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

Arias-R., Omar Fdo. (2013): A remark on definable paths in regular O-minimal equilibrium manifolds.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: O-minimal manifold, cell decomposition, triviality, curve selection
• Subjects: D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D50 - General; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D51 - Exchange and Production Economies

References

Balasko, Y. (1988). Foundations of the theory of general equilibrium. Academic press, Boston.

Blume, L. and Zame, W. (1992). The algebraic geometry of competitive equilibrium. Economic theory and international trade; essays in memoriam J. Trout Rader, ed. por W. Neuefeind y R. Reizman, Springer-Verlag, Berlin.

Blume, L. and Zame, W. (1994). The algebraic geometry of perfect and sequential equilibrium. Econometrica 62, No. 4, pp. 783-794.

Bochnak, J., Coste, M. y Roy, M. (1991). Real Algebraic Geometry. Springer Verlag-Berlin.

Matta, W. (2005). A riemannian metric on the equilibrium manifold. Economics bulletin, volume 4, No 7, pp 1-7

Van den Dries, L. (1998). Tame topology and O-minimal structures. Cambridge university press.