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Existence of Equilibrium on a Manifold

Schofield, Norman (1984) Existence of Equilibrium on a Manifold. Mathematics of Operations Research, 9 (4). pp. 545-557. ISSN 0364-765X. doi:10.1287/moor.9.4.545.

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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:Article
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Additional Information:© 1984 INFORMS. Published Online: November 1, 1984.
Subject Keywords:equilibrium; choice; preference; manifold
Issue or Number:4
Record Number:CaltechAUTHORS:20171002-103618964
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Official Citation:Existence of Equilibrium on a Manifold Norman Schofield Mathematics of Operations Research 19849:4 , 545-557
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81945
Deposited By: Tony Diaz
Deposited On:02 Oct 2017 18:00
Last Modified:15 Nov 2021 19:47

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