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A remark on definable paths in regular O-minimal equilibrium manifolds

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  • Arias-R., Omar Fdo.

Abstract

The main purpose of this paper is to remark that any definable continuous path linking two regular equilibria in a regular O-minimal equilibrium manifold intersects a finite number of definable connected components locally determined. We apply the cell decomposition theorem to decompose the definable equilibrium manifold in finite connected components, the definable triviality theorem to local determinacy in each component, and the definable curve selection to have continuous paths in the manifold.

Suggested Citation

  • Arias-R., Omar Fdo., 2013. "A remark on definable paths in regular O-minimal equilibrium manifolds," MPRA Paper 51820, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:51820
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    File URL: https://mpra.ub.uni-muenchen.de/51820/1/MPRA_paper_51820.pdf
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    References listed on IDEAS

    as
    1. Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-794, July.
    2. Stefano Matta, 2005. "A riemannian metric on the equilibrium manifold," Economics Bulletin, AccessEcon, vol. 4(7), pages 1-7.
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    Cited by:

    1. Arias-R., Omar Fdo., 2014. "A short note on the definable Debreu map in regular O-minimal equilibrium manifolds," MPRA Paper 52759, University Library of Munich, Germany.

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    More about this item

    Keywords

    O-minimal manifold; cell decomposition; triviality; curve selection;
    All these keywords.

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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