市教委科学技术研究项目(KJQN201800837)

Essential Stability and Hadamard Well-Posedness of Excess Demand Equilibrium Problems

Zeng Jing^*(),Peng Jiayu()

School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067

Received:2022-06-22 Revised:2023-02-06 Online:2023-06-26 Published:2023-06-01
Contact: Jing Zeng E-mail:zengjing1983@ctbu.edu.cn;pjjpjy@163.com
Supported by:
NSFC(12001445);Basic and Research Project of Chongqing(cstc2019jcyj-msxmX0605);Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN201800837)

摘要/Abstract

摘要：

考虑有限维欧氏空间中的一般经济均衡问题. 首先在超需映射和价格参数集均扰动的情况下, 建立了一般经济均衡解映射半连续性与本质平衡解, 本质集之间的关系. 其次在Baire分类意义下, 证明一般经济均衡是稳定的. 最后, 通过引入一个标量化函数来定义一个集合, 得到一般经济均衡Hadamard适定性成立的充分性条件.

关键词: 一般经济均衡问题, 本质平衡解, 本质集, 超需映射, Hadamard适定性

Abstract:

In this paper, we considered the excess demand equilibrium problems in finite dimensional Euclidean spaces. Firstly, the relationship among the semicontinuity of solution mapping, the essential equilibrium solution and the essential set is established, when both the excess demand mapping and the price parameter set are disturbed. Secondly, it is proved that the excess demand equilibrium problems is stable in the sense of Baire classification. Finally, taking advantage of a set defined by a scalar function, sufficient conditions of Hadamard well-posedness of the excess demand equilibrium problems are obtained.

Key words: The excess demand equilibrium problem, Essential equilibrium solution, Essential set, Excess demand function, Hadamard well-posedness

中图分类号:

O224

曾静,彭家玉. 一般经济均衡的本质稳定性及Hadamard适定性[J]. 数学物理学报, 2023, 43(3): 930-938.

Zeng Jing,Peng Jiayu. Essential Stability and Hadamard Well-Posedness of Excess Demand Equilibrium Problems[J]. Acta mathematica scientia,Series A, 2023, 43(3): 930-938.

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