Abstract

http://ssrn.com/abstract=887412
 
 

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Pure and Randomized Equilibria in the Stochastic Von Neumann-Gale Model


Igor V. Evstigneev


University of Manchester - Economics, School of Social Sciences

Klaus Reiner Schenk-Hoppé


University of Leeds - Leeds University Business School; University of Leeds - School of Mathematics; Norwegian School of Economics (NHH) - Department of Finance

February 2006

University of Manchester Economics Discussion Paper No. EDP-0603

Abstract:     
The paper examines the problem of the existence of equilibrium for the stochastic analogue of the von Neumann-Gale model of economic growth. The mathematical framework of the model is a theory of set-valued random dynamical systems defined by positive stochastic operators with certain properties of convexity and homogeneity. Existence theorems for equilibria in such systems may be regarded as generalizations of the Perron-Frobenius theorem on eigenvalues and eigenvectors of positive matrices. The known results of this kind are obtained under rather restrictive assumptions. We show that these assumptions can be substantially relaxed if one allows for randomization. The main result of the paper is an existence theorem for randomized equilibria. Some special cases (models defined by positive matrices) are considered in which the existence of pure equilibria can be established.

Number of Pages in PDF File: 25

Keywords: C61, C62, O41

JEL Classification: randomized von Neumann paths, sunspots

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Date posted: March 2, 2006  

Suggested Citation

Evstigneev, Igor V. and Schenk-Hoppé, Klaus Reiner, Pure and Randomized Equilibria in the Stochastic Von Neumann-Gale Model (February 2006). University of Manchester Economics Discussion Paper No. EDP-0603. Available at SSRN: http://ssrn.com/abstract=887412 or http://dx.doi.org/10.2139/ssrn.887412

Contact Information

Igor V. Evstigneev (Contact Author)
University of Manchester - Economics, School of Social Sciences ( email )
Oxford Road
Manchester, M13 9PL
United Kingdom
+44 161 2754275 (Phone)
+44 161 2754812 (Fax)
HOME PAGE: http://www.evstigneev.net
Klaus Reiner Schenk-Hoppé
University of Leeds - Leeds University Business School ( email )
Keyworth Building
Leeds, LS2 9JT
United Kingdom
+44 113 343 4513 (Phone)
+44 113 343 4495 (Fax)
HOME PAGE: http://www.schenk-hoppe.net
University of Leeds - School of Mathematics ( email )
Woodhouse Lane
Leeds, LS2 9JT
United Kingdom
+44 113 343 5187 (Phone)
+44 113 343 5090 (Fax)
HOME PAGE: http://www.schenk-hoppe.net
Norwegian School of Economics (NHH) - Department of Finance ( email )
Helleveien 30
N-5045 Bergen
Norway
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