The Core of an Economy Without Ordered Preferences

  • Nicholas C. Yannelis
Part of the Studies in Economic Theory book series (ECON.THEORY, volume 1)

Abstract

Core existence results are proved for exchange economies with an infinite dimensional commodity space. In particular, the commodity space may be any ordered Hausdorff linear topological space, and agents’ preferences need not be transitive, complete, monotone or convex; preferences may even be interdependent. Under these assumptions a quasi equilibrium may not exist.

Keywords

Hull Topo Nite Allo 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aliprantis, C.D. and Burkinshaw, O., Positive Operators, Academic Press, New York.Google Scholar
  2. Araujo, A., 1985, “Lack of Pareto Optimal Allocations in Economies with Infinitely Many Commodities: The Need for Impatience,” Econometrica 53, 455–461.CrossRefGoogle Scholar
  3. Aumann, R. J., 1964, “The Core of a Cooperative Game Without Side Payments,” Trans. Amer. Math. Soc., 539–552.Google Scholar
  4. Bewley, T., 1972, “Existence of Equilibria in Economies with Infinitely Many Commodities,” J. Econ. Theory 64, 514–540.CrossRefGoogle Scholar
  5. Berninghaus, S., 1977, “Individual and Collective Risks in Large Economies,” J. Econ. Theory 15, 279–294.CrossRefGoogle Scholar
  6. Border, K. C., 1984, “A Core Existence Theorem for Games Without Ordered Preferences,” Econometrica 52, 1537–1542.CrossRefGoogle Scholar
  7. Borglin, A. and Keiding, H., 1976, “The Existence of Equilibrium Actions and of Equilibrium: A Note on the ‘New’ Existence Theorems,” J. Math. Econ. 3, 313–316.CrossRefGoogle Scholar
  8. Browder, F., 1968, “The Fixed Point Theory of Multivalued Mappings in Topological Vector Spaces,” Math. Ann. 177, 283–301.CrossRefGoogle Scholar
  9. Debreu, G., 1952, “A Social Equilibrium Existence Theorem,” Proc. Natl. Acad. Sci. USA 38, 886–893.CrossRefGoogle Scholar
  10. Debreu, G., 1959, Theory of Value, John Wiley and Sons, New York.Google Scholar
  11. Fan, K., 1952, “Fixed Point and Minimax Theorems in Locally Convex Topological Linear Spaces,” Proc. Natl. Acad. Sci. USA 38, 131–136.CrossRefGoogle Scholar
  12. Fan, K., 1962, “A Generalization of Tychonoff’s Fixed Point Theorem,” Math. Ann. 143, 305–310.Google Scholar
  13. Fan, K., 1969, “Extensions of Two Fixed Point Theorems of F. E. Browder,” Math. Z. 112, 234–240.CrossRefGoogle Scholar
  14. Gale, D. and Mas-Colell, A., 1975, “An Equilibrium Existence Theorem for a General Model without Ordered Preferences,” J. Math. Econ. 2, 9–15.CrossRefGoogle Scholar
  15. Hildenbrand, W., 1974, Core and Equilibrium of a Large Economy, Princeton University Press, Princeton, New Jersey.Google Scholar
  16. Ichiichi, T., 1981, Game Theory for Economic Analysis, Academic Press, New York.Google Scholar
  17. Ichiichi, T., 1981a, “On the Knaster-Kuratowski-Mazurkiewicz-Shapley Theo-rem,” J. Math. Anal. Appl. 81, 297–299.CrossRefGoogle Scholar
  18. Ichiichi, T. and Schaffer, S. T., 1983, “The Topological Core of a Game without Side Payments,” Econ. Stud. Q. 34, 1–8.Google Scholar
  19. Jones, L. E., 1986, “Special Problems Arising in the Study of Economies with Infinitely Many Commodities,” in Models of Economic Dynamics, H. F. Sonnenschein, ed., Springer-Verlag Lecture Notes in Economics and Mathematical Systems #264, Berlin-New York, 184–205.Google Scholar
  20. Kajii, A., 1989, “A Generalization of Scarf’s Theorem: An α-Core Existence Theorem without Transitivity,” Harvard University, mimeo.Google Scholar
  21. Kelley, J. and Namioka, I., 1963, Linear Topological Spaces, Springer, New York.Google Scholar
  22. Kim, T. and Richter, M. K., 1986, “Nontransitive, Nontotal Consumer Theory,” J. Econ. Theory 38, 324–363.CrossRefGoogle Scholar
  23. McKenzie, L. W., 1981, “The Classical Theorem on Existence of Competitive Equilibrium,” Econometrica 49, 819–841.CrossRefGoogle Scholar
  24. Mas-Colell, A., 1974, “An Equilibrium Existence Theorem Without Complete or Transitive Preferences,” J. Math. Econ. 1, 237–246.CrossRefGoogle Scholar
  25. Mas-Colell, A., 1986, “The Price Equilibrium Existence Problem in Topological Vector Lattices,” Econometrica 54, 1039–1054.CrossRefGoogle Scholar
  26. Scarf, H., 1967, “The Core of an N-Person Game,” Econometrica 35, 50–69.CrossRefGoogle Scholar
  27. Scarf, H., 1971, “On the Existence of a Cooperative Solution for a General Class of N-Person Games,” J. Econ. Theory 3, 169–181.CrossRefGoogle Scholar
  28. Schaefer, H. H., 1971, Topological Vector Spaces, Springer-Verlag, Berlin.CrossRefGoogle Scholar
  29. Schaefer, H. H., 1974, Banach Lattices and Positive Operators, Springer-Verlag, Berlin.CrossRefGoogle Scholar
  30. Shafer, W. J., 1974, “The Nontransitive Consumer,” Econometrica 42, 913–919.CrossRefGoogle Scholar
  31. Shafer, W. J. and Sonnenschein, H., 1975, “Equilibrium in Abstract Economies Without Ordered Preferences,” J. Math. Econ. 2, 345–348.CrossRefGoogle Scholar
  32. Shapley, L. S., 1973, “On Balanced Games without Side Payments,” in Mathematical Programming, T. C. Hu and S. M. Robinson, eds., Academic Press, New York.Google Scholar
  33. Sonnenschein, H., 1971, “Demand Theory without Transitive Preferences with Applications to the Theory of Competitive Equilibrium,” in Preferences, Utility, and Demand, J. Chipman, L. Hurwicz, M. K. Richter and H. Sonnenschein, eds., Harcourt Brace Jovanovich, New York.Google Scholar
  34. Toussaint, S., 1984, “On the Existence of Equilibria in Economies with Infinitely Many Commodities and without Ordered Preferences,” J. Econ. Theory 33, 98–115.CrossRefGoogle Scholar
  35. Yannelis, N. C. and Prabhakar, N. D., 1983, “Existence of Maximal Elements and Equilibria in Linear Topological Spaces,” J. Math. Econ. 12, 233–245.CrossRefGoogle Scholar
  36. Yannelis, N. C. and Zame, W. R., 1984, “Equilibria in Banach Lattices without Ordered Preferences,” Preprint no 71, Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, MN, (a shortened version appeared in the J. Math. Econ. 15, 1986, 85–110 ).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Nicholas C. Yannelis

There are no affiliations available

Personalised recommendations