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Quasi-equilibrium problems and constrained multiobjective games in generalized convex space

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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.

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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.

    Google Scholar 

  2. Noor M A, Oettli W. On general nonlinear complementarity problems and quasiequilibria[J].Le Mathematiche, 1994,49: 313–331.

    MATH  MathSciNet  Google Scholar 

  3. Cubiotti P. Existence of solutions for lower semicontinuous quasi-equilibrium problems[J].Compu Math Appl, 1995,30(12): 11–22.

    Article  MATH  MathSciNet  Google Scholar 

  4. DING Xie-ping. Existence of solutions for equilibrium problems[J].J Sichuan Normal Univ, 1998,21(6): 603–608.

    Google Scholar 

  5. DING Xie-ping. Quasi-equilibrium problems in noncompact generalized convex spaces[J].Applied Mathematics and Mechanics (English Edition), 2000,21(6): 637–644.

    MathSciNet  Google Scholar 

  6. Lin L J, Park S. On some generalized quasi-equilibrium problems[J].J Math Anal Appl, 1998,224(1): 167–191.

    Article  MATH  MathSciNet  Google Scholar 

  7. Nash J F. Equilibrium point inn-person games[J].Proc Nat Acad Sci USA, 1950,36(1): 48–49.

    Article  MATH  MathSciNet  Google Scholar 

  8. Nash J F. Noncooperative games[J].Ann Math, 1951,54: 286–295.

    Article  MATH  MathSciNet  Google Scholar 

  9. Szidarovszky F, Gershon M E, Duckstein L.Techniques for Multiobjective Decision Marking in System Management[M]. Amsterdam Holland: Elsevier, 1986.

    Google Scholar 

  10. Zeleny M. Game with multiple payoffs[J].International J Game Theory, 1976,4(1): 179–191.

    MathSciNet  Google Scholar 

  11. Bergstresser K, Yu P L. Domination structures and multicriteria problem inN-person games[J].Theory and Decision, 1977,8(1): 5–47.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    MATH  Google Scholar 

  13. Yu P L. Second-order game problems: Decision dynamics in gaming phenomena[J].J Optim Theory Appl, 1979,27(1): 147–166.

    Article  MATH  MathSciNet  Google Scholar 

  14. Chose D, Prasad U R. Solution concepts in two-person multicriteria games[J].J Optim Theory Appl, 1989,63(1): 167–189.

    MathSciNet  Google Scholar 

  15. Wang S Y. An existence theorem of a Pareto equilibrium[J].Appl Math Lett, 1991,4(3): 61–63.

    Article  MATH  MathSciNet  Google Scholar 

  16. Wang S Y. Existence of a Pareto equilibrium[J].J Optim Theory Appl, 1993,79(2): 373–384.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    MathSciNet  Google Scholar 

  18. Yuan X Z, Tarafdar E. Non-compact Pareto equilibria for multiobjective games[J].J Math Anal Appl, 1996,204(1): 156–163.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  20. DING Xie-ping. Existence of Pareto equilibria for constrained multiobjective games inH-spaces [J].Compu Math Appl, 2000,39(9): 115–123.

    Article  Google Scholar 

  21. Park S, Kim H. Coincidence theorems for admissible multifunctions on generalized convex spaces [J].J Math Anal Appl, 1996,197(1): 173–187.

    Article  MATH  MathSciNet  Google Scholar 

  22. Park S, Kim H. Foundation of the KKM theory on generalized convex spaces[J].J Math Anal Appl, 1997,209(3): 551–571.

    Article  MATH  MathSciNet  Google Scholar 

  23. Tan K K.G-KKM theorem, minimax inequalities and saddle points[J].Nonlinear Anal, 1997,30 (7): 4151–4160.

    Article  MATH  MathSciNet  Google Scholar 

  24. Aubin J P.Mathematical Methods of Game and Economic Theory [M]. Amsterdam: North-Holland, 1982.

    Google Scholar 

  25. Aubin J P, Ekeland I.Applied Nonlinear Analysis[M]. New York: Wiley, 1984.

    Google Scholar 

  26. DING Xie-ping. Quasi-variational inequalities and social equilibrium[J].Applied Mathematics and Mechanics (English Edition), 1991,12(7): 639–646.

    Google Scholar 

  27. DING Xie-ping. Generalized quasi-variational inequalities, optimization and equilibrium problems [J].J Sichuan Normal Univ, 1998,21(1): 22–27.

    Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  30. DING Xie-ping. Generalized variational inequalities and equilibrium problems in generalized convex spaces[J].Compu Math Appl, 1999,38(7–8): 189–197.

    Google Scholar 

  31. DING Xie-ping. Fixed points, minimax inequalities and equilibria of noncompact abstract economies[J].Taiwanese J Math, 1998,2(1): 25–55.

    MathSciNet  Google Scholar 

  32. Zhou J X, Chen G. Diagonally convexity conditions for problems in convex analysis and quasivariational inequalities[J].J Math Anal Appl, 1988,132(2): 213–225.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

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

    Ding Xie-ping

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Paper from DING Xie-ping, Member of Editorial Committee, AMM

Foundation item: the National Natural Science Foundation of China (19871059); the NSF of Education Department of Sichuan Province

Biography: DIGN Xie-ping (1938-), Professor

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Xie-ping, D. Quasi-equilibrium problems and constrained multiobjective games in generalized convex space. Appl Math Mech 22, 160–172 (2001). https://doi.org/10.1007/BF02437881

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  • DOI: https://doi.org/10.1007/BF02437881

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