[1]何基好,向淑文,贾文生,等.基于有限理性的信息集广义多目标博弈[J].深圳大学学报理工版,2018,35(1):105-109.[doi:10.3724/SP.J.1249.2018.01105]
　HE Jihao,XIANG Shuwen,et al.Information set generalized multi-objective games based on bounded rationality[J].Journal of Shenzhen University Science and Engineering,2018,35(1):105-109.[doi:10.3724/SP.J.1249.2018.01105]
点击复制

基于有限理性的信息集广义多目标博弈()
分享到：

《深圳大学学报理工版》[ISSN:1000-2618/CN:44-1401/N]

卷:
第35卷
期数:
2018年第1期
页码:
105-109
栏目:
数学与应用数学
出版日期:
2018-01-12

文章信息/Info

Title:
Information set generalized multi-objective games based on bounded rationality
文章编号:
201801016
作者:
何基好1; 2; 向淑文2; 贾文生2; 邓喜才3
1）贵州大学计算机科学与技术学院，贵州贵阳 550025
2）贵州大学数学与统计学院，贵州贵阳 550025
3）贵州师范学院数学与计算机系，贵州贵阳 550018
Author(s):
HE Jihao1;  2;  XIANG Shuwen2;  JIA Wensheng2;  and DENG Xicai3
1) College of Computer Science and Technology, Guizhou University, Guiyang 550025, Guizhou Province, P.R.China
2) School of Mathematics and Statistics, Guizhou University, Guiyang 550025, Guizhou Province, P.R.China
3) Department of Mathematics and Computer, Guizhou Normal College, Guiyang 550018, Guizhou Province, P.R.China
关键词:
运筹学; 博弈论; 信息集广义多目标博弈; 弱Pareto-Nash平衡点; 有限理性; 稳定性
Keywords:
operation research;  game theory;  information sets generalized multio-bjective game;  weak Pareto-Nash equilibrium point;  bounded rationality;  stability
分类号:
O 177.9
DOI:
10.3724/SP.J.1249.2018.01105
文献标志码:
A
摘要:
研究基于有限理性的信息集广义多目标博弈的弱Pareto-Nash平衡问题的稳定性.在信息集广义多目标博弈的弱Pareto-Nash平衡问题的度量空间是完备度量空间的结论下,运用博弈论语言描述的有限理性模型建立此问题的有限理性模型,通过验证一些假设得到，弱Pareto-Nash平衡问题是结构稳定的,对ε-平衡是鲁棒的.
Abstract:
On the base of the bounded rationality, we investigate the stability of the problem of the weak Pareto-Nash equilibrium for information set generalized multi-objective games. Based on the conclusion that the metric space of the problem of information set generalized multi-objective games are complete, the bounded rationality model is established according to the bounded rationality model described by the game theory language, and the result shows that the problem of the weak Pareto-Nash equilibrium is structurally stable and robust to ε-equilibrium by identifying some assumptions.

参考文献/References:

［1］ BLACKWELL O. An analogy of minimax theorem for vector payoffs［J］. Pacific Journal of Mathematics, 1956, 6(1):1-8.
［2］ SHAPLEY L S. Equilibrium points in games with vector payoffs［J］. Naval Research Logistics Quarterly, 1959, 6(1): 57-61.
［3］ 杨辉,俞建.向量拟平衡问题的本质解及解集的本质连通区［J］.系统科学与数学,2004,24(1):74-84.
YANG Hui, YU Jian. Essential solutions and essential components of solution set of vector quasi-equilibrium problems［J］. Journal of Systems Science and Mathematical Sciences, 2004, 24(1):74-84.(in Chinese)
［4］ XIE Pingding. Nonempty intersection theorems and generalized multi-objective games in product FC-Spaces［J］. Journal of Global Optimization. 2007, 37(1):63-73.
［5］ 贾文生,向淑文.信息集广义多目标博弈弱Pareto-Nash 平衡点存在性和稳定性［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 multi-objective games［J］.Operations Research Transactions, 2015, 19(1): 9-17.(in Chinese)
［6］ ANDERLINI L, CANNING D. Structural stability implies robustness to bounded rationality［J］. Journal of Economic Theory, 2001, 101(2): 395-422.
［7］ YU Chao,YU Jian. On structural stability and robustness to bounded rationality［J］. Nonlinear Analysis: Theory, Methods & Applications, 2006, 65(3): 583-592.
［8］ YU Chao,YU Jian. Bounded rationality in multi-objective games［J］. Nonlinear Analysis: Theory, Methods & Applications, 2007, 67(3): 930-937.
［9］ 俞建.几类考虑有限理性平衡问题解的稳定性［J］.系统科学与数学,2009,29(7):999-1008.
YU Jian. Bounded rationality and stability of solutions of some equilibrium problems［J］. Journal of Systems Science and Mathematical Sciences, 2009, 29(7): 999-1008.(in Chinese)
［10］ YU Jian, YANG Hui, YU Chao. Structural stability and robustness to bounded rationality for non-compact cases［J］. Journal of Global Optimization, 2009, 44(1): 149-157.
［11］ 俞建.博弈论与非线性分析续论［M］.北京:科学出版社,2011.
YU Jian. Game theory and introduction of nonlinear analysis［M］. Beijing: Science Press, 2011.

相似文献/References:

[1]吴　舟,赵春晖.MIMO系统中连续博弈RRM算法[J].深圳大学学报理工版,2007,24(2):117.
　WU Zhou and ZHAO Chun-hui.Successive game RRM algorithm for MIMO system[J].Journal of Shenzhen University Science and Engineering,2007,24(1):117.
[2]吴舟,张凌雁,赵春晖.基于博弈论的BLAST系统干扰避免算法[J].深圳大学学报理工版,2008,25(3):265.
　WU Zhou,ZHANG Ling-yan,and ZHAO Chun-hui.Distributed interference avoidance algorithm based on game theory in BLAST system[J].Journal of Shenzhen University Science and Engineering,2008,25(1):265.
[3]孙宗岐,刘宣会,陈思源,等.基于注资-有界分红的随机微分投资-再保博弈[J].深圳大学学报理工版,2017,34(4):364.[doi:10.3724/SP.J.1249.2017.04364]
　Sun Zongqi,Liu Xuanhui,Chen Siyuan,et al.Stochastic differential investment-reinsurance games with capital injection-barrier dividend[J].Journal of Shenzhen University Science and Engineering,2017,34(1):364.[doi:10.3724/SP.J.1249.2017.04364]
[4]马江山,李昱莹.基于卷积的自助银行选址分析[J].深圳大学学报理工版,2018,35(1):92.[doi:10.3724/SP.J.1249.2018.01092]
　MA Jiangshan and LI Yuying.Self-help bank location analysis based on convolution[J].Journal of Shenzhen University Science and Engineering,2018,35(1):92.[doi:10.3724/SP.J.1249.2018.01092]
[5]孙宗岐,杨鹏.带投资和障碍分红的破产时刻Laplace变换[J].深圳大学学报理工版,2021,38(2):214.[doi:10.3724/SP.J.1249.2021.02214]
　SUN Zongqi and YANG Peng.The Laplace transform of ruin time with investment and barrier dividend[J].Journal of Shenzhen University Science and Engineering,2021,38(1):214.[doi:10.3724/SP.J.1249.2021.02214]

备注/Memo

备注/Memo:
Received：2017-06-08；Accepted：2017-10-10
Foundation：National Natural Science Foundation of China(11561013,11761023); Ph.D. Programs Foundation of Ministry of Education of China(20115201110002)
Corresponding author：Professor XIANG Shuwen．E-mail: shwxiang@vip.163.com
Citation：HE Jihao，XIANG Shuwen，JIA Wensheng, et al．Information set generalized multi-objective games based on bounded rationality［J］. Journal of Shenzhen University Science and Engineering, 2018, 35(1): 105-109.（in Chinese）
基金项目：国家自然科学基金资助项目（11561013,11761023）; 教育部博士点基金资助项目（20115201110002）
作者简介：何基好(1976—),男,贵州大学数学与统计学院讲师.研究方向:博弈论与非线性分析. E-mail:jhhe1@gzu.edu.cn
引文：何基好,向淑文,贾文生,等.基于有限理性的信息集广义多目标博弈［J］. 深圳大学学报理工版，2018，35(1)：105-109.
更新日期/Last Update: 2017-12-22