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Existence of Equilibrium on a Manifold

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  • Schofield, Norman.

Abstract

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.
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  • Schofield, Norman., "undated". "Existence of Equilibrium on a Manifold," Working Papers 482, California Institute of Technology, Division of the Humanities and Social Sciences.
  • Handle: RePEc:clt:sswopa:482
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    Cited by:

    1. Sebastian Galiani & Norman Schofield & Gustavo Torrens, 2014. "Factor Endowments, Democracy, and Trade Policy Divergence," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(1), pages 119-156, February.
    2. Norman Schofield, 2013. "The “probability of a fit choice”," Review of Economic Design, Springer;Society for Economic Design, vol. 17(2), pages 129-150, June.
    3. Dalton, Patricio & Ghosal, Sayantan, 2008. "Behavioural Decisions and Welfare," The Warwick Economics Research Paper Series (TWERPS) 834, University of Warwick, Department of Economics.
    4. Dalton, P.S. & Ghosal, S., 2010. "Behavioral Decisions and Welfare (Replaces CentER DP 2010-22)," Discussion Paper 2010-143, Tilburg University, Center for Economic Research.

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