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Core Theory with Strongly Convex Preferences

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  • Robert M. Anderson

    (Princeton University)

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    Abstract

    We consider economies with preferences drawn from a very general class of strongly convex preferences, closely related to the class of convex (but intransitive and incomplete) preferences for which Mas-Colell proved the existence of competitive equilibria [13]. We prove a strong core limit theorem for sequences of such economies with a mild assumption on endowments (the largest endowment is small compared to the total endowment) and a uniform convexity condition. The results extend corresponding results in Hildenbrand's book [8]. The proof, which is based on our earlier result for economies with more general preferences [2], is elementary.

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    File URL: http://cowles.econ.yale.edu/P/cd/d05b/d0578.pdf
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    Bibliographic Info

    Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 578.

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    Length: 18 pages
    Date of creation: Jan 1981
    Date of revision:
    Handle: RePEc:cwl:cwldpp:578

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    Web page: http://cowles.econ.yale.edu/
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    Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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    References

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    1. DEBREU, Gérard, . "Smooth preferences," CORE Discussion Papers RP -132, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Brown, Donald J. & Robinson, Abraham, 1974. "The cores of large standard exchange economies," Journal of Economic Theory, Elsevier, vol. 9(3), pages 245-254, November.
    3. Dierker, Egbert, 1975. "Gains and losses at core allocations," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 119-128.
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    Cited by:
    1. Alejandro Manelli, 1990. "Core Convergence Without Monotone Preferences or Free Disposal," Discussion Papers 891, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer, vol. 19(1), pages 113-185, March.
    3. Anderson, Robert M., 2010. "Core allocations and small income transfers," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 373-381, July.
    4. Hara, C., 2004. "Existence of Equilibria and Core Convergence in Economies with Bads," Cambridge Working Papers in Economics 0413, Faculty of Economics, University of Cambridge.
    5. Hervés-Beloso, Carlos & Moreno-García, Emma, 2009. "Walrasian analysis via two-player games," Games and Economic Behavior, Elsevier, vol. 65(1), pages 220-233, January.

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