GENERALIZATIONS OF THE NASH EQUILIBRIUM THEOREM ON GENERALIZED CONVEX SPACES

  • Park, Se-Hie
  • Published : 2001.07.01

Abstract

Generalized forms of the von neumann-Sion type minimax theorem, the Fan-Ma intersection theorem, the Fan-a type analytic alternative, and the Nash-Ma equilibrium theorem hold for generalized convex spaces without having any linear structure.

Keywords

generalized convex(G-convex) space;${\Phi}$-map;$\Gamma$-convex hull;minimax theorem;intersection theorem;analytic alternative;equilibrium theorem

References

  1. Nonlinear Funct. Anal. Appl. v.1 Applications of the Idzik fixed point theorem
  2. Vietnam J. Math. v.27 Ninety years of the Brouwer fixed point theorem
  3. Proc. Sympos. Pure Math., Amer. Math. Soc. v.45 Two-function minimax theorems and variational inequalities for functions on compact and noncompact sets, with some comments on fixed-point theorems S. Simons
  4. Ergeb. Math. Kolloq. v.8 Uber ein okonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes
  5. Proc. Amer. Math. Soc. v.3 A further generalization of the Kakutani fixed point theorem with application to Nash equilibrium points I. L. Glicksberg
  6. J. Austral. Math. Soc. v.53 Fixed point theorems in H-spaces and equilibrium points of abstract economies E. Tarafdar
  7. Pacific J. Math. v.5 Note on non-cooperative games H. Nikaldo;K. Isoda
  8. Math. Ann. v.100 Zur Theorie der Gesellschaftsspiele J. von Neumann
  9. J. Math. Anal. Appl. v.27 On sets with convex sections T. W. Ma
  10. J. Korean Math. Soc. v.31 Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps S. Park
  11. Soochow J. Math v.15 A generalization of KKM principle and its applications S. Y. Chang
  12. J. Comput. Appl. Math. v.113 Acyclic versions of the von Neumann and Nash equilibrium theorems
  13. C. R. Acad. Sci. Paris Ser. I Math. v.295 Une Alternative non lineaire en analyse convexe et applications H. Ben-El-Mechaiekh;P. Deguire;A. Granas(et)
  14. J. Math. Anal. Appl. v.127 Simplical convexity and its applications R. Bielawski
  15. Korean J. Comp. Appl. Math. v.7 Elements of the KKM theory for generalized convex spaces
  16. Int. J. Math. Math. Sci. v.24 Fixed points, intersection theorems, variational inequalities and equilibrium theorems
  17. Colloq. Math. v.71 The Idzik type quasivariational inequalities and non-compact optimization problems S. Park;J. A. Park
  18. Ann. of Math. v.54 Non-cooperative games J. Nash
  19. Josai Math. Monogr. v.1 Minimax theorems and the Nash equilibria on generalized convex spaces
  20. Numer. Funct. Anal. Optim v.20 Continuous selection theorems in generalized convex spaces
  21. Duke Math. J. v.8 A generalization of Brouwer's fixed-point theorem S. Kakutani
  22. J. Korean Math. Soc. v.28 Variational inequalities and extremal principles Sehie Park
  23. Internat. J. Game Theory v.24 Existence theorems of Nash equilibria for non-cooperative N-person games K. K. Tan;J. Yu;X. Z. Yuan
  24. Non-linear Anal. v.39 The Knaster-Kuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications W. A. Kirk;B. Sims;G. X. Z. Yuan
  25. J. Korean Math Soc. v.37 Fixed points of better admissible maps on generalized convex spaces
  26. Non-linear Anal. New topological versions of the Fan-Browder fixed point theorem
  27. C. R. Acad. Sci. Paris Ser. I Math. v.259 Sur un theoreme minimax
  28. Proc. Natl. Acad. Sci. v.38 Fixed point and minimax theorems in locally convex linear spaces K. Fan
  29. Math. Ann. v.163 Applications of a theorem concerning sets with convex sections
  30. Appl. Math. Lett. v.11 no.5 Remarks on a social equilibrium existence theorem of G. Debreu
  31. Pacific J. Math v.8 On general minimax theorems M. Sion
  32. Lect. Notes in Nonlinear Anal v.2 Leray-Schauder type theorems and equilibrium existance theorems A. Idzik;S. Park
  33. Bull. Korean Math. Soc. v.27 On generalized extremal principles S. Park;S. K. Kim