QUASI-EQUILIBRIUM PROBLEMS AND CONSTRAINED MULTIOBJECTIVE GAMES IN GENERALIZED CONVEX SPACE

Abstract

Abstract: A class of quasi-equilibrium problems and a class of constrained multiobjective games were introduced and studied in generalized convex spaces without linear structure. First, two existence theorems of solutions for quasi-equilibrium problems are proved in noncompact generalized convex spaces. Then, as applications of the quasi-equilibrium existence theorem, several existence theorems of weighted Nash-equilibria and Pareto equilibria for the constrained multiobjective games are established in noncompact generalized convex spaces. These theorems improve, unify and generalize the corresponding results of the multiobjective games in recent literatures.

Key words: quasi-equilibrium problem, constrained multiobjective game, weighted Nash-equilibria, Pareto equilibria, generalized convex space

2010 MSC Number:

O225

DING Xie-ping . QUASI-EQUILIBRIUM PROBLEMS AND CONSTRAINED MULTIOBJECTIVE GAMES IN GENERALIZED CONVEX SPACE. Applied Mathematics and Mechanics (English Edition), 2001, 22(2): 160-172.

TrendMD

References

[1] DING Xie-ping.Quasi-equilibrium problems with applications to infinite optimization and constrained games in general topological spaces[J].Appl Math Lett,2000,12(3):21-26.
[2] Noor M A,Oettli W.On general nonlinear complementarity problems and quasiequilibria[J].Le Mathematiche,1994,49:313-331.
[3] Cubiotti P.Existence of solutions for lower semicontinuous quasi-equilibrium problems[J].Compu Math Appl,1995,30(12):11-22.
[4] DING Xie-ping.Existence of solutions for equilibrium problems[J].J Sichuan Normal Univ,1998,21(6):603-608.
[5] DING Xie-ping.Quasi-equilibrium problems in noncompact generalized convex spaces[J].Applied Mathematics and Mechanics(English Edition),2000,21(6):637-644.
[6] Lin L J,Park S.On some generalized quasi-equilibrium problems[J].J Math Anal Appl,1998,224(1):167-191.
[7] Nash J F.Equilibrium point in n-person games[J].Proc Nat Acad Sci USA,1950,36(1):48-49.
[8] Nash J F.Noncooperative games[J].Ann Math,1951,54:286-295.
[9] Szidarovszky F,Gershon M E,Duckstein L.Techniques for Multiobjective Decision Marking in System Management[M].Amsterdam Holland:Elsevier,1986.
[10] Zeleny M.Game with multiple payoffs[J].International J Game Theory,1976,4(1):179-191.
[11] Bergstresser K,Yu P L.Domination structures and multicriteria problem in N-person games[J].Theory and Decision,1977,8(1):5-47.
[12] 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(2):303-312.
[13] Yu P L.Second-order game problems:Decision dynamics in gaming phenomena[J].J Optim Theory Appl,1979,27(1):147-166.
[14] Chose D,Prasad U R.Solution concepts in two-person multicriteria games[J].J Optim Theory Appl,1989,63(1):167-189.
[15] Wang S Y.An existence theorem of a Pareto equilibrium[J].Appl Math Lett,1991,4(3):61-63.
[16] Wang S Y.Existence of a Pareto equilibrium[J].J Optim Theory Appl,1993,79(2):373-384.
[17] DING Xie-ping.Pareto equilibria of multicriteria games without compactness,continuity and concavity[J].Applied Mathematics and Mechanics(English Edition),1996,17(9):847-854.
[18] Yuan X Z,Tarafdar E.Non-compact Pareto equilibria for multiobjective games[J].J Math Anal Appl,1996,204(1):156-163.
[19] Yu J,Yuan X Z.The study of Pareto equilibria for multiobjective games by fixed point and Ky Fan minimax inequality methods[J].Compu Math Appl,1998,35(9):17-24.
[20] DING Xie-ping.Existence of Pareto equilibria for constrained multiobjective games in H-spaces[J].Compu Math Appl,2000,39(9):115-123.
[21] Park S,Kim H.Coincidence theorems for admissible multifunctions on generalized convex spaces[J].J Math Anal Appl,1996,197(1):173-187.
[22] Park S,Kim H.Foundation of the KKM theory on generalized convex spaces[J].J Math Anal Appl,1997,209(3):551-571.
[23] Tan K K.G-KKM theorem,minimax inequalities and saddle points[J].Nonlinear Anal,1997,30(7):4151-4160.
[24] Aubin J P.Mathematical Methods of Game and Economic Theory[M].Amsterdam:North-Holland,1982.
[25] Aubin J P,Ekeland I.Applied Nonlinear Analysis[M].New York:Wiley,1984.
[26] DING Xie-ping.Quasi-variational inequalities and social equilibrium[J].Applied Mathematics and Mechanics(English Edition),1991,12(7):639-646.
[27] DING Xie-ping.Generalized quasi-variational inequalities,optimization and equilibrium problems[J].J Sichuan Normal Univ,1998,21(1):22-27.
[28] Tian G.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.
[29] Yuan X Z,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.
[30] DING Xie-ping.Generalized variational inequalities and equilibrium problems in generalized convex spaces[J].Compu Math Appl,1999,38(7-8):189-197.
[31] DING Xie-ping.Fixed points,minimax inequalities and equilibria of noncompact abstract economies[J].Taiwanese J Math,1998,2(1):25-55.
[32] Zhou J X,Chen G.Diagonally convexity conditions for problems in convex analysis and quasi-variational inequalities[J].J Math Anal Appl,1988,132(2):213-225.