Core Theory with Strongly Convex Preferences
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 . 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 . The proof, which is based on our earlier result for economies with more general preferences , is elementary.
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- Dierker, Egbert, 1975. "Gains and losses at core allocations," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 119-128.
- 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.
- Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-15, July.
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