局部凸<em>H-</em>空间内的约束多目标对策

丁协平

局部凸H-空间内的约束多目标对策

丁协平

四川师范大学数学与软件科学学院, 成都, 610066

基金项目: 国家自然科学基金资助项目(19871059);四川省教育厅重点科研资助项目([2000]25)

详细信息

作者简介:
丁协平(1938- ),男,四川自贡人,教授(E-mail:dingxip@sicnu.edu.cn)

中图分类号: O225;O177.92
计量
- 文章访问数: 2466
- HTML全文浏览量: 154
- PDF下载量: 677
- 被引次数: 0
出版历程
- 收稿日期: 2001-07-06
- 修回日期: 2003-03-07
- 刊出日期: 2003-05-15

Constrained Multiobjective Games in Locally Convex H-Spaces

DING Xie-ping

Department of Mathematics, Sichuan Normal University, Chengdu 610066, P.R.China

摘要

摘要: 在没有线性结构的非紧局部凸H-空间内引入和研究了一类新的约束多目标对策。由应用对上半连续零调值映象的Fan-Glicksbery型不动点定理和极大定理,在非紧局部凸H-空间内对约束多目标对策的加权Nash-平衡和Pareto平衡证明了几个平衡存在定理。这些定理改进,统一和推广了最近文献内多目标对策的相应结果。
- 约束多目标对策 /
- 极大定理 /
- 不动点 /
- 加权Nash-平衡 /
- Pareto平衡 /
- 局部凸H-空间
Abstract: A new class of constrained multiobjective games with infinite players in noncompact locally convex H-spaces without linear structure are introduced and studied.By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem,several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces.These theorems improve,unify and generalize the corresponding results of the multiobjective games in recent literatures.
- constrained multiobjective game /
- maximum theorem /
- fixed point /
- weighted Nash-equilibria /
- Pareto equilibria /
- locally convex H-space

HTML全文

参考文献(30)

[1]	Nash J F.Equilibrium point in n-person games[J].Proc Nat Acad Sci USA,1950,36(1):48-49.
[2]	Nash J F.Noncooperative games[J].Ann Math,1951,54(2):286-295.
[3]	Szidarovszky F M E,Gershon M E,Duckstein L.Techniques for Multiobjective Decision Marking in System Management[M].Amsterdam Holland: Elsevier,1986.
[4]	Zeleny M.Game with multiple payoffs[J].Internat J Game Theory,1976,4(2):179-191.
[5]	Bergstresser K,Yu P L.Domination structures and multicriteria problem in N-person games[J].Theory and Decision,1977,8(1):5-47.
[6]	Brom P E M,Tijs S H,Van Den Aarssen J C M.Pareto equilibrium in multiobjective games[J].Methods of Operations Research,1990,60(2):303-312.
[7]	Yu P L.Second-order game problems:Decision dynamics in gaming phenomena[J].J Optim Theory Appl,1979,27(1):147-166.
[8]	Chose D,Prasad U R.Solution concepts in two-person multicriteria games[J].J Optim Theory Appl,1989,63(1):167-189.
[9]	Wang S Y.An existence theorem of a Pareto equilibrium[J].Appl Math Lett,1991,4(1):61-63.
[10]	Wang S Y.Existence of a Pareto equilibrium[J].J Optim Theory Appl,1993,79(2):373-384.
[11]	丁协平.没有紧性,连续性和凹性的多准则对策的帕雷多平衡[J].应用数学和力学,1996,17(9):801-808.
[12]	DING Xie-ping.Existence of pareto equilibria for constrained multiobjective games in H-space[J].Comput Math Appl,2000,39(9):125-134.
[13]	DING Xie-ping.Constrained multiobjective games in general topological space[J].Comput Math Appl,2000,39(3/14):23-30.
[14]	YUAN Xian-zhi,Tarafdar E.Non-compact Pareto equilibria for multiobjective games[J].J Math Anal Appl,1996,204(1):156-163.
[15]	YU Jiao,YUAN Xian-zhi.The study of pareto equilibria for multiobjective games by fixed point and Ky Fan minimax inequality methods[J].Comput Math Appl,1998,35(9):17-24.
[16]	WU Xian.Approximate selection theorems in H-spaces with application[J].J Math Anal Appl,1999,231(1):118-132.
[17]	TIAN Guo-qiang,ZHOU Jian-xin.Transfer continuities,generalizations of the Weierstrass and maximum theorems:a full characterization[J].J Math Economics,1995,24(2):281-303.
[18]	Bardaro C,Ceppitelli L.Some further generalizations of Knaster-Kuratowski-Mazurkiewicz theorem and minimax inequalities[J].J Math Anal Appl,1988,132(3):484-490.
[19]	Bardaro C,Ceppitelli L.Applications of generalized Knaste-Kuratowskir-Mazurkiewicz theorem to variational inequalities[J].J Math Anal Appl,1989,137(1):46-58.
[20]	Horvath C.Points fixes et coincidences dans les espaces topologiques compacts contractiles[J].C R Acad Sci Paris,1984,299:519-521.
[21]	Horvath C.Some results on multivalued mappings and inequalities without convexity[A].In:Lin B L,Simons S Eds.Nonlinear and Convex Analysis:Lecture Notes in Pure and Applied Mathematics[C].Vol 107,New York:Dekker,1987,99-106.
[22]	Aubin J P.Mathematical Methods of Game and Economic Theory[M].Amsterdam: North-Holland,1982.
[23]	Aubin J P,Ekeland I.Applied Nonlinear Analysis[M].New York:Wiley,1984.
[24]	丁协平.拟变分不等式和社会平衡[J].应用数学和力学,1991,12(7):599-606.
[25]	DING Xie-ping.Generalized quasi-variational inequalities,optimization and equilibrium problems[J].J Sichuan Normal Univ,1998,21(1):22-27.
[26]	TIAN Guo-qiang.Generalizations of the FKKM theorem and the Fan minimax inequality with applications to maximal elements,price equilibrium and complementarity[J].J Math Anal Appl,1992,170(2):457-471.
[27]	YUAN Xian-zhi,Isac G,Tan K K,et al.The study of minimax inequalities,abstract economics and applications to variational inequalities and Nash equilibria[J].Acta Appl Math,1998,54(1):135-166.
[28]	Tarafdar E.A fixed point theorem in H-space and related results[J].Bull Austral Math Soc,1990,42(1):133-140.
[29]	Massey W S.Singular Homology Theory[M].New York:Springer-Verlag,1980.
[30]	Fan Ky.Fixed points and minmax theorems in locally convex spaces[J].Proc Nat Acad Sci U S A,1952,38:121-126.