信息集广义多目标博弈弱Pareto-Nash平衡点的存在性和稳定性

运筹学学报 ›› 2015, Vol. 19 ›› Issue (1): 9-17.

信息集广义多目标博弈弱Pareto-Nash平衡点的存在性和稳定性

贾文生¹, 向淑文^1,*

1. 贵州大学理学院, 贵阳 550025

收稿日期:2013-09-12 出版日期:2015-03-15 发布日期:2015-03-15
通讯作者: 向淑文 E-mail:shwxiang@vip.163.com
基金资助:
国家自然科学基金(No. 11161008), 教育部博士点基金(No. 20115201110002), 贵州省自然科学基金(No. 20122139)

Existence and stability of weakly Pareto-Nash equilibrium points for information sets generalized multiobjective games

JIA Wensheng¹, XIANG Shuwen^1,*

1. College of Science, Guizhou University, Guiyang 550025, China

Received:2013-09-12 Online:2015-03-15 Published:2015-03-15

摘要/Abstract

摘要：

首先把信息集的概念引入到多目标博弈, 建立了信息集广义多目标博弈模型, 并指出了信息集广义多目标博弈以广义多目标博弈、广义n人非合作博弈、一般n人非合作博弈为特例, 然后用Fan-Glicksberg不动点定理证明了信息集广义多目标博弈弱Pareto-Nash平衡点的存在性, 最后在本质解和强本质解的意义下,
分别研究了信息集广义多目标博弈弱Pareto-Nash平衡点的通有稳定性和强本质连通区的存在性.

关键词: 信息集, 多目标博弈, 本质解, 强本质解, 强本质连通区

Abstract:

In this paper, the information sets generalized multiobjective game model is established by introducing information sets to the multiobjective game, and it is presented that the generalized multiobjective game, the generalized $n$-person game, the n-person noncooperative finite game as some special cases of the information sets generalized multiobjective game. Then the existence theorem of weakly Pareto-Nash equilibrium points for the information sets generalized multiobjective game is proved by using Fan-Glicksberg fixed point theorem. Furthermore, from the viewpoint of the essential solution and strongly essential solution, we prove that the generic stability and the existence of strongly essential component for information sets generalized multiobjective games.

Key words: information set, multiobjective game, essential solution, strongly essential solution, strongly essential component

中图分类号:

O225

贾文生, 向淑文. 信息集广义多目标博弈弱Pareto-Nash平衡点的存在性和稳定性[J]. 运筹学学报, 2015, 19(1): 9-17.

JIA Wensheng, XIANG Shuwen. Existence and stability of weakly Pareto-Nash equilibrium points for information sets generalized multiobjective games[J]. Operations Research Transactions, 2015, 19(1): 9-17.

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