DING Xie-ping, Lee Chin-san, YAO Jen-chih. Generalized Constrained Multiobjective Games in Locally FC-Uniform Spaces[J]. Applied Mathematics and Mechanics, 2008, 29(3): 272-280.
Citation: DING Xie-ping, Lee Chin-san, YAO Jen-chih. Generalized Constrained Multiobjective Games in Locally FC-Uniform Spaces[J]. Applied Mathematics and Mechanics, 2008, 29(3): 272-280.

Generalized Constrained Multiobjective Games in Locally FC-Uniform Spaces

  • Received Date: 2007-01-06
  • Rev Recd Date: 2008-01-16
  • Publish Date: 2008-03-15
  • A new class of generalized constrained multiobjective games is introduced and studied in locally FC-uniform spaces without convexity structure where the number of players may be finite or infinite and all payoff functions get their values in an infinite-dimensional space. By using a Himmelberg type fixed point theorem in locally FC-uniform spaces, some existence theorems of weak Pareto equilibria for the generalized constrained multiobjective games are established in locally FC-uniform spaces, which improve, unify and generalize the corresponding results in recent literatures.
  • loading
  • [1]
    Szidarovszky F,Gershon M E,Duckstein L.Techniques for Multiobjective Decision Marking in System Management[M].Amsterdam, Holland:Elsevier,1986.
    Zeleny M.Game with multiple payoffs[J].International J Game Theory,1976,4(1):179-191.
    Bergstresser K, Yu P L.Domination structures and multicriteria problem in N-person games[J].Theory and Decision,1977,8(1):5-47. doi: 10.1007/BF00133085
    Borm P E M, Tijs S H, Van Den Aarssen J C M. Pareto equilibrium in multiobjective games[J].Methods of Operations Research,1990,60(1):303-312.
    Yu P L.Second-order game problems: Decision dynamics in gaming phenomena[J].J Optim Theory Appl,1979,27(1):147-166. doi: 10.1007/BF00933332
    Chose D, Prasad U R. Solution concepts in two-person multicriteria games[J].J Optim Theory Appl,1989,63(1):167-189. doi: 10.1007/BF00939572
    Wang S Y. An existence theorem of a Parteo equilibrium[J].Appl Math Lett,1991,4(1):61-63.
    Wang S Y.Existence of a Parteo equilibrium[J].J Optim Theory Appl,1993,79(2):373-384. doi: 10.1007/BF00940586
    Wang S Y, Li Z. Pareto equilibria in multicriteria metagames[J].Top,1995,3(2):247-263. doi: 10.1007/BF02568588
    DING Xie-ping.Parteo equilibria of multicriteria games without compactness, continuity and concavity[J].Appl Math Mech,1996,17(9):847-854. doi: 10.1007/BF00127184
    Yuan X Z, Tarafdar E.Non-compact Pareto equilibria for multiobjective games[J].J Math Anal Appl,1996,204(1):156-163. doi: 10.1006/jmaa.1996.0429
    Yu J, Yuan X Z.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.
    DING Xie-ping. Constrained multiobjective games in general topological spaces[J].Comput Math Appl,2000,39(3/4):23-30.
    DING Xie-ping.Existence of Pareto equilibria for constrained multiobjective games in H-spaces[J].Comput Math Appl,2000,39(9):125-134.
    DIGN Xie-ping, Park J Y, Jung I H. Pareto equilibria for constrained multiobjective games in locally L-convex spaces[J].Comput Math Appl,2003,46(10/11):1589-1599. doi: 10.1016/S0898-1221(03)90194-5
    Yu H. Weak Pareto equilibria for multiobjective constrained games[J].Appl Math Lett,2003,16(5):773-776. doi: 10.1016/S0893-9659(03)00081-8
    Lin Z, Yu J.The existence of solutions for the system of generalized vector quasi-equilibrium problems[J].Appl Math Lett,2005,18(4):415-422. doi: 10.1016/j.aml.2004.07.023
    Lin L J, Cheng S F.Nash-type equilibrium theorems and competitive Nash-type equilibrium theorems[J].Comput Math Appl,2002,44(10/11):1369-1378. doi: 10.1016/S0898-1221(02)00263-8
    DING Xie-ping.Weak Pareto equilibria for generalized constrained multiobjective games in locally FC-spaces[J].Nonlinear Anal,2006,65(3):538-545. doi: 10.1016/j.na.2005.09.029
    DING Xie-ping.Collectively fixed point theorem in product locally FC-uniform spaces and applications[J].Nonlinear Anal,2007,66(11):2604-2617. doi: 10.1016/j.na.2006.03.043
    Luc D T.Theory of Vector Optimization[M].Vol.319. Lecture Notes in Economics and Mathematical Systems.Berlin:Springer-Verlag,1989.
    Lin L J, Yu Z T. On some equilibrium problems for multimaps[J]. J Comput Appl Math, 2001, 129(1/2):171-183. doi: 10.1016/S0377-0427(00)00548-3
    DING Xie-ping.Maximal element theorems in product FC-spaces and generalized games[J].J Math Anal Appl,2005,305(1):29-42. doi: 10.1016/j.jmaa.2004.10.060
    Kelly J L.General Topology[M].Princeton,NJ:Van Nostrand, 1955.
    Kthe G.Topological Vector Spaces Ⅰ[M].New York,Berlin:Springer-Verlag,1983,30.
    Horvath C. Contractibility and general convexity[J].J Math Anal Appl,1991,156(2):341-357. doi: 10.1016/0022-247X(91)90402-L
    Tarafdar E. Fixed point theorems in locally H-convex uniform spaces[J].Nonlinear Anal,1997,29(9):971-978. doi: 10.1016/S0362-546X(96)00174-5
    Park S.Fixed point theorems in locally G-convex spaces[J].Nonlinear Anal,2002,48(6):869-879. doi: 10.1016/S0362-546X(00)00220-0
    DING Xie-ping.System of generalized vector quasi-equilibrium problems in locally FC-spaces[J].Acta Math Sinica,2006,22(5):1528-1538.
    DING Xie-ping,Liou Y C, Yao J C.Generalized R-KKM type theorems in topological spaces with applications[J].Appl Math Lett,2005,18(12):1345-1350. doi: 10.1016/j.aml.2005.02.022
    DING Xie-ping.Continuous selection, collectively fixed points and system of coincidence theorems in product topological spaces[J].Acta Math Sinica,2006,22(6):1629-1638. doi: 10.1007/s10114-005-0831-y
    Aubin J P, Ekeland I.Applied Nonlinear Analysis[M].New York:Wiley,1984.
    Fan Ky. Fixed points and minimax theorems in locally convex spaces[J]. Proc Nat Acad Sci USA,1952,38(1):121-126. doi: 10.1073/pnas.38.2.121
  • 加载中


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2439) PDF downloads(787) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint