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Social Equilibrium and Cycles on Compact Sets

Schofield, Norman (1983) Social Equilibrium and Cycles on Compact Sets. Social Science Working Paper, 484. California Institute of Technology , Pasadena, CA.

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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 we show the existence of a local equilibrium for a preference field which satisfies, not convexity, but the weaker local acyclicity. 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 v(σ)-2, where v(σ) is the Nakumura 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.

Item Type:Report or Paper (Working Paper)
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Additional Information: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 Thanks are due to T. Bergstrom and J. Strnad for making available some of their unpublished work. Published as Schofield, Norman. "Social equilibrium and cycles on compact sets." Journal of Economic Theory 33.1 (1984): 59-71.
Group:Social Science Working Papers
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Nuffield FoundationUNSPECIFIED
Series Name:Social Science Working Paper
Issue or Number:484
Record Number:CaltechAUTHORS:20170921-163009131
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81721
Deposited By: Jacquelyn Bussone
Deposited On:22 Sep 2017 17:48
Last Modified:03 Oct 2019 18:46

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