Download this Paper Open PDF in Browser

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

University of Manchester Economics Discussion Paper No. EDP-0603

25 Pages Posted: 2 Mar 2006  

Igor V. Evstigneev

University of Manchester - Economics, School of Social Sciences

Klaus Reiner Schenk-Hoppé

University of Manchester - Department of Economics; Norwegian School of Economics (NHH) - Department of Finance

Date Written: February 2006

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.

Keywords: C61, C62, O41

JEL Classification: randomized von Neumann paths, sunspots

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: https://ssrn.com/abstract=887412 or http://dx.doi.org/10.2139/ssrn.887412

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 Manchester - Department of Economics ( email )

Arthur Lewis Building
Oxford Road
Manchester, M13 9PL
United Kingdom

Norwegian School of Economics (NHH) - Department of Finance ( email )

Helleveien 30
N-5045 Bergen
Norway

Paper statistics

Downloads
56
Rank
316,056
Abstract Views
480