COINCIDENCE THEOREMS ON A PRODUCT OF GENERALIZED CONVEX SPACES AND APPLICATIONS TO EQUILIBRIA

  • Park, Se-Hie (Department of Mathematics Seoul National University) ;
  • Kim, Hoon-Joo (Department of Computer Science Daebul University)
  • Published : 1999.07.01

Abstract

In this paper, we give a Peleg type KKM theorem on G-convex spaces and using this, we obtain a coincidence theorem. First, these results are applied to a whole intersection property, a section property, and an analytic alternative for multimaps. Secondly, these are used to proved existence theorems of equilibrium points in qualitative games with preference correspondences and in n-person games with constraint and preference correspondences for non-paracompact wetting of commodity spaces.

Keywords

G-convex space;$\Gamma$-convex set;G-KKM;abstract economy;correspondence;n-person game;equilibrium;qualitative game;$\tau$-quasiconcave

References

  1. Fixed Point Theory and Applications Fixed point theorems and equilibria on noncompact generalized games X.P. Ding;E. Tarafdar;K.-K. Tan(ed.)
  2. Proc. Internat. Conf. on Math. Anal. Appl.(Chinju, 1998) v.1-A New subclasses of generalized convex spaces S. Park
  3. Proc. Coll. Natur. Sci. Seoul Nat. U. v.18 Admissible classes of multifunctions on generalized convex spaces S. Park;H. Kim
  4. J. Math. Anal. Appl. v.209 Foundations of the KKM Theory on generalized convex spaces S. Park
  5. J. Math. Anal. Appl. v.186 Fixed point theorems with an application in generalized games Y. Huang
  6. J. Math. Econom. v.12 Exstence of maximal elements and equilibria in linear topological spaces N.C. Yannelis;N.D. Prabhakar
  7. J. Austral Math. Soc. v.53 no.A Fixed point theorems in H-spaces and equilibrium points of abstract economies E. Tarafdar
  8. J. Math. Anal. Appl. v.177 On equilibria of noncompact generalized games X.P. Ding;K.K. Tan
  9. Ind. J. Pure Appl. Math. v.29 Generalizations of the KKM type theorems on generalized convex spaces S. Park
  10. Nonlinear Analysis v.TMA 24 Some new minimax inequalities and applications to existence of equilibria in H-spaces K.K. Tan;J. Yu;X.Z. Yuan
  11. Equilibrium and Disequilibrium in Economic Theory On the role of complete, transitive preferences in equilibrium theory G. Schwodiauer(ed.)
  12. Ann. Fac. Sci. Toulouse v.2 Extension and selection theorems in topological spaces with a generalized convexity structure C.D. Horvath
  13. J. Math. Anal. Appl. v.132 Some further generalizations of knaster-Kuratowski-Mazurkiewicz theorem and minimax inequalities C. Bardaro;R. Cellitelli
  14. J. Math. Econom. v.3 Existence of equilibrium action and of equilibrium: A note on the 'new' existence theorems A. Borglin;H. Keiding
  15. J. Math. Anal. Appl. v.164 KKM principle, fixed points and Nash equilibria M. Lassonde;C. Schenkel
  16. Fund. Math. v.14 Ein Beweis des Fixpunktsatzes fur n-dimensionals Simplexe B. Knaster;K. Kuratowski;S. Mazurkiewicz
  17. J. Math. Anal. Appl. v.156 Contractibility and generalized convexity C.D. Horvath
  18. J. Math. Anal. Appl. v.197 Conicidence theorems of admissible maps on generalized convex spaces S. Park
  19. Canad. J. Math. v.19 Equilibrium points for open acyclic relations B, Peleg
  20. Bull. Austral. Math. Soc. v.47 A minimax inequality with applications to existence of equilibrium points K.K. Tan;X.Z. Yuan
  21. J. Math. Anal. Appl. v.222 Abstract convexity and fixed points H. Ben-El-Mechaiekh;S. Chebbi;M. Florenzano;J.V. Llinares
  22. Fixed Point Theory and Applications Some coincidence theorems on acyclic multifunctions and applications to KKM theory S. Park
  23. Top. Meth. Nonlin. Anal. v.2 A generalization of Fan-Browder's fixed point theorem and its applications E. Marchi;J.E. Martinez-Legaz
  24. J. Math. Anal. Appl. v.97 On the use of KKM multifunctions in fixed point theory and related topics M. Lassonde
  25. J. Math. Anal. Appl. v.179 Section theorems on H-spaces with applications S.S. Chang;L. Yang