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Social equilibrium and cycles on compact sets

Schofield, Norman (1984) Social equilibrium and cycles on compact sets. Journal of Economic Theory, 33 (1). pp. 59-71. ISSN 0022-0531. doi:10.1016/0022-0531(84)90040-1.

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One proof of existence of general equilibrium assumes convexity and continuity of a preference correspondence on a compact convex feasible set W. Here the existence of a local equilibrium for a preference field which satisfies, not convexity, but the weaker local acyclicity is shown. The theorem is then applied to a voting game, σ, without veto players. It is shown that if the dimension of the policy space is no greater than ν(σ) − 2, where ν(σ) is the Nakamura number of the game, then no local cycles may occur and a local equilibrium must exist. With convex preferences, then, there will exist a choice of the game from W.

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Additional Information:© 1984 by Academic Press, Inc. Received March 24, 1981; revised May 25, 1983. Earlier versions of this paper were presented at the World Congress of the Econometric Society, Aix en Provence, August 1980, and the European Public Choice Meeting, Oxford, April 1981. The final version was prepared while the author was Hallsworth Research Fellow in Political Economy at Manchester University. Support from the Nuffield Foundation is gratefully acknowledged. Thanks are due to T. Bergstrom and J. Strnad for making available some of their unpublished work. Formerly SSWP 484.
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ID Code:83233
Deposited By: Jacquelyn Bussone
Deposited On:15 Nov 2017 22:53
Last Modified:15 Nov 2021 19:56

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