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Core Theory with Strongly Convex Preferences

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  • Robert M. Anderson

    (Princeton University)

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.

Suggested Citation

  • Robert M. Anderson, 1981. "Core Theory with Strongly Convex Preferences," Cowles Foundation Discussion Papers 578, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:578
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d05/d0578.pdf
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    References listed on IDEAS

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    1. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-615, July.
    2. Dierker, Egbert, 1975. "Gains and losses at core allocations," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 119-128.
    3. 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.
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    Cited by:

    1. 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.
    2. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    3. 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.
    4. Anderson, Robert M., 2010. "Core allocations and small income transfers," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 373-381, July.
    5. 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.

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