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The Core of an Economy Without Ordered Preferences

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Equilibrium Theory in Infinite Dimensional Spaces

Part of the book series: Studies in Economic Theory ((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.

The results of this paper were obtained in 1984. The present version is virtually identical to the Discussion paper No. 214, June 1985, University of Minnesota. The minor changes are due to suggestions made by Charles Holly to whom I am very thankful. It should be noted that Atsumi Kajii has recently obtained cr-core existence results for normal form games without ordered preferences.

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References

  • Aliprantis, C.D. and Burkinshaw, O., Positive Operators, Academic Press, New York.

    Google Scholar 

  • Araujo, A., 1985, “Lack of Pareto Optimal Allocations in Economies with Infinitely Many Commodities: The Need for Impatience,” Econometrica 53, 455–461.

    Article  Google Scholar 

  • Aumann, R. J., 1964, “The Core of a Cooperative Game Without Side Payments,” Trans. Amer. Math. Soc., 539–552.

    Google Scholar 

  • Bewley, T., 1972, “Existence of Equilibria in Economies with Infinitely Many Commodities,” J. Econ. Theory 64, 514–540.

    Article  Google Scholar 

  • Berninghaus, S., 1977, “Individual and Collective Risks in Large Economies,” J. Econ. Theory 15, 279–294.

    Article  Google Scholar 

  • Border, K. C., 1984, “A Core Existence Theorem for Games Without Ordered Preferences,” Econometrica 52, 1537–1542.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Browder, F., 1968, “The Fixed Point Theory of Multivalued Mappings in Topological Vector Spaces,” Math. Ann. 177, 283–301.

    Article  Google Scholar 

  • Debreu, G., 1952, “A Social Equilibrium Existence Theorem,” Proc. Natl. Acad. Sci. USA 38, 886–893.

    Article  Google Scholar 

  • Debreu, G., 1959, Theory of Value, John Wiley and Sons, New York.

    Google Scholar 

  • Fan, K., 1952, “Fixed Point and Minimax Theorems in Locally Convex Topological Linear Spaces,” Proc. Natl. Acad. Sci. USA 38, 131–136.

    Article  Google Scholar 

  • Fan, K., 1962, “A Generalization of Tychonoff’s Fixed Point Theorem,” Math. Ann. 143, 305–310.

    Google Scholar 

  • Fan, K., 1969, “Extensions of Two Fixed Point Theorems of F. E. Browder,” Math. Z. 112, 234–240.

    Article  Google Scholar 

  • Gale, D. and Mas-Colell, A., 1975, “An Equilibrium Existence Theorem for a General Model without Ordered Preferences,” J. Math. Econ. 2, 9–15.

    Article  Google Scholar 

  • Hildenbrand, W., 1974, Core and Equilibrium of a Large Economy, Princeton University Press, Princeton, New Jersey.

    Google Scholar 

  • Ichiichi, T., 1981, Game Theory for Economic Analysis, Academic Press, New York.

    Google Scholar 

  • Ichiichi, T., 1981a, “On the Knaster-Kuratowski-Mazurkiewicz-Shapley Theo-rem,” J. Math. Anal. Appl. 81, 297–299.

    Article  Google Scholar 

  • Ichiichi, T. and Schaffer, S. T., 1983, “The Topological Core of a Game without Side Payments,” Econ. Stud. Q. 34, 1–8.

    Google Scholar 

  • 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 

  • Kajii, A., 1989, “A Generalization of Scarf’s Theorem: An α-Core Existence Theorem without Transitivity,” Harvard University, mimeo.

    Google Scholar 

  • Kelley, J. and Namioka, I., 1963, Linear Topological Spaces, Springer, New York.

    Google Scholar 

  • Kim, T. and Richter, M. K., 1986, “Nontransitive, Nontotal Consumer Theory,” J. Econ. Theory 38, 324–363.

    Article  Google Scholar 

  • McKenzie, L. W., 1981, “The Classical Theorem on Existence of Competitive Equilibrium,” Econometrica 49, 819–841.

    Article  Google Scholar 

  • Mas-Colell, A., 1974, “An Equilibrium Existence Theorem Without Complete or Transitive Preferences,” J. Math. Econ. 1, 237–246.

    Article  Google Scholar 

  • Mas-Colell, A., 1986, “The Price Equilibrium Existence Problem in Topological Vector Lattices,” Econometrica 54, 1039–1054.

    Article  Google Scholar 

  • Scarf, H., 1967, “The Core of an N-Person Game,” Econometrica 35, 50–69.

    Article  Google Scholar 

  • Scarf, H., 1971, “On the Existence of a Cooperative Solution for a General Class of N-Person Games,” J. Econ. Theory 3, 169–181.

    Article  Google Scholar 

  • Schaefer, H. H., 1971, Topological Vector Spaces, Springer-Verlag, Berlin.

    Book  Google Scholar 

  • Schaefer, H. H., 1974, Banach Lattices and Positive Operators, Springer-Verlag, Berlin.

    Book  Google Scholar 

  • Shafer, W. J., 1974, “The Nontransitive Consumer,” Econometrica 42, 913–919.

    Article  Google Scholar 

  • Shafer, W. J. and Sonnenschein, H., 1975, “Equilibrium in Abstract Economies Without Ordered Preferences,” J. Math. Econ. 2, 345–348.

    Article  Google Scholar 

  • 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 

  • 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 

  • Toussaint, S., 1984, “On the Existence of Equilibria in Economies with Infinitely Many Commodities and without Ordered Preferences,” J. Econ. Theory 33, 98–115.

    Article  Google Scholar 

  • Yannelis, N. C. and Prabhakar, N. D., 1983, “Existence of Maximal Elements and Equilibria in Linear Topological Spaces,” J. Math. Econ. 12, 233–245.

    Article  Google Scholar 

  • 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 

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© 1991 Springer-Verlag Berlin Heidelberg

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Yannelis, N.C. (1991). The Core of an Economy Without Ordered Preferences. In: Khan, M.A., Yannelis, N.C. (eds) Equilibrium Theory in Infinite Dimensional Spaces. Studies in Economic Theory, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07071-0_4

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  • DOI: https://doi.org/10.1007/978-3-662-07071-0_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08114-9

  • Online ISBN: 978-3-662-07071-0

  • eBook Packages: Springer Book Archive

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