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Existence of Equilibrium on a Manifold

Schofield, Norman (1983) Existence of Equilibrium on a Manifold. Social Science Working Paper, 482. California Institute of Technology , Pasadena, CA. (Unpublished)

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Existence of equilibrium of a continuous preference relation p or correspondence P on a compact topological space W can be proved either by assuming acyclicity or convexity (no point belongs to the convex hull of its preferred set). Since both properties may well be violated in both political and economic situations, this paper considers instead a "local" convexity property appropriate to a "local" preference relation or preference field. The local convexity property is equivalent to the nonexistence of "local" cycles. When the state space W is a convex set, or is a smooth manifold of a certain topological type, then the "local" convexity property is sufficient to guarantee the existence of a set of critical optima.

Item Type:Report or Paper (Working Paper)
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Additional Information:An earlier version of this paper was presented at the International Conference on the Economics of Information, Luminy, Marseille, September 1981, and the final version prepared while the author was Hallsworth Research Fellow in Political Economy at Manchester University. Support from the Nuffield Foundation is also gratefully acknowledged. Discussion with Mike Martin of Essex University was extremely helpful. Published as Schofield, Norman. "Existence of equilibrium on a manifold." Mathematics of Operations Research 9.4 (1984): 545-557.
Group:Social Science Working Papers
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Nuffield FoundationUNSPECIFIED
Subject Keywords:Economic theory, Mathematical manifolds, Convexity, Topological spaces, Diagonal lemma, Curves, Mathematics, Social choice, Nash equilibrium, Mathematical integrals
Series Name:Social Science Working Paper
Issue or Number:482
Record Number:CaltechAUTHORS:20170921-164236395
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81723
Deposited By: Jacquelyn Bussone
Deposited On:22 Sep 2017 17:45
Last Modified:03 Oct 2019 18:46

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