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 Manchester - Department of Economics; Norwegian School of Economics (NHH) - Department of Finance
University of Manchester Economics Discussion Paper No. EDP-0603
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
Date posted: March 2, 2006
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